Nonlinear Mechanics of Beams With Partial Piezoelectric Layers

Abstract

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 a piezoelectric-beam configuration. The nonlinear dynamical resonance characteristics of the electromechanical system are examined under simultaneous DC and AC piezoelectric actuations, while highlighting the effects of modal energy transfer and internal resonances. A multiphysics coupled model of the beam-piezoelectric system is proposed based on the nonlinear beam theory of Bernoulli–Euler and the piezoelectric constitutive equations. The discretized 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.

Thermal coupling model of a traveling flexible printing electronical membrane subjected to nonlinear electrostatical force

“…Shao et al 4 applied the quartic Runge-Kutta technique to calculate the nonlinear vibration characteristics of the axially moving membrane caused by the velocity amplitude and aspect ratio. To analyze the influence of modal energy transfer and internal resonance, Farokhi et al 5 introduced a high-dimensional nonlinear model of a piezoelectric beam structure. According to the Mindlin structure theory, According to Timoshenko beam theory, Liang et al 6 investigated the dynamic response of the simply supported beam.…”