Free vibration and active control of pre-stretched multilayered electroactive plates

Abstract

Investigations on soft electro-active materials (SEAMs) have attracted increasing attention in the fields of mechanics and related engineering disciplines. Multi-field coupling and finite deformation are both regarded as effective means to actively control the material properties and geometry of SEAM structures. In this paper, the free vibration analysis of a pre-stretched SEAM plate is investigated based on the linearized biasing theory of electro-elasticity. A three-dimensional solution is obtained by using the new-type state-space formulations. Two decoupled state equations are derived, which correspond to the in-plane vibration and the flexural vibration, respectively. In the numerical part, the single-layered plate is assumed to be loaded in two ways, i.e. by the fixed in-plane stretches or the fixed in-plane forces. As an attempt on structural optimization, a few pre-stretched layers are bonded together to get a layered configuration of SEAM plate. The influences of pre-voltage and pre-stretch on the natural frequencies are studied for single-layered, two-layered and graded plates. The active control of SEAM plates is demonstrated and some interesting phenomena, such as frequency jumping, pre-stretch stiffening, and pre-voltage softening effects, are observed. Optimal frequency is also obtained by the layered configuration of SEAM plate. Two different kinds of layered plates with laminations achieved through mechanical and electrical means, respectively, are introduced. The effective material properties in both plates can vary along the thickness direction in a controllable way. The present paper reports more possibilities to control the free vibration characteristics of SEAM plates.