Dynamic Morphing of Elastic Plates via Principal Parametric Resonance

Abstract

Principal parametric resonances of elastic plates actuated by periodic in-plane stresses effected by embedded piezoelectric wires are investigated to describe the morphing scenarios of flexible, ultra-lightweight panels. A mechanical model of elastic plate including geometric nonlinearities and the parametric actuation provided by the piezoelectric wires, is adopted to formulate the nonlinear equation of motion. A bifurcation analysis is carried out by means of an asymptotic approach based on the method of multiple scales leading to a comprehensive parametric study on the effect of the wires width on the morphing regions (i.e., parametric instability regions) associated with the principal parametric resonances. The threshold voltages triggering the onset of the principal parametric resonances of the lowest three symmetric modes are also calculated as a function of the wires size so as to determine the voltage requirements for the morphing activation.