Analytical solution for the cylindrical bending vibration of piezoelectric composite plates

An analytical solution for the cylindrical bending vibrations of linear piezoelectric laminated plates is obtained by extending the Stroh formalism to the generalized plane strain vibrations of piezoelectric materials. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thickness and width. Fourier basis functions for the mechanical displacements and electric potential that identically satisfy the equations of motion and the charge equation of electrostatics are used to solve boundary value problems via the superposition principle. The coefficients in the infinite series solution are determined from the boundary conditions at the edges and continuity conditions at the interfaces between laminae, which are satisfied in the sense of Fourier series. The formulation admits different boundary conditions at the edges of the laminated piezoelectric composite plate. Results for laminated elastic plates with either distributed or segmented piezoelectric actuators are presented for different sets of boundary conditions at the edges. � 2003 Elsevier Ltd. All rights reserved.

[1]  R. Batra,et al.  Missing frequencies in previous exact solutions of free vibrations of simply supported rectangular plates , 2003 .

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

[3]  Romesh C. Batra,et al.  Exact solution for the cylindrical bending of laminated plates with embedded piezoelectric shear actuators , 2001 .

[4]  Paul R. Heyliger,et al.  Exact Solutions for Simply Supported Laminated Piezoelectric Plates , 1997 .

[5]  Romesh C. Batra,et al.  The vibration of a simply supported rectangular elastic plate due to piezoelectric actuators , 1996 .

[6]  Romesh C. Batra,et al.  Comparison of Active Constrained Layer Damping by Using Extension and Shear Mode Piezoceramic Actuators , 2002 .

[7]  S. Vel,et al.  Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates , 2002 .

[8]  Jiashi Yang,et al.  The cylindrical bending vibration of a laminated elastic plate due to piezoelectric actuators , 1994 .

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

[10]  Romesh C. Batra,et al.  Shape control of plates using piezoceramic elements , 1995, Other Conferences.

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

[12]  Jong S. Lee,et al.  Exact electroelastic analysis of piezoelectric laminae via state space approach , 1996 .

[13]  Paul R. Heyliger,et al.  Static Behavior of Piezoelectric Laminates with Distributed and Patched Actuators , 1994 .

[14]  Romesh C. Batra,et al.  Deflection control during dynamic deformations of a rectangular plate using piezoceramic elements , 1995 .

[15]  T. C. T. Ting,et al.  Anisotropic Elasticity: Theory and Applications , 1996 .

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

[17]  A. N. Stroh.  Dislocations and Cracks in Anisotropic Elasticity , 1958 .

[18]  Fu-Kuo Chang,et al.  Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators , 1992 .

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

[20]  Dimitris A. Saravanos,et al.  Exact free‐vibration analysis of laminated plates with embedded piezoelectric layers , 1995 .

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

[22]  E. Crawley,et al.  Detailed models of piezoceramic actuation of beams , 1989 .

[23]  Romesh C. Batra,et al.  Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators , 2001 .

[24]  J. D. Eshelby,et al.  Anisotropic elasticity with applications to dislocation theory , 1953 .

[25]  S. Vel,et al.  Exact Thermoelasticity Solution for Cylindrical Bending Deformations of Functionally Graded Plates , 2003 .

[26]  T. Hughes,et al.  Finite element method for piezoelectric vibration , 1970 .

[27]  Romesh C. Batra,et al.  Cylindrical Bending of Laminated Plates with Distributed and Segmented Piezoelectric Actuators/Sensors , 2000 .

[28]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[29]  Romesh C. Batra,et al.  Finite dynamic deformations of smart structures , 1997 .

[30]  O. Dickman,et al.  Intelligent material systems and structures: The interface , 1993 .

[31]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[32]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[33]  Romesh C. Batra,et al.  Shape Control of Vibrating Simply Supported Rectangular Plates , 1996 .

[34]  Paolo Bisegna,et al.  An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates , 1996 .

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

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

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