Three-dimensional analysis of freely vibrating multilayered piezoelectric plates through adaptive global piecewise-smooth functions

In this article, freely vibrating multilayered piezoelectric plates are analyzed through a set of adaptive global piecewise-smooth functions along with governing differential equations and associated boundary conditions, which are consistently derived from the classical theorem of virtual displacements. The analysis demonstrates the capability of the adaptive global piecewise-smooth functions to treat any multilayered plate as if it were made up of a single layer even in the presence of multiphysics analyses such as piezoelectric layers. The relevant model is essentially two-dimensional because it is based on an expansion through the thickness of the plate aimed at modeling a three-dimensional dynamical behavior. In order to demonstrate the effectiveness of the model, all the results are compared to exact three-dimensional results; these latter are extracted through a three-dimensional model based on a transfer matrix technique whose numerical stability is achieved using scaled electric potentials. The exact graphical results are herein illustrated, thus showing both the effectiveness of using weighted electric potentials and the capability of adaptive global piecewise-smooth functions to converge at exact results through a minimum computational effort.