Geometrically nonlinear theory of viscoelastic multilaminate piezoelectric plates and shells

Abstract

Multilaminate metal--ceramic plates and shells are being widely used in different areas of technology [;3]. The article [15] presented a survey of studies attempting to construct linear models of elastic single-layer piezoceramic plates and shells. We should also note the work done in this direction in [4-6, ;;, 14-16]. The level achieved to date in attempts to construct linear models of elastic multilaminate plates is reported in the article [!3]. It follows from these articles that there is no attempt in the literature to construct a geometrically nonlinear theory of layered metal--ceramic plates and shells, particularly with allowance for the effects of viscosity. Nevertheless, such a theory needs to be developed in connection with the need to solve a whole range of nonlinear static and dynamic problems arising in the case of large deflections, when the strains and displacements are non!inearly related to each other. Also, as experiments show [;2, 2;], the piezoceramic materials presently in use have viscoelastic properties which may significantly affect the electromechanical behavior of elements made of them. In particular, there may be an undesirable increase in the temperature associated with dissipative heating. The dissipative heating of plates and shells under long-term harmonic loads was discussed in [9, I0] within the framework of a geometrically linear theory.