Dynamic Morphing of Actuated Elastic Membranes

Abstract

Parametric resonances of elastic membranes actuated by harmonic in-plane strains prescribed along given directions are exploited to drive dynamic morphing of lightweight, flexible panels employed in engineering applications which require active, shape-changing surfaces. An approximate nonlinear model of a pretensioned membrane together with its Galerkin discretization are adopted to describe the membrane out-of-plane motion. The method of multiple scales is used to explore the bifurcation scenarios and the instability regions (i.e., morphing regions) associated with the principal parametric resonances. Moreover, parameter continuation of the periodic solutions of the ordinary differential equations describing the membrane motion is performed via a path following procedure implemented in Matlab. The study shows that single- and multi-mode parametric responses can be achieved by suitable tuning of the excitation amplitude and frequency.