Parametric excitation of wrinkles in elastic sheets on elastic and viscoelastic substrates

TL;DR

This paper investigates how periodic lateral pressure variations induce parametric resonance in wrinkling patterns of elastic sheets on elastic and viscoelastic substrates, revealing unique dynamic behaviors and thresholds relevant for experimental systems.

Contribution

It introduces a detailed analysis of parametric excitation effects on wrinkling, highlighting differences from static patterns and the role of substrate viscoelasticity.

Findings

Dynamic wrinkle wavelength depends differently on sheet thickness compared to static cases.

A discontinuous decrease in wrinkle wavelength occurs at high excitation frequencies.

Resonant wrinkling in viscoelastic substrates requires surpassing a threshold excitation amplitude.

Abstract

Thin elastic sheets supported on compliant media form wrinkles under lateral compression. Since the lateral pressure is coupled to the sheet's deformation, varying it periodically in time creates a parametric excitation. We study the resulting parametric resonance of wrinkling modes in sheets supported on semi-infinite elastic or viscoelastic media, at pressures smaller than the critical pressure of static wrinkling. We find distinctive behaviors as a function of excitation amplitude and frequency, including (a) a different dependence of the dynamic wrinkle wavelength on sheet thickness compared to the static wavelength; and (b) a discontinuous decrease of the wrinkle wavelength upon increasing excitation frequency at sufficiently large pressures. In the case of a viscoelastic substrate, resonant wrinkling requires crossing a threshold of excitation amplitude. The frequencies for observing these phenomena in relevant experimental systems are of the order of a kilohertz and above. We discuss experimental implications of the results.