Nonlinear mechanics of beams with partial piezoelectric layers

This paper investigates the nonlinear static response as well as nonlinear forced dynamics of a clamped-clamped beam actuated by piezoelectric patches partially covering the beam from both sides. This study is the first to develop a high-dimensional nonlinear model for such piezoelectric-beam configuration. The nonlinear dynamical resonance characteristics of the electromechanical system is examined under simultaneous DC and AC piezoelectric actuations, while highlighting the effects of modal energy transfer and internal resonances. A multi-physics coupled model of the beam-piezoelectric system is proposed based on the nonlinear beam theory of Bernoulli-Euler and the piezoelectric constitutive equations. The discretised model of the system is obtained with the help of the Galerkin weighted residual technique while retaining 32 degrees of freedom. Three-dimensional finite element analysis is conducted as well in the static regime to validate the developed model and numerical simulation. It is shown that the response of the system in the nonlinear resonant region is strongly affected by a three-to-one internal resonance.