A refined hybrid plate theory for composite laminates with piezoelectric laminae

In this paper, a refined theory of laminated composite plates with piezoelectric laminae is developed. The equations of motion of the theory are developed using an energy principle. This formulation is based on linear piezoelectricity, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The theory developed herein is hybrid in the sense that an equivalent single-layer theory is used for the mechanical displacement field, whereas the potential function for piezoelectric laminae is modeled using a layerwise discretization in the thickness direction. For the equivalent single layer, the third-order shear deformation theory of Reddy is used. This hybrid feature is good in that it demonstrates a way in which multilayered smart skin piezoelectric structures may be analysed to accommodate multiple voltage inputs and/or sensor outputs.

[1]  Nesbitt W. Hagood,et al.  Improving transverse actuation of piezoceramics using interdigitated surface electrodes , 1993, Smart Structures.

[2]  Martin L. Dunn,et al.  Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites , 1993 .

[3]  H. S. Tzou,et al.  Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems , 1993 .

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

[5]  Satya N. Atluri,et al.  Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading , 1989 .

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

[7]  H. F. Tiersten,et al.  Electrostatic interactions and the piezoelectric equations , 1980 .

[8]  John Anthony Mitchell,et al.  On refined nonlinear theories of laminated composite structures with piezoelectric laminae , 1995 .

[9]  I. M. Ward,et al.  The measurement of the shear piezoelectric coefficients of polyvinylidene fluoride , 1986 .

[10]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[11]  Ali H. Nayfeh,et al.  A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors , 1993 .

[12]  Inderjit Chopra,et al.  Structural modeling of composite beams with induced-strain actuators , 1993 .

[13]  Horn-Sen Tzou,et al.  Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings , 1993 .

[14]  Vijay K. Varadan,et al.  Measurement of all the elastic and dielectric constants of poled PVDF films , 1989, Proceedings., IEEE Ultrasonics Symposium,.

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

[16]  J. Reddy.  An introduction to the finite element method , 1989 .

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

[18]  Hermann A. Haus,et al.  Electrodynamics of Moving Media , 1968 .

[19]  Horn-Sen Tzou,et al.  Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls , 1989 .