Instruments and machines requiring very high stability should be isolated from their normally less stable environment. Exact constraint mounting using six, single-constraint flexures provides a stiff connection between the instrument and its environment while isolating the instrument from low frequency deformations of the environment, such as thermal expansion. Higher frequency disturbances, however, transfer through the flexures and excite vibration modes of the instrument. Traditionally, passive or active vibration isolation is employed to attenuate environmental disturbances reaching the instrument. However, strict alignment requirements for the instrument preclude the use of low-frequency isolation, unless active methods are used. Therefore, the solution is to provide damping in parallel with the flexures to reduce the vibration amplitudes of the instrument. Flexures concentrate strain energy in blades making them excellent candidates for damping treatments. A properly designed damping treatment across the flexures can provide as much as 8% to 10% viscous damping to the isolation modes and will also help attenuate the instrument vibration modes. Thus, through the use of six damped single-constraint flexures the instrument's requirements for stability, alignment, stress, and vibration may be met. An application of this approach will be employed on the Reflection Grating Array (RGA) for the X-ray Multi-mirror Mission for the European Space Agency. The RGA is an array of 200 diffraction gratings aligned to sub-micron and sub-arc-second tolerances relative to each other. This produces a coherent wavefront for spectrum analysis. The launch vehicle will be an Ariane 5 scheduled for 1998.

A Hughes Space Company study was undertaken to (1) acquire the analytical capability to design effective passive damping treatments and to predict the damped dynamic performance with reasonable accuracy; (2) demonstrate reasonable test and analysis agreement for both baseline and damped baseline hardware; and (3) achieve a 75% reduction in peak transmissibility and 50% reduction in rms random vibration response. Hughes Space Company teamed with CSA Engineering to learn how to apply passive damping technology to their products successfully in a cost-effective manner. Existing hardware was selected for the demonstration because (1) previous designs were lightly damped and had difficulty in vibration test; (2) multiple damping concepts could be investigated; (3) the finite element model, hardware, and test fixture would be available; and (4) damping devices could be easily implemented. Bracket, strut, and sandwich panel damping treatments that met the performance goals were developed by analysis. The baseline, baseline with damped bracket, and baseline with damped strut designs were built and tested. The test results were in reasonable agreement with the analytical predictions and demonstrated that the desired reduction in dynamic response could be achieved. Having successfully demonstrated this approach, it can now be used with confidence for future designs as a means for reducing weight and enhancing reliability.

Experiments performed aboard the space shuttle often utilize sensitive scientific equipment which cannot withstand high launch loads without damage. It would be highly advantageous to reduce the severity of the dynamic launch environment so that space-qualification of such equipment would be faster and less expensive. This is the goal of the Soft Ride to Orbit program. This program has identified passive damping as one technology which will reduce loads seen by equipment and thereby provide a softer ride. Finite element structural modeling was used to predict both undamped and damped responses to simulated launch loads. The modal strain energy method was used to design the passive damping treatment. This treatment was manufactured and applied to the drawer. All analyses were verified by modal and vibration testing. It was found that predicted and tested frequencies, damping values, and vibration response levels agreed reasonably well, thus showing that passive damping may be designed into future equipment drawers to reduce launch loads on sensitive equipment.

This paper describes the development of damped structure for the Supportable Technology for Affordable Fighter Structures (STAFS) Program. The study started with analytical design trade studies and progressed through a series of tests to characterize adhesive behavior, performance testing of a component level integrally damped panel concept, and full scale design integration. Analyses were performed on finite element panel models with viscoelastic elements in the bond areas to determine the sensitivities of configuration and adhesive type to overall damping achieved. The concepts studied showed that as much as 10 percent structural damping could be obtained in the structural modes of interest. Test panels with and without damping treatments were fabricated using super plastically formed-adhesive bonded 2095 aluminum, and tested to measure the comparative response improvement in the damped panels. A substantial weight savings was realized in comparison to the monolithic metal panels which would be required to withstand the acoustic environment.

A concept for measuring dynamic strain distributions on structural surfaces is presented. The concept uses an array of small piezoelectric polymer film -- polyvinylidene fluoride (PVDF) -- strain sensors coupled with an inexpensive multi-channel signal processor to produce strain `maps.' The strain `maps' are intended to aid the placement of damping treatments. The current approach is to measure displacement mode shapes, measurement of the strain shapes is a more direct approach. As the structure bends, the PVDF sensor produces a voltage proportional to the dynamic strain over the effective surface area. The concept was first applied to an aluminum beam. An array of PVDF sensors was bonded to the surface of the beam to produce strain `maps' for the first three vibration modes. The resonant frequencies, damping, and strain `maps' were identified from captured transient time domain responses of the beam using the Eigensystem Realization Algorithm and compared to the parameters predicted by a finite element model. This paper compares the experimental and analytical strain `maps' of the beam and discusses the techniques required to conduct the experiment. Results presented in the paper show reasonably accurate strain `maps' which allowed the modal strain to be directly measured.

An analytical procedure to incorporate viscoelastic damping into advanced composite bladed structures is described. A constrain layer damping technique is used to damp out specific modes in a cantilevered pre-twisted plate. A viscoelastic material, 3M Scotchdamp ISD 113 (ISD113), is placed in a small pocket at a specified location within the plate to isolate the damping of a particular vibration frequency. Analytical and experimental results are presented for a flat and pretwisted plate with the [O₂/+0/-0₂/+0/O₂/ISD113-border material]_s lay-up. The results show that for a given patch size of the ISD113 the location can have a significant effect on the damping level and only a negligible effect on the structural stiffness. The results also show that the border material can be varied in such a way as to increase the damping level with only a slight decrease in the structure's natural frequency.

Viscoelastic material (VEM) adds damping to structures. In order to enhance the damping effects of the viscoelastic material, a constraining layer is attached. If this constraining layer is a piezoelectric patch, the system is said to have active constrained layer damping (ACLD). In this paper, the damping effects due to viscoelastic material which has an active constraining layer is modeled using the Golla-Hughes-McTavish (GHM) damping method. The piezoelectric patch and structure are modeled using a Galerkin approach in order to account for the effect of the constraining layer on the beam.

A piezoelectric element and a constrained layer damping element are combined to allow for an active constrained layer damping treatment. The development of these elements is reviewed and results are compared with the literature to insure that the elements work together. A procedure for placing patches damping treatments or other material anomalies on structures is introduced. The patch placement process uses a grid deformation procedure to realign elements with the patch boundaries. This makes the process of optimally locating the damping treatment one of continuous variables. The patch placement process is used in conjunction with the combined elements and an optimization algorithm to design an active constrained layer damping treatment and the beam to which it is attached.

This paper is to develop a mathematical model to predict bending, twisting, and axial vibration response of a composite beam with intelligent constrained layer (ICL) or active constrained layer (ACL) damping treatments. In addition, preliminary experiments are conducted on composite beams to evaluate this new technique. The ICL composite beam model is obtained by integrating the existing ICL composite plate model proposed by Shen. When the plate width (along the x-axis) is much smaller than the plate length (along the y-axis), integration of the ICL composite plate equations and linearization of displacement fields with respect to x leads to a set of equations that couples bending, tosional, and axial vibrations of a composite beam. The equations of motion and associated boundary conditions are normalized and rearranged in a state-space matrix form, and the vibration response is predicted through the distributed transfer function method developed by Yang and Tan. A numerical example is illustrated on a composite beam with bending-torsion coupling stiffness. Numerical results show that ICL damping treatments may or may not reduce coupled bending and torsional vibrations of a composite beam simultaneously. When the deflection is fed back to actuate the ICL damping treatment, a sensitivity analysis shows that only those vibration modes with significant bending response are suppressed simultaneously with their torsional components. In the preliminary experiments, two different ICL setups are tested on a composite beam without bending-torsion coupling. Damping performance of both ICL setups agrees qualitatively with existing mathematical models and experimental results obtained from other researchers. The damping performance, however, is not optimized due to the availability of materials and their dimensions in the laboratory. An optimization strategy needs to be developed to facilitate design of ACL damping treatments with maximized damping performance.

A qualitative comparison between a piezoelectric vibration absorber and a constrained layer damping treatment is presented. Piezoelectric materials convert mechanical strains into electrical charge. Dissipation of the charge results in attenuation of vibration. The damping is concentrated to a single mode by constructing a piezoelectric absorber. The damped vibration absorber is comprised of the piezoelectric material and a passive electronic shunt. Previous research has applied the piezoelectric absorber to one-dimensional structures. This paper applies the absorber to a two-dimensional planar problem. The simple mathematical description of the absorber is modified for the two-dimensional problem. An analytical means of estimating the effectiveness of the piezoelectric absorber is derived. The effectiveness is estimated for an electronics chassis box subjected to random excitation. A typical constrained layer damping treatment is also analytically designed for the problem. The piezoelectric absorber and the constrained layer damping treatment are experimentally applied to identical boxes. Results show that the piezoelectric absorber can provide vibration suppression comparable to that obtained by the constrained layer damping treatment.

This paper examines the use of smart materials for passive damping. Among the smart materials considered are electrorheological and magnetorheological (ER and MR) fluids, piezoelectrics, electrostrictives, magnetostrictives, and shape memory alloys. The specific mechanism exploited for energy dissipation by passive or semi-passive means is described for each material. A distinction is made between internal and external energy dissipation. The external stimuli required for each of the semi-passive mechanisms are noted. Selected examples of damping results with each material are provided. Practical limitations for engineering design and implementation are considered, and recommendations are made for the more promising materials.

Particle dampers are utilized to damp the fundamental modes of vibration of two antennae mounted at the tip end of cantilever beams. The damper is composed of a closed container which is partially filled with metallic particles. The damper is bolted near the tip of the booms where the amplitude of vibratory motion is greatest. It is shown experimentally that significant damping can be obtained with this very simple and low cost device.

This paper describes the efforts by Honeywell and MIT to develop a second generation hybrid D-Strut^TM (patent pending). The D-Strut is a passive viscous damping and stiffening device used for structural control and isolation. The concept of using an active element synergistically with passive elements was presented in the 1994 SPIE Conference on Smart Structures and Materials paper titled `Actuator with Built-in Viscous Damping for Isolation and Structural Control.' A second generation hybrid D-Strut or active D-Strut with many applications to isolation of spacecraft hardware has been built and tested. The utilization of the device for several system applications is discussed. The primary advantage of the hybrid is that the passive elements are designed for small gravity sag and acceptable mount resonance and the active control is designed to reduce transmissibility over broad or narrow frequency ranges. The payload is then robustly isolated even in the unpowered (active stage off) state. Modeling, dynamic tests, and several single axis isolation experimental results are presented. Also, specific designs for six-axis implementations for microgravity isolation and optical payload isolation, pointing, and suppression are described.

The requirements for spacecraft and launch vehicles have driven numerous investigations of vibration suppression techniques and devices. Appendages on spacecraft and component vibrations on launch vehicles are common problems for which vibration attenuation is beneficial or necessary. This paper documents the hardware development and component and system level demonstration of a viscous fluid damper design in a very low frequency appendage application. The resulting design has significant advantages over state-of-the-art viscous damper designs and can meet the requirements of many future systems. Potential applications include damping struts, isolation systems, and tuned dampers. Advantages of the design include excellent predictability and linearity, the capability for high forces and displacements, high hydraulic stiffness, the absence of elastomeric seals and the potential for passive control of damper property variations with temperature.

Theoretical models of the behavior within the pseudoelastic hysteresis loop of shape memory alloys are presented. These models are considered in the analysis of the dynamic response of a cantilevered beam constrained by shape memory wires. Quantitative results of damping and shift in natural frequencies of the structure are presented, and the effect inner hysteresis loops have on structural dynamics are compared to those found experimentally. The results suggest the possibility of the existence of two trigger lines, one for loading and one for unloading, within the hysteresis loop, and a relationship between the trigger line angle and a maximum dissipation principle.

Significant progress has been made in the development of passive control techniques in earthquake (EQ) engineering during the last two decades. Today, the most successful passive structural control technique in earthquake engineering is base isolation. Following the successful history of implementation of base isolation technology, passive energy dissipation devices are currently making inroads. In this paper a simple comparison of various passive control techniques is performed. This paper demonstrates the comparative merits of various techniques and assesses the effectiveness of passive control technology in mitigating seismic hazard for structures.

Passive control of the dynamic response of civil structures utilizing shape-memory alloy (SMA) damping techniques is reviewed. An important class of SMA damper -- the center- tapped (CT) device -- is described. Coverage includes: (1) characterization of damping requirements and passive damping approaches for civil structures; (2) characterization of SMA material behaviors relevant to civil structural applications; (3) overview of our SMA passive damping device technology and description of the center-tapped device operation and structure; (4) precis of an experimental program conducted to verify the CT device behavior, the detailed results of which are reported in another paper by the Earthquake Engineering Research Center; (5) review of a design study of SMA passive damping for retrofit of an extant nonductile concrete building.

In the wake of damaging earthquakes in both the United States and Japan over the past year, the performance of structures, in addition to traditional life-safety concerns, has become an important issue for designers and owners. Many possible approaches to enhancing the seismic performance of structures have been proposed, and one promising family of solutions which is receiving attention today is passive damping devices. The work presented here is part of an ongoing experimental and analytical study of the applicability of one particular type of damping device for controlling the response of civil structures. Two different types of reduced-scale dampers using shape memory alloys have been tested over a range of strain amplitudes, loading frequencies, and temperatures. The purpose of the tests was to thoroughly characterize an alloy and examine variations in device design and installation configurations that could lead to a number of different hysteretic shapes. The ultimate behavior of the devices was also examined. Parallel to the device development and testing, a series of analyses of a steel frame building incorporating shape memory alloys has been undertaken to quantify the benefits of using these devices in an actual structure. Preliminary results of these analyses are presented.

The remarkably long central spans of the Rio-Niteroi bridge are set into vortex-induced oscillations by cross winds of relatively low velocities. Whenever winds reach certain threshold speed ranges the response amplitudes grow large and the bridge is closed to traffic of any vehicle for the user's comfort and safety. This deterrent aspect of the world's largest span steel box girders bridge is explored to forward an explicit proposal for installing tuned vibration absorbers (TVAs) to attenuate oscillation amplitudes and, consequently, to improve bridge service life. A simple mathematical model, which yields response amplitudes that correlate favorably with wind-tunnel test results of a sectional model, is combined with optimization techniques to investigate and compare performances of both passive and active/passive feasible control devices. The obtained numerical results are then used to demonstrate that simple mechanical and robust TVAs come to be an advantageous intent to upgrade this bridge's serviceability.

The effects of elongation on the audiofrequency dynamic mechanical properties of a natural rubber (Hevea) gum stock have been described previously in terms of the elastic (J') and the viscous (J') components of a complex shear compliance, J* equals J' - iJ'. In this prior work emphasis was on the changes in compliance levels and the frequency dependencies of the elastic and viscous components at static elongations from 0 to 400%, and after retractions to elongations below 300%. At elongations above 300%, several large, sharp resonances appeared in the compliance-frequency plots coincident with the well known stretch-induced, oriented crystallinity above 300% elongation for the initially amorphous rubber at room temperatures. In the present work attention is on the loss tangent, J'/J', which governs vibration damping, and for which no data were given in the earlier report. After extensions to 400%, as described above, followed by retraction to 275%, for example, values of loss tangent were two or three times those found at any of the first elongations from 0 to 400%. Current measurements using an automated measurement system yield similar results. Additional information on the effect of time at an elongation and the elongation-retraction sequence on enhanced damping has also been gathered. In any case, it is evident that natural rubber gum stocks, ordinarily with low damping, when treated smartly can be changed to high damping materials at some audio frequencies.

Viscoelastic adhesives are commonly used as vibration damping treatments for mechanical systems. When using these adhesives, knowledge of the shear modulus and loss factor at a given temperature is essential. The standard method for determining shear modulus and loss factor yields values at only a few frequency points for any given temperature. The method presented in this report offers a continuous curve for the two material properties over a broad frequency range.

The Advanced Photon Source (APS), under construction at Argonne National Laboratory (ANL), requires precise alignment of several large magnets. Submicron vibratory displacements of the magnets can degrade the performance of this important facility. Viscoelastic materials (VEM) have been shown to be effective in the control of the vibration of these magnets. Damping pads, placed under the magnet support structures in the APS storage ring, use thin layers of VEM. These soft VEM layers are subject to both high-energy radiation environment and continuous through-the-thickness compressive loads. Material experiments were conducted to answer concerns over the long term effects of the radiation environment and creep in the viscoelastic damping layers. The effects of exposure to radiation as high as 10⁸ rad on the complex modulus were measured. Through-the-thickness creep displacements of VEM thin layers subjected to static loads of 50 psi were measured. Creep tests were conducted at elevated temperatures. Time-temperature equivalence principles were used to project creep displacements at room temperatures over several years. These damping material measurements should be of interest to vibration control engineers working with a variety of applications of fields ranging from aerospace to industrial machinery.

In order to predict accurately the vibration characteristics of viscoelastic elements and viscoelastically damped structures, the use of frequency-dependent parameters such as complex modulus and Poisson's ratio is important. Several techniques have been developed for measuring the frequency-dependent complex modulus of viscoelastic materials. However, the accurate determination of Poisson's ratio of viscoelastic materials is much less developed. This quantity is important as its commonly quoted value of 0.5 can be very different when a viscoelastic material is in its transition or glassy region or if the material is compressible. In this paper, prismatic viscoelastic samples are employed to predict the value of Poisson's ratio using the finite element method (FEM). The transmissibility characteristics of these prismatic samples are established experimentally and FEM is used in conjunction with measured complex Young's modulus and iterated values of Poisson's ratio such that the predicted FEM results agree as well as possible with the experimental data. It is shown that the method suggested is able to predict accurately the Poisson's ratio of incompressible and compressible viscoelastic materials.

A procedure is presented for computing the transient response of a multiple degree of freedom finite element model of a beam system containing a viscoelastic material. A complex, frequency and temperature dependent shear modulus is used in representing the properties of this material. The beam is struck with an arbitrary transient input pulse, which is transformed to the frequency domain via the fast Fourier transform (FFT) algorithm. The frequency dependent response of the beam may then easily be computed. Applying the inverse fast Fourier transform to this result then yields the transient, damped response of the complete beam system. This `approximate' approach is compared against an exact, modal solution for a system with viscous damping and excellent correlation is observed between the two. Finally, a procedure is presented to incorporate the finite element code ANSYS into the prediction procedure. Through the use of this code, a model constrained layer damped beam may be analyzed to obtain its transient response to an applied load.

Representation of frequency-dependent viscoelastic material properties has long been problematical in the frequency domain and especially in the time domain. The method of Golla, Hughes, and McTavish (GHM) addresses this problem with a Laplace-domain model of the complex material modulus, in which a number of parameters are determined by curve- fitting to experimental data. The result is well suited to finite element formulations because the equations of motion retain the familiar second-order, constant-coefficient form, at the expense of some extra scalar degrees of freedom. This paper reports on an implementation of GHM in MATLAB, using FEM data imported from NASTRAN. Sample problems demonstrate the efficacy and practicality of the method.

The use of scaled models to validate the dynamic characteristics of structures is common. For linear elastic structures, the dynamic characteristics such as natural frequencies can be determined from the scaled models by a scaling factor. This scaling factor is the ratio of the physical dimensions between the scaled model and the structure. However, in the case of viscoelastic elements, the viscoelastic properties of the material are frequency dependent. Hence, in order to use the results of the scaled model, the scaling factor must include the frequency dependent characteristics of the viscoelastic material. In this paper, simple elements are used to illustrate the importance of including the material viscoelastic properties in determining the scaling factor and a procedure is described which can be used to determine the dynamic characteristics of scaled models.

The use of multi-layer constrained layer damping treatments on plate-like structures provides broadband vibration damping over a wide temperature range. A difficulty with the design of such treatments is their modeling. The current state of the art requires a separate plate element for each constraining layer plus a solid element for each viscoelastic layer in the thickness direction. The number of degrees of freedom is large conflicting with the iterative approach necessitated by the frequency and temperature dependance of the material properties which dictates that a small model size must be maintained. The large model size also slows optimization. The goal of this research was to produce a true plate finite element model which uses only a few degrees of freedom per node. This model is obtained by using a variational asymptotical theory to correctly capture the layerwise jumps in the stress and strain fields. A model is developed for simply supported plates which can later be extended to a more general finite element. Results are compared with the exact elasticity solution of Pagano. They show an excellent match exists in the predicted stress and strain field. The model is also compared with RKU analysis for plates again demonstrating its accuracy. A future finite element model based on this theory would require only six extra degrees of freedom per node with only one element in the thickness direction, thus simplifying the modeling of constrained layer damping treatments.

In this paper, a new constrained layer damping configuration is proposed for beams of circular cross section that may experience both bending and torsional vibrations. The `barberpole' configuration consists of narrow strips of damping treatment oriented at a pitch angle relative to lines parallel to the beam centerline. The individual damping strips may be continuous over the length of the beam, or periodically segmented along the strip length. A quasistatic analysis is developed to evaluate the effectiveness of the barberpole configuration for damping bending and torsional vibrations. It is shown that damping for both bending and torsion is attainable with the same damping treatment if the constraining layer strips are periodically segmented. It is also shown that for the pure bending problem, the unsegmented barberpole geometry provides an improvement in damping over unsegmented straight strips. At each crossing of the beam neutral plane, the constraining layer is free of extensional stress, which provides a `virtual segmentation' effect. This virtual segmentation provides an alternative to conventional segmentation of the damping layer when the more conventional approach is undesirable due to environmental or operational reasons.

This paper documents the design, fabrication, and testing of a co-cured damped composite strut that uses the extension-shear coupling mechanism of off-angle composite materials to enhance the damping performance of a viscoelastic material. The viscoelastic material was placed between two graphite shells. The inner shell contains plies oriented at a positive ply angle in the first half of the tube and plies oriented at a negative ply angle in the second half of the strut. Due to the extension-shear coupling, the tube center section rotates when the tube undergoes axial deformation. The outer tube plies are oriented in the opposite manner so that the tube center rotates in the opposite direction as the inner tube for a given axial deformation. The relative rotation between the two shells places the viscoelastic material into shear providing damping, where the ply is determined that maximizes the damping performance. The same extension-shear coupling mechanism also allows the tube to damp torsion motion. The two shells were hard mounted to each other at their ends, by replacing the viscoelastic material with composite material, so that both tubes carry static loads. A finite element model was developed to predict axial and torsion properties. Stiffness properties were `measured' analytically via static condensation of the complex stiffness matrix. Trade studies were performed to determine optimal ply orientation and to determine the strut's effectiveness as a torsion damper for structural components such as a damped composite drive shaft. The approach is validated by performing a modal survey on a fabricated damped strut and on a baseline undamped strut (i.e. viscoelastic material is replaced with 4 plies of unidirectional graphite/epoxy with fibers oriented in the hoop direction). Natural frequency damping levels are presented for both strut's first bending and first axial modes.

A quantum leap in the performance of vibration damping for structural panels has been provided by the development of a practical spacer (or stand off) layer. The thicker the stand off layer, the greater the performance and the efficiency of the damping treatment. The thickness of the stand off layer behaves much as the depth of an I-beam with regard to structural efficiency. Selected experimental results as well as some theory and practicalities of spaced or stand off damping for structural panels are presented and discussed. The basic theory of spaced or stand off damping has been well known since the late 1950s. The two essential features of a spacer or stand off layer are that the shear stiffness must be relatively high and that the flexural stiffness must be relatively low. For a homogeneous layer, these are mutually exclusive requirements. Practical stand off damping treatment systems originally developed in the late 1980s are described. A variety of applications in the laboratory, in flight, and in service have been developed and selected data are presented. Passive stand off vibration damping treatment systems have achieved a large degree of success and maturity, even though there are many significant opportunities for further technological advancements. There have been high payoff applications where passive damping has played a vital role in suppressing vibration and noise.

A viscoelastic tuned-mass damper was used to suppress specific structural modes of a prototype lithography platen. The platen is magnetically levitated and it is repositioned and held in position by a closed-loop feedback control system. Important capabilities of the platen control system are precise positioning and rapid repositioning, which tend to require high frequency bandwidth. The high bandwidth excites structural vibration modes which are disruptive to the control system. The present work was to develop and demonstrate a means to suppress these modes using passive vibration damping techniques. The motivation is to increase the robustness of the platen positioning and control system by reducing unwanted modal accelerations excited by high control system bandwidth. Activities performed and discussed in this paper include the analytical design of viscoelastic tuned-mass dampers and the demonstration/testing of their effectiveness on the platen while levitated and controlled.

The dynamic behavior of most polymeric materials become non-linear at a moderately large strain amplitude excitation. In order to optimize their uses for noise and vibration attenuation, it is necessary to characterize their damping properties as a function of strain amplitude. This work reports the strain amplitude dependent non-linear dynamic behavior of two elastomer compounds, NBR and Neoprene, studied at various frequencies and strain amplitudes using the Fourier transform mechanical analysis (FTMA) technique, developed by us. The basic theory and experimental results are presented for a one-dimensional isothermal simple shear deformation. The Green-Rivlin constitutive equation was used to model the observed behavior. The results indicate that a complete characterization of non-linear dynamic properties is rather complex. The energy dissipation is governed, however, by a simple mechanism. It is shown that the energy dissipation is governed only by the first harmonic loss modulus term of the Green-Rivlin representation, but the energy storage is related to many material functions. An expression for the energy dissipation of a non-linear viscoelastic material is derived. It is also shown that irrespective of the material constitutive law the energy dissipation can occur only at the frequency of excitation but it can be stored in a complex manner. The results are rather generalized to show that the amplitude dependence can be modeled by a power law function. It is also shown that an examination of the stress Fourier spectra can give a quantitative indication of material non-linearity and suggest a direction for developing an adequate model of these complex materials.

The electromechanical surface damping technique (EMSD) is applied to suppress the bending and twisting peak vibration amplitudes of a cantilever plate. The technique is a combination of the constrained layer damping (CLD) and the shunted piezoelectric methods in which the constraining layer of the CLD is replaced by a shunted piezoelectric ceramic. The frequency responses, to a white noise random base excitation, of the EMSD-treated plate at the vicinity of the first and second bending and twisting resonant frequencies are determined and compared with the corresponding responses of the CLD-treatment. It is shown that, in general, the EMSD treatment provides more suppression of the bending and twisting peak vibration amplitudes than the conventional CLD treatment. The EMSD treatment, however, is more effective at higher frequencies and lower temperatures, which suggests that the EMSD method can be applied to extend the effective range of frequencies and/or temperatures of the conventional CLD method. The work presented is primarily analytical, however crude and preliminary experimental results are presented in order to demonstrate the feasibility of the EMSD technique.

Bending vibration of flat plates is controlled using patches of active constrained layer damping (ACLD) treatments. Each ACLD patch consists of a visco-elastic damping layer which is sandwiched between two piezo-electric layers. The first layer is directly bonded to the plate to sense its vibration and the second layer acts as an actuator to actively control the shear deformation of the visco-elastic damping layer according to the plate response. With such active/passive control capabilities the energy dissipation mechanism of the visco-elastic layer is enhanced and its damping characteristics of the plate vibration is improved. A finite element model is developed to analyze the dynamics and control of flat plates which are partially treated with multi-patches of ACLD treatments. The model is validated experimentally using an aluminum plate which is 0.05 cm thick, 25.0 cm long, and 12.5 cm wide. The plate is treated with two ACLD patches. Each of which is made of SOUNDCOAT (Dyad 606) visco- elastic layer sandwiched between two layers of AMP/polyvinylidene fluoride (PVDF) piezo- electric films. The piezo-electric axes of the patches are set at zero degrees relative to the plate longitudinal axis to control the bending mode. The effect of the gain of a proportional control action on the system performance is presented. Comparisons between the theoretical predictions and the experimental results suggest the validity of the developed finite element model. Also, comparisons with the performance of conventional passive constrained layer damping clearly demonstrate the merits of the ACLD as an effective means for suppressing the vibration of flat plates.