Vibration characteristics of piezoelectric fiber composites under thermo-electro-mechanical loadings

In this paper, vibration characteristics of piezoelectric fiber composite beams are presented. An asymptotic method based on virtual work principle is introduced first. The primary variables in thermo-electro-mechanical problems are asymptotically expanded in terms of the small parameter, which is done by taking the geometric slenderness of the beams. This subsequently renders a set of recursive virtual works at each order, in which the virtual works are separated into two parts: 2D microscopic problems and 1D macroscopic problems. These microscopic and macroscopic problems are systematically associated with each other, and thus the boundary conditions are affected by both of them. Cantilever beams under multiphysics environment are taken as a test-bed in order to illustrate the significance of edge effects and asymptotical correctness to the vibration characteristics of the beams. For the displacement prescribed boundary such as the clamped boundary, the stress weighted average conditions are applied to obtain the accurate prediction, which are known to be a good approximation (possibly the best candidate up to date).