Smart Plates: Reduced Models and Numerical Simulations

Abstract: In this paper asymptotic models describing the mechanical and electric equilibrium state of two types of smart structures are presented and justified. The first structure consists of an anisotropic elastic thin plate with two surface bonded anisotropic piezoelectric patches and the second one is an anisotropic elastic sandwich thin plate with an inserted anisotropic piezoelectric patch. The two unknowns of the corresponding asymptotic models, the mechanical displacements of the structures and the electric potentials of the patches, are partially decoupled. The former are the solution of modified Kirchhoff-Love plate models, while the latter can be derived as explicit functions of the mechanical displacements. Moreover, different formulas for the electric potential arise as a consequence of diverse electric boundary conditions. We report numerical simulations with these asymptotic models.