In this paper, the topology optimization methodology for the synthesis of distributed actuation system with specific applications to the morphing air vehicle is discussed. The main emphasis is placed on the topology optimization problem formulations and the development of computational modeling concepts. For demonstration purposes, the inplane morphing wing model is presented. The analysis model is developed to meet several important criteria: It must allow large rigid-body displacements, as well as variation in planform area, with minimum strain on structural members while retaining acceptable numerical stability for finite element analysis. Preliminary work has indicated that addressed modeling concept meets the criteria and may be suitable for the purpose. Topology optimization is performed on the ground structure based on this modeling concept with design variables that control the system configuration. In other words, states of each element in the model are design variables and they are to be determined through optimization process. In effect, the optimization process assigns morphing members as 'soft' elements, non-morphing load-bearing members as 'stiff' elements, and non-existent members as 'voids.' In addition, the optimization process determines the location and relative force intensities of distributed actuators, which is represented computationally as equal and opposite nodal forces with soft axial stiffness. Several different optimization problem formulations are investigated to understand their potential benefits in solution quality, as well as meaningfulness of formulation itself. Sample in-plane morphing problems are solved to demonstrate the potential capability of the methodology introduced in this paper.

Achieving multi-mission capability with a single aircraft through in-flight morphing of the wing is highly beneficial due to its efficiency under different flight conditions such as cruise and dash. In addition higher maneuverability is possible from using such a vehicle. As opposed to traditional wing morphing where discrete surfaces such as hinged flaps and ailerons are used, the current research focus is directed towards achieving continuous morphing in order to reduce drag from geometric discontinuities. The present research aims to achieve continuous wing morphing by employing a wing structure comprised of an optimized internal layout of cables and struts. Cables are used as actuators while struts provide rigidity to the wing. In addition to achieving continuous morphing by changing cable length, this structure has the advantage of being light in weight. Also, distributed actuation may be achieved from this scheme. Topology optimization is utilized to optimally place cables and struts in a "bay" or a section of the wing. The optimization is achieved by using Genetic Algorithm. A Generic Algorithm, the Non-dominated Sorting Genetic Algorithm II (NSGA II) has been used in this work. The current paper gives an overview of the algorithm and discusses obtained results.

In this paper, the optimal location of a distributed network of actuators within a scissor wing mechanism is investigated. The analysis begins by developing a mechanical understanding of a single cell representation of the mechanism. This cell contains four linkages connected by pin joints, a single actuator, two springs to represent the bidirectional behavior of a flexible skin, and an external load. Equilibrium equations are developed using static analysis and the principle of virtual work equations. An objective function is developed to maximize the efficiency of the unit cell model. It is defined as useful work over input work. There are two constraints imposed on this problem. The first is placed on force transferred from the external source to the actuator. It should be less than the blocked actuator force. The other is to require the ratio of output displacement over input displacement, i.e., geometrical advantage (GA), of the cell to be larger than a prescribed value. Sequential quadratic programming is used to solve the optimization problem. This process suggests a systematic approach to identify an optimum location of an actuator and to avoid the selection of location by trial and error. Preliminary results show that optimum locations of an actuator can be selected out of feasible regions according to the requirements of the problem such as a higher GA, a higher efficiency, or a smaller transferred force from external force. Results include analysis of single and multiple cell wing structures and some experimental comparisons.

This paper investigates the optimal topology of an actively controlled piezoelectric actuator bonded to an elastic cantilever beam under steady-state harmonic loading. The actuator is discretized using finite elements, and control is applied to the actuator based on the sensor's degrees of freedom using proportional control. This study investigates the optimal distribution of actuator material for one and five layers of finite elements. The optimized actuator topology shows substantial improvement over initial piezoelectric topologies and over traditional actuator placement.

In this paper, the dynamic analysis of a satellite dish with respect to spherical polar coordinate system is investigated. In this complex three-dimensional case, the method of separation of variables is employed to obtain the explicit solution of the partial differential governing equation of the adaptive composite satellite dish. Then, the mode shape functions are expanded in combination of periodic functions, associated Legendre functions, and spherical Bessel functions. The validation of the theoretical model is performed by comparing the developed analytical mode shapes with finite element analysis mode shapes. Three actuator parameters, i.e., actuator number, location, and placement configuration are considered in the Genetic Algorithms (GAs). Also, employing the developed model, the norm-2 of LQR optimal feedback gain vector is set as the objective function in the GAs to obtain the optimal actuator placement coupled with the control law, with which good structural vibration suppression as well as less control energy consumption can be achieved by the linear quadric regulator (LQR).

Active vibration control is implemented using multiple piezoelectric actuators and sensors bonded to the top and bottom surfaces of a cantilever beam. The control is exercised using closed-loop displacement feedback. The objective of the study is to determine the optimal locations of patch actuators and sensors such that the frequency gap between higher frequencies of the beam is maximized. Maximizing the frequency gaps is useful in those cases where the excitation frequency can be placed in between two higher order frequencies to avoid the resonance. In these cases the design requirement is to maximize the difference between the two higher order frequencies such as between the first and second frequencies or between the second and third frequencies, etc. In the present study the frequency gaps between the higher order frequencies are investigated with respect to actuator and sensor locations with a view towards determining the optimal locations for largest frequency gaps. The differential equation governing the vibrations of a beam/piezo patch system is solved using an integral equation approach. The equivalent integral equation formulation of the problem avoids the discontinuities which arise due to partial length piezo patches. The solution is approximated using the eigenfunctions of the freely vibrating structure which leads to a system of algebraic equations. The numerical results are given for various patch combinations and the optimal locations of the actuators and the sensors are determined. It is observed that the optimal locations of the piezo patches depend on the specific frequency gap as well as the patch configurations.

Functionally Graded Materials (FGMs) possess continuous variation of material properties and are characterized by spatially varying microstructures. Recently, the FGM concept has been explored in piezoelectric materials to improve properties and to increase the lifetime of bimorph piezoelectric actuators. Elastic, piezoelectric, and dielectric properties are graded along the thickness of a piezoceramic FGM. Thus, the gradation of piezoceramic properties can influence the performance of piezoactuators. In this work, topology optimization is applied to find the optimum gradation variation in piezoceramics in order to improve actuator performance measured in terms of output displacements. A bimorph type actuator design is investigated. The corresponding optimization problem is posed as finding the optimized gradation of piezoelectric properties that maximizes output displacement or output force at the tip of the bimorph actuator. The optimization algorithm combines the finite element method with sequential linear programming. The finite element method is based on the graded finite element concept where the properties change smoothly inside the element. This approach provides a continuum approximation of material distribution, which is appropriate to model FGMs. The present results consider gradation between two different piezoceramic properties and two-dimensional models with plane stress assumption.

Piezoelectric actuators offer significant promise in a wide range of applications. The piezoelectric actuators considered in this work essentially consist of a flexible structure actuated by piezoceramics that must generate output displacement and force at a certain specified point of the domain and direction. The flexible structure acts as a mechanical transformer by amplifying and changing the direction of piezoceramics output displacements. The design of these piezoelectric actuators are complex and a systematic design method, such as topology optimization has been successfully applied in the latest years, with appropriate formulation of the optimization problem to obtain optimized designs. However, in these previous design formulations, piezoceramics position are usually kept fixed in the design domain and only the flexible structure is designed by distributing only some non-piezoelectric material (Aluminum, for example). This imposes a constraint in the position of piezoelectric material in the optimization problem limiting the optimality of the solution. Thus, in this work, a formulation that allows the simultaneous search for an optimal topology of a flexible structure as well as the optimal positions of the piezoceramics in the design domain, to achieve certain specified actuation movements, will be presented. This can be achieved by allowing the simultaneous distribution of non-piezoelectric and piezoelectric material in the design domain. The optimization problem is posed as the design of a flexible structure together with optimum positions of piezoelectric material that maximizes output displacements or output forces in a certain specified direction and point of the domain. The method is implemented based on the SIMP material model where fictitious densities are interpolated in each finite element, providing a continuum material distribution in the domain. Presented examples are limited to two-dimensional models, once most of the applications for such piezoelectric actuators are planar devices.

The micro-tools considered in this work consist essentially of multi-flexible structures actuated by two or more piezoceramic devices that must generate different output displacements and forces at different specified points of the domain and on different directions. The multiflexible structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics output displacements. Micro-tools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, and micro/nanotechnology processes. Although the design of these micro-tools is complicated due to the coupling among movements generated by various piezoceramics, it can be realized by means of topology optimization concepts. Recently, the concept of functionally graded materials (FGMs) has been explored in piezoelectric materials to improve performance and increase lifetime of piezoelectric actuators. Usually for an FGM piezoceramic, elastic, piezoelectric, and dielectric properties are graded along the thickness. Thus, the objective of this work is to study the influence of piezoceramic property gradation in the design of the multiflexible structures of piezoelectric micro-tools using topology optimization. The optimization problem is posed as the design of a flexible structure that maximizes different output displacements or output forces in different specified directions and points of the domain, in response to different excited piezoceramic portions: while minimizing the effects of movement coupling. The method is implemented based on the solid isotropic material with penalization (SIMP) model where fictitious densities are interpolated in each finite element, providing a continuum material distribution in the domain. As examples, designs of a single piezoactuator and an XY nano-positioner actuated by two FGM piezoceramics are considered. The resulting designs are compared with designs considering homogeneous piezoceramics. The present examples are limited to two-dimensional models because most of the applications for such micro-tools are planar devices.

This paper introduces hydrodynamic loads for tensegrity structures, to examine their behavior in marine environments. Wave compliant structures are of general interest when considering large marine structures, and we are motivated by the aquaculture industry where new concepts are investigated in order to make offshore installations for seafood production. This paper adds to the existing models and software simulations of tensegrity structures exposed to environmental loading from waves and current. A number of simulations are run to show behavior of the structure as a function of pretension level and string stiffness for a given loading condition.

Due to stresses encountered in combat, it is known that soldier marksmanship noticeably decreases regardless of prior training. Active stabilization systems in small arms have potential to address this problem to increase soldier survivability and mission effectiveness. The key to success is proper actuator design, but this is highly dependent on proper specification which is challenging due to the human/weapon interaction. This paper presents a generic analytical dynamic model which is capable of defining the necessary actuation specifications for a wide range of small arms platforms. The model is unique because it captures the human interface--shoulder and arm--that introduces the jitter disturbance in addition to the geometry, inertial properties and active stabilization stiffness of the small arms platform. Because no data to date is available for actual shooter-induced disturbance in field conditions, a method is given using the model to back-solve from measured shooting range variability data the disturbance amplitude information relative to the input source (arm or shoulder). As examples of the applicability of the model to various small arms systems, two different weapon systems were investigated: the M24 sniper weapon and the M16 assault rifle. In both cases, model based simulations provided valuable insight into impact on the actuation specifications (force, displacement, phase, frequency) due to the interplay of the human-weapon-active stabilization interface including the effect of shooter-disturbance frequency, disturbance location (shoulder vs. arm), and system parameters (stiffness, barrel rotation).

Future space-based optical reflectors will be driven by the desire for large apertures versus the constraints of low weight and compactness of packaging. One possible way to satisfy these competing factors is through the use of piezoelectric in-plane actuated, tensioned, deformable mirrors. These configurations typically exhibit both plate-like and membrane-like behavior. Proposed is a new approximation method for the solution to this class of mirror, where the normalized plate stiffness to tension ratio is small. The approximation function is based on the exact analytical solution to this class of problems. The approximation method allows the problem to be reduced to a simple pressure forced membrane equation, a geometry which may be more readily analyzed. A case study comparing the results of the approximation method to a high fidelity finite element model constructed in MSC.Nastran is provided.

Reptation, or accommodation, is manifested in ferromagnetic materials in a variety of operating regimes and hence must be incorporated in models used for comprehensive material characterization or model-based control design. Because the microscopic mechanisms which cause reptation are complex, we characterize the effect in a phenomenological macroscopic manner within the context of a homogenized energy framework for ferromagnetic hysteresis. Attributes of the model are illustrated through comparison with experimental data.

The dynamics of magneto-elastic materials is described by a nonlinear parabolic hyperbolic system which couples the equations of the magnetization and the displacements. We propose a model for the two-dimensional case and establish the existence of weak solutions. Our starting point is the Gilbert-Landau-Lifshitz equation introduced for describing the dynamics of micromagnetic processes. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals, neglecting, in this approach, the contributions due to the anisotropy and the demagnetization effects. The analysis of the equations is carried out in 2D framework which allows us further simplificative hypotheses mainly concerning the assumption of small plane displacements. The existence theorem for the proposed differential system is proved combining the Faedo-Galerkin approximation with the penalty method which introduces a small parameter. The convergence as the parameter vanishes is deduced from compactness properties.

D.C. and A. C. characteristics of a magnetic sensor, based on Metal Oxide Semiconductor Field Effect Transistor (MOSFET) structure, have been investigated using an efficient two-dimensional physical simulator. With the coupling scheme between the magnetic field equation and the carrier transport equations in the present simulator, the effects of the device geometric parameters, the bias conditions, and the magnetic field on the current deflection due to magnetic field and on the magnetic sensor relative sensitivity are accurately determined. The MOSFET magnetic sensor capability is further enhanced by using an integrated smart structure which is able to fully detect the magnetic field variations in two directions. The current deflection and relative sensitivity for the smart two-directions magnetic sensor under different operating conditions are finally investigated with the present efficient physical simulator.

The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers (IPT). Due to the fact that a universally accepted morphological model for the structure of Nafion has not been defined, this initial work is aimed to investigate the relationship between ion transport performance inside Nafion and the cluster morphology. A two-dimensional ion hopping model has been built to describe ion transport in IPT with Monte-Carlo simulation. In the simulation, a 50nm x 50nm x 1nm lattice holds 200 cations and 200 anions. The initial distribution of anions is varied from uniformly random distribution to one with 15 clusters, 8 clusters and 4 clusters. A step voltage is applied between the electrodes of the IPT, causing thermally activated hopping. Periodic boundary conditions are applied when ions hop in the direction perpendicular to the electric field. The influence of the electrodes on both faces of IPT is presented by the method of image charges. The results of current response, charge density and ion distribution are compared for different initial ion distributions.

Ionic polymers are compliant, light weight materials that operate under low voltage levels as transducers. They can be used as both sensors and actuators for various applications, primarily those involving flexible structures. The electromechanical transduction properties of these materials were discovered just over a decade ago, spawning the development of ionic polymer research. While the debate continues over the dominant physical mechanisms of actuation, several model forms have been proposed. The majority of these existing models are stated to be linear approximations and some were derived with input-dependence. However, nonlinear characteristics have been observed in both the electrical and mechanical response of cantilever actuators, including harmonic distortion in the time-domain and magnitude scaling of the frequency response. Characterization results indicate that the nonlinear mechanisms are dynamic since they have dominance at low frequencies, but are essentially negligible as the excitation frequency increases. This research uses knowledge gained from the characterization results to develop a dynamic model that can predict the observed nonlinear behavior. The empirical model is constructed from input-output data collected using a Gaussian input current signal and is validated using the measured frequency response function and single-frequency sinusoidal responses.

Ionomeric polymers are a promising class of intelligent material which exhibit electromechanical coupling similar to that of piezoelectric bimorphs. Ionomeric polymers are much more compliant than piezoelectric ceramics or polymers and have been shown to produce actuation strain on the order of 5% at operating voltages between 1 V and 5 V. This performance indicates the potential for self-actuating devices manufactured from ionomeric polymers, such as deformable mirrors or low pressure pump diaphragms. This paper presents a variational approach to the dynamic modeling of ionic polymer plates in rectangular coordinates. A linear matrix equation, which relates displacement and charge to applied forces and voltage, is developed to determine the response of the structure to applied forces and applied potentials. The modeling method is based on the incorporation of empirically determined material properties, which have been shown to be highly frequency dependent. The matrices are calculated at discrete frequencies and solved frequency-by-frequency to determine the response of the ionomeric plate structures. A model of a thin rectangular plate is developed and validated experimentally. Simulated frequency response functions are compared to experimental results for several locations on the plate. The response of the plate at certain frequencies is computed and compared to experimentally-determined response shapes. The results demonstrate the validity of the modeling approach in predicting the dynamic response of the ionomeric plate structure. These spatial solutions are also compared to experimentally determined response shapes.

Nonlinear phenomena such as mode localization have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Intrinsic Localized Modes (ILMs), which are defined as localization due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators, are of interest to the present work. Here, such localization is studied in the context of micro-cantilever arrays and micro-resonator arrays, and it is explored if an ILM can be realized as a nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to determine nonlinear normal modes are used to study the nonlinear vibrations of the resonator arrays. Preliminary investigations reported in this article suggest that it is possible to realize an ILM as a nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.

In the present work, the non-linear analysis of smart beams and plates is performed, using FE techniques. A coupled constitutive formulation between thermal, electrical and mechanical fields is presented incorporating non-linearity due to large displacements. An 8-node plate element was implemented in combination with a discrete layer approximation (LW) for the through the thickness representation of the structure. The issues of the critical buckling load under different electrical conditions as well as thermal and electrical loading are also presented. Experimental results contribute in order to verify the numerical analysis results.

In this paper an electro-mechanical model to describe the behavior of a PVDF multi-layer smart structure is presented and proposed for I-Swarm mm³ microrobot actuators. The study is based on the modal analysis of the partial differential equations governing the motion of an Euler-Bernouilly cantilever beam. A pair of linearly coupled piezoelectric equations between the mechanical and the electrical domains is presented. An important element in the modelization of such materials is the energy losses term. A viscous damping contribution is considered which allows us to extract more realistic constituent equations for the material to work as sensor or actuator. The development of this equation as an infinite linear combination of each mode allows us to extract a compact lumped equivalent electrical circuit to work at any frequency region instead of the classical reduced models.

This paper describes a method based on novelty detection and Discrete Wavelet Transform for damage detection. A statistical discordancy test is used to determine the presence of outliers in a set of features extracted from the Discrete Wavelet Transform of ultrasonic guided-wave signals; the outliers indicate a faulty condition of the structure under investigation. The proposed approach, which is general, is applied to the quantitative detection of notch-like defects in steel strands used as cable-stays or prestressing tendons. The effect of the number of features and the effect of the ultrasonic noise level on the sensitivity of the method to the presence and the size of the defects are discussed.

Although conventional methods such as the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) have been effectively used for the analysis of dispersive elastic waves, rapidly varying wave signals may not be accurately analyzed by these methods. Because the time-frequency tiling of conventional methods do not take into account dispersion phenomena, it is often difficult to trace accurately the time-frequency varying feature of the signals. The objective of this work is to develop advanced adaptive time-frequency analysis methods whose time-frequency tiling is varying to the dispersion characteristics of the signal to be analyzed. More specifically, a method called, "the dispersion-based short-time Fourier transform (D-STFT) and the dispersion-based continuous wavelet transform (DCWT)" are newly developed. In these methods, each time-frequency tiling is adaptively rotated in the time-frequency plane depending on the estimated local dispersion rate of a wave signal. In the proposed approach, the dispersion relationship is estimated iteratively from the ridge analysis of the result by the proposed adaptive methods where the initial estimation is based on the result by the standard methods. To verify the validity of the present approach, the Lamb waves measured in an aluminum plate were considered.

A multi-dimensional thermomechanical model has been developed to simulate the localized phase transformation and propagation of transformation front(s) in SMA materials. The current model is an extension of the one-dimensional model previously developed by the authors which consists of a constitutive relation and a transformation evolution rule (kinetic relation). The constitutive relation is constructed based on continuum mechanics principles, and the kinetic of transformation is expressed in terms of various transformation surfaces in stress-temperature space. The model captures the localized deformations in both forward and reverse transformation. The finite element simulation of the forward and reverse transformations in a short NiTi strip under quasi-static extension is presented.

The one-dimensional phase transformation model proposed by the author was applied to an analysis of bi-axial tensiletorsional pseudoelastic deformation behavior of a shape memory alloy (SMA) tube. In the one-dimensional phase model, virtual grains are sorted in order of energy required for transformation and the order of these grains is assumed to be unchanged irrespective of phases before and after the transformation. Accordingly, the transformation always takes place in the same order. Here a torsional stress induced martensitic phase was considered in addition to an austenitic phase and a tensile stress induced martensitic phase. Tensile and torsional stress-strain hysteresis loops for a pseudoelastic SMA thin tube were simulated. The simulated loops were in quantitatively good agreement with available experimental data for a pure tensile and a pure torsional strain loading. For combined loadings, the simulated loops qualitatively agreed with the experimental data.

The superelastic shape memory alloys (SMAs) have received increasing interest attributed to their unique mechanical properties. Modeling of SMAs' thermomechanical behavior has been an active area of research; however the existing models are generally valid only for quasi-static loading conditions and extremely complex for practical use. In this research, one-dimensional cyclic loading tests of superelastic shape memory alloy wires are first performed to determine their hysteresis properties. The effects of the strain amplitude and the loading rate on the mechanical properties are studied and formulized by least-square method. Based on the Graesser's model, an improved model is developed. The improved model divides the full loop into three parts: the loading branch, the unloading branch before the completion of the reverse transformation and the elastic unloading branch after the completion of reverse transformation, each part adopts its respective parameters. The improved model not only has the same advantages as the Graesser's model, such as relative simple formulation with parameters that can be easily acquired and being valid for dynamic loading conditions, but also overcomes the deficiency of the Graesser's model, i.e. ignoring the effects of loading path on the model parameters. Numerical simulations are conducted. Comparisons indicate that the improved Graesser's model accurately reflects all the hysteresis characteristics and provides a better prediction of the SMA's actual hyteresis behavior than the Graesser's model at varying levels of strain and loading rate.

In this paper authors examine the design and implementation of a cantilever beam-style probe for non-contacting electrostatic voltmeter. The beam is driven by a piezoelectric actuator with a feedback loop controlling amplitude of the electrostatic sensor displacement. Choice of the vibration mode and placement of the actuator and sensor are discussed. A simple model for the first three natural frequencies of the beam is constructed and compared with the experimental results.

Guided wave ultrasonic inspection is becoming an important method of non-destructive testing for long, slender structures such as pipes and rails. Often it is desirable to use transducers that can strongly excite a specific mode of wave propagation in the waveguide. Piezoelectric patch transducers are frequently employed, by researchers, for exciting waves in beam like structures. Sonar systems frequently make use of resonant transducers, such as sandwich transducers, for acoustic wave generation and this principle has been used to excite waves in a rail. This paper compares the two transduction approaches, for launching bending waves in rectangular waveguides, with numerical modeling. The numerical modeling combined a waveguide finite element model, of the waveguide, with conventional three-dimensional piezoelectric finite element models of the transducers. The waveguide finite elements were formulated using a complex exponential to describe the wave propagation along the structure and conventional finite element interpolation over the area of the element. Consequently, only a two-dimensional finite element mesh covering the cross-section of the waveguide is required. The harmonic forced response of the waveguide was used to compute a complex dynamic stiffness matrix which represented the waveguide in the transducer model. The effects of geometrical parameters of patch and sandwich transducers were considered before the comparison was made. It appears that piezoelectric patch transducers offer advantages at low frequencies while sandwich transducers are superior at high frequencies, where resonance can be exploited, at the cost of more complex design.

Non-linear smart actuators have attracted lately the interest of many researchers. It is well known that linear smart actuators have been used in a vast number of applications in different disciplines. However, most of the times a trade off between displacement and force must take place in order to increase their operational envelope. Taking into account this, it is not strange that research is headed towards non-linear mechanics in order to increase displacement, as well as force actuation in smart actuators. In the present work, issues related with the non-linear response of smart beams as well as snap-through performance are investigated. Beams with aluminum cores are equipped with continuous piezoelectric layers that cover only a certain part of the structure. A number of symmetrical and asymmetrical actuators have been realized with different core lengths and thus the amount of active material over the whole length of the actuator varies. These actuators were tested in order to evaluate their critical buckling load as well as their snap-through performance. The snap-through displacement was examined with respect to the post-buckling compression of the actuators for all the configurations and the difference between symmetrical and asymmetrical actuators raises a number of issues concerning the design of such actuators.

In this paper, recent efforts conducted to investigate the dynamic behavior of a pressure sensor diaphragm coupled with a cylindrical air-backed cavity are presented. Our study shows that a careful consideration of the coupling effect between the plate and the air-backed cavity is necessary to determine the design parameters of a pressure sensor, such as sensitivity and bandwidth. In the case of strong coupling, based on linear analysis of the coupled system, the model of the diaphragm center displacement and natural frequencies are found to be significantly different from the corresponding quantities obtained for a pure plate model. These analyses and results are expected to be valuable for carrying out the design of small pressure sensors (e.g., MEMS pressure sensors) for various applications.

Due to the inherent nonlinear nature of Electro-rheological(ER) fluid dampers, one of the challenging aspects for utilizing these devices to achieve high system performance is the development of accurate models and control algorithms that can take advantage of their unique characteristics. In this paper, the nonlinear damping force model is made to identify the properties of the ER damper using higher order spectrum. The higher order spectral analysis is used to investigate the nonlinear frequency coupling phenomena with the damping force signal according to the sinusoidal excitation of the damper. Also, this paper presents an inverse model of the ER damper, i.e., the model can predict the required voltage so that the ER damper can produce the desired force for the requirement of vibration control of vehicle suspension systems. The inverse model has been constructed by using a multi-layer perceptron. A quarter-car suspension model is considered in this paper for analysis and simulation. Simulation results show that the proposed inverse model of ER damper can obtain control voltage of ER damper for required damping force.

High performance nanopositioning stages, used in a variety of applications such as atomic force microscopy and three-dimensional nanometer-scale lithography, require stringent position control over relatively large displacements and a broad frequency range. Piezoelectric materials, which are typically employed in nanopositioining stages, provide excellent position control when driven at relatively low frequency and low field levels. However, in applications where the stage operates over a relatively large region (microns to millimeters) and broad frequency range (Hz - kHz), piezoelectric materials often exhibit nonlinear and rate-dependent hystereis which requires control designs that can effectively accommodate such behavior. In this paper, a nonlinear, thermal-relaxation, piezoelectric constitutive law is incorporated into an open loop optimal tracking control design to accurately track a desired reference signal when nonlinearities, thermal relaxation and hyteresis are present. A comparison between linear optimal control and the nonlinear optimal control design is given to illustrate performance enhancements when the constitutive behavior is included in the control design.

This paper focuses on the development of an ANSYS finite element analysis (FEA) environment with integrated PID control scheme for simultaneous precision positioning and vibration suppression of smart composite structures with piezoelectric flat patches acting as actuators. This environment includes three modules: structural modeling, PID controller design, and dynamic analysis of smart structures. Two types of PID controllers are investigated, namely, PID vibration suppression (PID-VS) controller and PID simultaneous precision positioning and vibration suppression (PIDSPPVS) controller. The PID-VS controller is suitable to perform only vibration suppression with no positioning capability. The PID-SPPVS controller is equipped with SPPVS capabilities. The characteristics of individual control gains and their behavior with respect to each other for the two PID controllers are also studied. The gain selection for the PID-VS controller is based on obtaining the best VS while the gain selection for the PID-SPPVS controller is based on achieving the best positioning accuracy and VS simultaneously. In this study, a horizontal cantilevered graphite/epoxy composite beam with one surface-mounted ACX piezoelectric flat patch located at the beam root is first modeled. Next, the FE modal analysis is performed to determine the natural frequencies and hence the time step interval needed for the FE transient analysis. During the transient analysis, the mid-point of the beam tip is subjected to different types of external excitations such as sine loadings with different frequencies as well as random forces to evaluate the two PID controller performances. It is demonstrated that the FEA model with integrated PID-SPPVS controller is able to reach the desired position in a much shorter time in comparison to the PID-VS controller. Vibration amplitude reduction capabilities for the both PID controllers are very similar, although the PID-VS controller performs slightly better. This study also implies that the integrated FEA environment, consisting of the structural modeling of active composite structures with piezoelectric flat patches, modal and transient analyses, controller design, and simulation, provides a powerful tool for the design, analysis, and control of smart structures with SPPVS capabilities.

Future NASA exploration missions will increasingly require sampling, in-situ analysis and possibly the return of material to Earth for further tests. One of the challenges to addressing this need is the ability to drill using minimal reaction force and torque while operating from light weight platforms (e.g., lander, rover, etc.) as well as operate at planets with low gravity. For this purpose, the authors developed the Ultrasonic/Sonic Driller/Corer (USDC) jointly with Cybersonics Inc. Studies of the operation of the USDC at high power have shown there is a critical need to self-tune to maintain the operation of the piezoelectric actuator at resonance. Performing such tuning is encountered with difficulties and to address them an extremum-seeking control algorithm is being investigated. This algorithm is designed to tune the driving frequency of a time-varying resonating actuator subjected to both random and high-power impulsive noise disturbances. Using this algorithm, the performance of the actuator is monitored on a time-scale that is compatible with its slowly time-varying physical characteristics. The algorithm includes a parameter estimator, which estimates the coefficients of a function that characterizes the quality factor of the USDC. Since the parameter estimator converges sufficiently faster than the time-varying drift of the USDC's actuator physical parameters, this extremum-seeking estimation and control algorithm potentially allows for use in closed-loop monitoring of the operation of the USDC. Specifically, this system may be programmed to automatically adjust the duty-cycle of the sinusoidal driver signal to monitor the quality factor of the USDC not to fall below a user-defined set-point. Such fault-tolerant functionality is especially important in automated drilling applications where it is essential not to inadvertently drive the piezoelectric ceramic elements of the USDC beyond their operation capability. The details of the algorithm and experimental results are described and discussed in this paper.

This study deals with damage detection and vibration control of a smart beam and proposes a method for crack identification when the vibration of the beam is suppressed using active control. A finite-element model of a cracked beam is established by applying fracture mechanics methods. This model is applied to a cantilever beam, and the natural frequencies are determined for different crack lengths and locations. First, the crack length and locations are identified by using the relationship between the crack and the natural frequency of the beam. However, the crack length and locations are difficult to identify when the vibration is suppressed by active control, because the natural frequency is obtained by fast Fourier transform (FFT) of the vibration data. This study proposes a crack identification algorithm under vibration control where crack detection is repeated more than once. Furthermore, the gain-scheduled controller design considers both the crack length and the location. Once cracks are present in structures, control performance becomes worse because both the eigenvalue and eigenvector of the beam vary. A linear parameter-varying (LPV) model considering the crack length and locations is developed for the gain-scheduled controller design. To obtain the LPV model, the discrepancy between the state-space representations of the reduced-order model and the LPV model is measured by its Frobenius norm. This norm is minimized by simultaneously optimizing the coefficient functions and the state-space representations contained in the model. The efficiencies of this crack identification method and the gain-scheduled controller design are verified by simulation and experiment.

Active shape and vibration control of large structures have long been desired for many practical applications. PVDF being one of the most suitable materials for these applications due to its strong piezoelectric properties and availability in thin sheets has been the focal point of most researchers in this area. Most of the research has been done to find an open loop solution, which would be able to shape the structure as per the desired requirements in an ideal atmosphere. Unmodeled dynamics and external disturbances prevent the open loop (no feedback) solution from achieving the desired shape. This research develops a dynamic model of a laminated plate consisting of two layers of PVDF film joined with a layer of epoxy. The orthotropic properties of PVDF have been modeled and the epoxy layer is considered to be isotropic. A general control model is developed, which would work for most boundary conditions and developed for a simply supported beam with patch actuators. The methodology is then extended for a simply supported laminated plate. This model could be used for real time dynamic disturbance rejection and shape and vibration control of the structure.

In this paper the application of distributed vibration control for a flexible structure is studied both analytically and experimentally. The purpose is to investigate the effectiveness of distributed vibration control strategies and compare them with centralized and decentralized methods. A simply supported beam is chosen as the illustrative flexible structure. A distributed control architecture is designed based on a system identification model and is used to minimize broadband vibration disturbances. The experiment results are presented for the control of the beam's vibration modes under 600 Hz. It is shown that distributed control approaches the performance of centralized control if the same control effort is applied. In addition, in comparison to centralized control, the distributed controller has the advantage that it will continue to work even when some processors fail, although probably with diminished capability.

Semi-active control of torsional vibration can be realized through the use of variable friction brakes or clutches applied to a primary system acted on by oscillating torques. The performance of a given vibration control approach will depend greatly on the bandwidth of the actuators used to realize control. Three commercially available torsional actuators, a dry friction brake, a magneto-rheological fluid brake, and a magnetic particle brake have been tested and analyzed to assess their applicability for use in semi-active torsional vibration control. A test stand was constructed and used to run specific tests including step responses to determine "on" and "off" response times, open-loop bandwidth determination via swept-sine tests, and friction as a function of rotating speed. The data can be used to create general mathematical models to predict the behavior of the different actuators when excited with different control signals. The results indicate some of the limitations of the different actuators and will be used to provide a basis for determining the actuators' applicability to general torsional vibration control problems.

Within this work a model of a 6 DOF (degree-of-freedom) vibration isolation system with semi-active control, using magnetorheological (MR) technology, is investigated. Parallel platform mechanisms are ideal candidates for 6 DOF positioning and vibration isolation. While active and passive vibration control have been extensively used in parallel platforms, a 6 DOF parallel platform which utilizes semi-active vibration control has not received as much attention. The advantages of semi-active control include reduced cost by using a simpler actuator intended for only positioning, reduced power requirements, and improved stability. Within this work, the legs of a parallel platform model are investigated by implementing a two DOF Simulink model. Each leg of the platform is modeled as a two DOF system with a magnetorheological (MR) damper for adjustable damping.

Ultrasonic Motors are devices with micro or even nano-positioning capabilities. This feature derives from voltage-strain characteristic of piezoelectric ceramics. Furthermore, to accomplish fine positioning, a high resolution control system is required. This paper presents simulated results from a VHDL description of a micro-positioning control system for linear traveling wave ultrasonic motors (TWUSM). The controller is dedicated to TWUSM control, and uses motor dynamic characteristics for estimating the exact slider end positioning point, from real time acquired data.

The problem of actuator and sensor placement in a flexible plate is revisited within the context of an intelligent control scheme. Instead of considering individual actuators and sensors, we consider groups of actuators and sensors that have the same capacity to address specific modes. The placement optimization procedure chooses actuators and sensors within a given group so that can collectively address a specific range of modal frequencies. Integrated into the control scheme is the ability to select, over a time interval of fixed length, a given group that can best address spatiotemporally varying disturbances in which the spatial distribution of disturbances changes with time. For the numerical studies on a thin aluminum plate, clamped on all sides and employing piezoceramic patches as collocated actuators/sensors, we consider four groups of PZT actuators/sensors wherein each actuator in each group is designed to have a high level of modal controllability with respect to a given modal shape. Incorporated into the above optimization is the influence of each PZT on the plate's modal shapes. The intelligent control then provides the switching scheme in which, at a given time instance, only one of the four groups is active with the remaining three being kept dormant in order to reduce power consumption.

There exist many methods of adding damping to a vibrating structure; however, very few can function without ever coming into contact with that structure. One such method is eddy current damping. This magnetic damping scheme functions through the eddy currents that are generated in a conductive material when it is subjected to a time changing magnetic field. Due to the circulation of these currents, a magnetic field is generated that interacts with the applied field resulting in a force. In this manuscript, an active damper will be theoretically developed that functions by actively modifying the current flowing through a coil, thus generating a time varying magnetic field. By actively controlling the strength of the field around the conductor, the eddy currents induced and the resulting damping force can be controlled. This actuation method is easy to incorporate into the system and allows significant forces to be applied without every coming into contact with the structure. Therefore vibration control can be applied without inducing mass loading or added stiffness, which are downfalls of other methods. This manuscript will provide a theoretical derivation of the equations defining the electric fields generated and the dynamic forces induced in the structure. This derivation will show that when eddy current are generated due to a variation in the strength of the magnetic source the resulting force occurs at twice the frequency of the applied current. This frequency doubling effect will be experimentally verified. Furthermore, a feedback controller will be designed to account for the frequency doubling effect and simulated to show that significant vibration suppression the can be achieved with this technique.

Hydrogen storage alloy, such as LaNi₅ indicates as much as 25% of volume change in the course of H₂ absorption and desorption. We examined to apply this phenomenon to a mechanical mover device as a driving force controlled by the amount of hydrogen in the alloy. In this study a unimorph structural mover device was tested using HSA thin film deposited on an inert substrate. We confirmed displacements generating drastically large stresses by applying H₂ gas. While the amount of hydrogen in the alloy is a function of H₂ pressure and temperature, we also tried to control the hydrogen amount in the HSA by electric current directly applied through the film in a closed system. We report discussions on results with precise relationship between current and displacement under different temperatures. Displacement can be achieved by the temperature change caused by the electric current placed under ambient H₂ pressure, therefore, the results indicate the possibility of mover devices with simple structure similar to an artificial muscle controlled by electric current. From the results obtained, the test device was expected as an artificial muscle driven by hydrogen sorption reactions, which could be also controlled by electric current.

In this article, the modeling and control of enclosed sound fields using shunted piezoelectric circuit is investigated. A spherical wave, which is generated by a noise source located in the near field, is transmitted into a rectangular enclosure through a flexible panel. Piezoelectric patches, which are bonded symmetrically to the top and bottom surfaces of the panel, are either shunted through electric shunt circuits, and hence acting as energy dissipaters, or used as sensors for vibration measurements. Microphone sensors are used inside and outside the enclosure for acoustic pressure measurements. The shunted circuits are developed such that the acoustical effects of two dominant vibration modes can be attenuated, and this feature makes it appealing for noise control schemes for multiple tones. The numerical predictions of the noise attenuation levels are found to be in good agreement with the corresponding experimental measurements.

A new scheme for designing closed-loop control of dispersive waves in elastic structures is reported in this article. This scheme takes advantage of the dissipative characteristics of visco-elastic materials, and the isospectral properties of the visco-elastic system are used to design the feedback controller for the undamped structural system to realize the desired characteristics of the closed-loop system. Numerical results are presented in the form of frequency-response and wave-transmission characteristics, and these results show the promise of the proposed scheme.

In this paper, piezoelectric smart panels featuring shunt damping are designed and tested for broadband noise reduction. Electrical admittance is introduced to represent electro-mechanical characteristics of piezoelectric smart structures and to predict the performance of piezoelectric shunt damping as a design index of the system. The location and size of piezoelectric patches on the host panel are optimized by taking the admittance as a cost function and by using Taguchi method. The admittance is calculated by finite element method in the design stage and experimentally verified after the optimal configuration is found. Shunt performance of smart panel is realized by vibration reduction in frequency domain. In order to illuminate the effect of noise reduction in the shunt system, a standard test setup according to SAE J1400 is used to measure the transmission loss and sound pressure distribution for the smart panel. In this paper, a broadband shunt technique for increasing transmission loss is experimentally investigated.

New miniaturization and integration capabilities available from the emerging MEMS technology will allow silicon-based artificial skins involving thousands of elementary actuators to be developed in the near future. SMART structures combining large arrays of elementary motion pixels coated with macroscopic components are thus being studied so that fundamental properties such as shape, stiffness, color, and even reflectivity of light and sound could be dynamically adjusted. This paper investigates acoustic impedance capabilities of a set of distributed transducers connected with suitable controlling laws. Basically, we search to design an integrated electro-mechanical system which presents a global behavior with appropriate acoustical characteristics. This problem is intrinsically connected with the control of multi physical system based on PDE and with the notion of multi-scaled physics when we dispose MEMS devices. By using specific techniques based on partial differential equation control theory, we have first build a simple boundary control equation able to annihilate wave reflection. The obtained control strategies can also be discretized to be implemented like a zero or first order spatial operator. Thus, we can use quasi-collocated transducers and their well-known poles-zeros interlacing property to guarantee robust stability. This paper aims at showing in a first part how a well controlled semi-distributed active skin can substantially modify transmissibility or reflectivity of the corresponding homogeneous wall. In a second part numerical and experimental results underline the capabilities of the method. Finally efficiency of such a device is compared theoretically with those obtained by classical x-filtered LMS strategy.

This paper addresses bending of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elastic theory. In the present model, the equations of motion are derived by expanding the displacement field using the Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.

Magnetorheological (MR) damper is a kind of intelligent actuator, which shows immense potential in the field of structural vibration control. The construction and mechanical behavior of MR damper are introduced firstly, and then a new mechanical model--double sigmoid model is proposed based on the experimental study of MR damper. The simulation system of the 3-floor frame-shear wall eccentric structure with MR dampers was built according to the coupled translation and torsion response control using MR damper, based on Matlab/Simulink software environment and hardware/software resources of dSPACE. The shaking table experiment of the structural model was implemented by using rapid control prototyping (RCP) technology. The validity of two passive control strategies and one semi-active control strategy is verified under three input earthquake excitation with different peak value. The experimental results show that the coupled translation and torsion response is significantly mitigated, and the semi-active control strategies can achieve higher performance levels as compared to those of the two passive control cases. Moreover, the location of the MR damper has an important effect on the control results.

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft's control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland's continuing study of active wing load control.

When a conductive material is subjected to a time changing magnetic field, eddy currents are formed in the conductor. These currents circulate inside the conductor such that a magnetic field is formed. This eddy current field then interacts with the applied field resulting in a dynamic force between the conductor and the magnetic source. The force can be considered dynamic because as the eddy currents circulate inside the conductor they are dissipated by the internal resistance of the conductor. Therefore, if a continuously changing field is not applied to the conductor the force will disappear. However, the eddy current forces can be utilized to form an actuator by applying a time changing current to an electromagnet that is in close proximity to a conductive material. This actuation method is easy to incorporate into the system and allows significant forces to be applied without every coming into contact with the structure. Therefore vibration control can be applied without inducing mass loading or added stiffness, which are downfalls of other methods. This manuscript will develop the concept and show that it can be accurately modeled and effectively used to control the vibration of a structure. This vibration control system will use a velocity feedback filter to actively modify the current applied to the coil. Using this system, experiments are performed on a cantilever beam showing the system can effectively suppress the each of the first five modes of vibration by upwards of 20dB.

The problem considered in this paper is about the collocation strategies of sensor and actuator for the active control of sound and vibration. It is well-known that a point collocated sensor-actuator pair offers an unconditional stability with very high performance when it is used with a direct velocity feedback (DVFB) control, because the pair has strictly positive real (SPR) property. In order to utilize this SPR characteristics, a matched piezoelectric sensor and actuator pair is considered, but this pair suffers from the in-plane motion coupling problem with the out-of-plane motion due to the piezo sensor and actuator interaction. This coupling phenomenon limits the stability and performance of the matched pair with DVFB control. As a new alternative, a point sensor and distributed piezoelectric actuator pair is also considered, which provides SPR property in all frequency range when the pair is implemented on a clamped-clamped beam. The use of this sensor-actuator pair is highly expected for the applications to more practical active control of sound and vibration systems with the DVFB control strategy.

The problem of bending vibrations is common in different engineering and physical applications. Bending vibrations of centrally clamped rotating circular disks play crucial role in functionality of hard disk drives. Lots of efforts are spent for dynamic stabilization, control and measurement of bending vibrations in such micromechanical systems. Nevertheless, measurement of microscopic deflections from the state of equilibrium is a challenging problem. Different optical measurement techniques are developed for experimental investigation of bending vibrations. Shadow moire is one of the popular methods for experimental analysis of bending vibrations of structures. Unfortunately, interpretation of experimental measurement results is a nontrivial inverse engineering problem often having non-unique solutions. Therefore there exists a definite need for hybrid numerical - experimental techniques that could help to interpret the measurement results. The procedure for the generation of digital stroboscopic shadow moire images for the eigenmodes of bending vibrations of a plate is developed. It is based on the methods of computer graphics and the method of finite elements for the analysis of bending vibrations of a plate. The construction of digital shadow moire images builds the ground for hybrid numerical-experimental procedures and enables to analyze the experimental results with greater precision.

Shape memory alloy (SMA) beams are used in a variety of applications such as, e.g., stents or microactuators. In this paper, a free energy based SMA model is implemented into the commercial finite element (FE) code ANSYS, and the bending problem of a SMA cantilever beam is studied. In order to determine optimal parameter settings for the finite element analysis, we systematically study convergence behavior and accuracy for different convergence criteria as well as other relevant parameters such as element, substep and integration point number. The simulation results demonstrate that the SMA model can represent both shape memory effect and superelasticity of SMA materials seamlessly.

The design of pseudoelastic shape memory alloy (SMA) passive damping devices for structural vibration is dependent on the geometry of the SMA. By changing the effective radius size of an attached SMA element, one simultaneously changes the nonlinear stiffness and damping contributed to the system by the SMA. In order to identify the coupled nonlinear dynamic behavior, this work focuses on the steady state frequency response functions of a simple SDOF system with an attached SMA element under base excitation. An equivalent linearization method is used to produce a qualitative representation of the frequency response of the structure for multiple radius sizes and excitation amplitudes. These results are then compared to corresponding frequency response functions produced from the Seelecke, Muller, and Achenbach SMA model. These results give insight into jump phenomenon, hysteretic damping effects, and identify the stable branches of the nonlinear frequency response. Additionally, optimal radius sizes are presented for a range of harmonic excitation amplitudes and frequencies. These results lead to an initial investigation into the physical mechanisms responsible for choosing optimal radius sizes for an arbitrary excitation.