Eur. Phys. J. E (2021) 44: 78
https://doi.org/10.1140/epje/s10189-021-00085-y

Regular Article – Soft Matter

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

School of Chemistry, Center for Physics and Chemistry of Living Systems, Tel Aviv University, 6997801, Tel Aviv, Israel

^a hdiamant@tau.ac.il

Received: 9 February 2021
Accepted: 1 June 2021
Published online: 14 June 2021

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 in the dominant 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.