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29 July 2004 Semi-analytic methods for analysis of laminated piezoelectric cylinders
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A semi-analytic method is presented for analyzing the behavior of layered, circular piezoelectric cylinders under axisymmetric mechanical and electric loads. Discretization occurs in the radial direction so that any number of layers with distinct material properties and thickness can be accommodated. Axial and circumferential behaviors are obtained analytically. Mechanical loads include axial force, torque, longitudinal and circumferential surface shears, and arbitrary pressure distributions. Electric loads include voltage and charge distributions along the axis of the cylinder that may be applied on any layer’s surface. In the present approach, all loads are represented by power series in the axial coordinate. There are several advantages provided by the semi-analytic method. First, as part of the solution is analytic, it is more accurate than any fully discrete (e.g., finite element) method. It is also computationally more efficient than discrete methods as the dimension of the problem is reduced, essentially, by one order. Second, the method is more accurate than technical (beam, plate, shell) theories as the deformation of the cross-section is not constrained by any simplifying kinematic hypothesis. Third, it provides solutions for complex geometry and material distributions for which there are no analytic solutions. The method may be extended to general, nonhomogeneous cross-sectional geometries. Veracity of our implementation is demonstrated by comparing the results for various problems with those obtained via three-dimensional finite element methods. We also provide the analysis of a bimodal actuator to demonstrate the utility of the present technique for evaluating designs of smart structures with layered, axisymmetric geometries.
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Chengwen Liu, Stanley B. Dong, and Ertugrul Taciroglu "Semi-analytic methods for analysis of laminated piezoelectric cylinders", Proc. SPIE 5391, Smart Structures and Materials 2004: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, (29 July 2004);

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