Post-buckling Dynamics of Spherical Shells

TL;DR

This paper investigates the post-buckling behavior of spherical shells in fluid environments using experiments, simulations, and a theoretical model, revealing softening effects and dissipation mechanisms relevant to microbubble acoustics.

Contribution

It introduces a simplified two-variable oscillator model for buckled shells and quantifies their softening and dissipation characteristics near buckling.

Findings

Shells exhibit effective softening above buckling threshold.

Dissipation in surrounding fluid is a key energy loss mechanism.

Theoretical model accurately predicts shell dynamics.

Abstract

We explore the intrinsic dynamics of spherical shells immersed in a fluid in the vicinity of their buckled state, through experiments and 3D axisymmetric simulations. The results are supported by a theoretical model that accurately describes the buckled shell as a two-variable-only oscillator. We quantify the effective "softening" of shells above the buckling threshold, as observed in recent experiments on interactions between encapsulated microbubbles and acoustic waves. The main dissipation mechanism in the neighboring fluid is also evidenced.