Electromechanical Vibration Response of Pre-stressed Bi-layered Piezoelectric Plate Under a Harmonic Mechanical Force

This study presents the outcomes of a finite element analysis (FEA) of forced vibrations by a time-harmonic loading of a bi-layered piezoelectric plate with two-axially pre-stressed layers.

The investigation is conducted based on the following assumptions: (i) the resultant system is resting on a rigid foundation, (ii) each layer is poled along the direction perpendicular to the free surface, (iii) a complete contact state exists at the interface of the plane in the plate, and (iv) the initial stress state at the layers is modeled based on the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS). First, we describe nonlinear governing equations of motion and boundary-contact conditions for the dynamical model of the current system and then apply a linearization and non-dimensionalization procedure to the problem under consideration. In terms of Hamilton principle, a finite element model (FEM) is developed based on the weak form.

The proposed and validated FEM approach can help to address several issues in the piezoelectric structure of finite lengths, either pre-stressed or not. In particular, we present an investigation of the effects of changing problem factors on the dynamic behavior as well as the frequency response of the composite plate. The numerical results demonstrate that the stress transition across the interface of the layers plays a key role in the resonance mode of the system, in both a quantitative sense and a qualitative sense.