Free vibration of laminated piezoelectric composite plates based on an accurate theory

An accurate theory for laminated piezoelectric composite plates in cylindrical bending is developed for free vibration analysis. The displacement and electric potential fields are depicted approximately by the accurate displacement and electric potential distribution functions through thickness, respectively. The two functions are formulated according to particular solutions to the three-dimensional elasticity equilibrium equations and the electrostatics charge equation. The complicated electromechanical coupling relations and the interfacial continuity conditions are enforced. Accordingly the two functions are coupled and make the displacement and potential fields coupled. The governing equations use only four displacement and potential variables, the number of which is independent of the number of layers involved. A corresponding finite element model is also developed. Natural frequencies of piezoelectric laminates subjected to different sets of boundary conditions are given and parameter studies are conducted in numerical examples. The high accuracy of this theory is demonstrated by comparing the present results with the existing exact three-dimensional solutions.

[1]  Dale A. Hopkins,et al.  Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates , 1997 .

[2]  Xiaoping Shu.  Vibration and bending of antisymmetrically angle-ply laminated plates with perfectly and weakly bonded layers , 2001 .

[3]  C. K. Lee.  Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships , 1990 .

[4]  Kostas P. Soldatos,et al.  An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions , 2001 .

[5]  Santosh Kapuria,et al.  Levy-type piezothermoelastic solution for hybrid plate by using first-order shear deformation theory , 1997 .

[6]  Dimitris A. Saravanos,et al.  Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators , 1995 .

[7]  John Anthony Mitchell,et al.  A refined hybrid plate theory for composite laminates with piezoelectric laminae , 1995 .

[8]  Kostas P. Soldatos,et al.  A method for improving the stress analysis performance of one- and two-dimensional theories for laminated composites , 1997 .

[9]  Shu Xiao-ping,et al.  An improved simple higher-order theory for laminated composite plates , 1994 .

[10]  Paul R. Heyliger,et al.  Exact Solutions for Laminated Piezoelectric Plates in Cylindrical Bending , 1996 .

[11]  M. C. Ray,et al.  Exact analysis of coupled electroelastic behaviour of a piezoelectric plate under cylindrical bending , 1992 .

[12]  Paul R. Heyliger,et al.  Free vibration of piezoelectric laminates in cylindrical bending , 1995 .

[13]  Kenneth B. Lazarus,et al.  Induced strain actuation of isotropic and anisotropic plates , 1991 .

[14]  Jin H. Huang,et al.  Analysis of hybrid multilayered piezoelectric plates , 1996 .

[15]  Craig A. Rogers,et al.  Laminate Plate Theory for Spatially Distributed Induced Strain Actuators , 1991 .

[16]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[17]  Xiaoping Shu,et al.  Improving the efficiency of finite element formulations in laminated composites , 2002 .

[18]  Xiaoping Shu,et al.  Cylindrical bending of angle-ply laminates subjected to different sets of edge boundary conditions , 2000 .

[19]  Paul R. Heyliger,et al.  Static behavior of laminated elastic/piezoelectric plates , 1994 .

[20]  D. H. Robbins,et al.  Analysis of piezoelectrically actuated beams using a layer-wise displacement theory , 1991 .

[21]  Santosh Kapuria,et al.  An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers , 2001 .

[22]  Jiaying Wang,et al.  THREE DIMENSIONAL ANALYSIS FOR FREE VIBRATION OF RECTANGULAR COMPOSITE LAMINATES WITH PIEZOELECTRIC LAYERS , 1998 .

[23]  Romesh C. Batra,et al.  Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates , 2000 .

[24]  Romesh C. Batra,et al.  The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators , 1997 .