An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates

An exact three-dimensional solution for the problem of a simply supported rectangular homogeneous piezoelectric plate is obtained, in the framework of the linear theory of piezoelectricity. The plate is made of a transversely isotropic material, is earthed on the lateral boundary, and is subjected to prescribed surface charge and tractions on the end faces. The limit of this solution as the plate thickness aspect ratio approaches zero is explicitly carried out. The analytical results obtained may constitute a reference case when developing or applying two-dimensional plate theories for the analysis of more complex piezoelectric problems. A numerical investigation in the case of a square uniformly loaded plate is also performed, in order to evaluate the influence of the thickness-to-side ratio on the three-dimensional solution of the plate problem.

[1]  E. M. Lifshitz,et al.  Electrodynamics of continuous media , 1961 .

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

[3]  W. P. Mason Piezoelectricity, its history and applications , 1980 .

[4]  A. Cemal Eringen,et al.  Constitutive Equations of Nonlinear Electromagnetic-Elastic Crystals , 1990 .

[5]  Raymond D. Mindlin,et al.  High frequency vibrations of piezoelectric crystal plates , 1972 .

[6]  Philippe G. Ciarlet,et al.  JUSTIFICATION OF THE TWO-DIMENSIONAL LINEAR PLATE MODEL. , 1979 .

[7]  Gérard A. Maugin,et al.  Electrodynamics Of Continua , 1990 .

[8]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

[9]  H. Tzou,et al.  Piezoelectric Shell Vibration Theory , 1993 .

[10]  T. Ikeda Fundamentals of piezoelectricity , 1990 .

[11]  Gérard A. Maugin,et al.  AN ASYMPTOTIC THEORY OF THIN PIEZOELECTRIC PLATES , 1990 .

[12]  Ahmed K. Noor,et al.  Three-dimensional solutions for antisymmetrically laminated anisotropic plates , 1990 .

[13]  E. Pan An exact solution for transversely isotropic, simply supported and layered rectangular plates , 1991 .

[14]  A three-dimensional solution for simply supported thick rectangular plates , 1967 .

[15]  M. Levinson The simply supported rectangular plate: An exact, three dimensional, linear elasticity solution , 1985 .

[16]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[17]  Gérard A. Maugin,et al.  Continuum Mechanics of Electromagnetic Solids , 1989 .

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