Oz Oshri

Thin elastic structures that interact with compressible gases arise in a wide range of natural and engineered systems, such as biological membranes in respiratory flows and bistable pneumatic microfluidic valves. Motivated by these applications, we study a prototypical system that consists of a closed chamber filled with a compressible gas, whose upper boundary is a thin elastic sheet. The sheet is initially deflected inward toward the interior of the chamber. As the internal pressure increases, the sheet remains in mechanical equilibrium with the gas until it reaches a threshold at which it snaps to an inverted configuration. We derive an analytical model that incorporates the elasticity of thin sheets and the hydrodynamics of compressible inviscid fluids, and use it to elucidate the coupled dynamics arising from bending and compressibility. Using this model, we identify multiple equilibrium branches and determine their stability through a linear analysis. We show that the primary branch loses stability at a critical pressure that depends on the elastic and geometric properties of the sheet. The dynamics near equilibrium exhibit two distinct regimes: an elastic-dominated regime, in which the motion is governed by the deformation of the sheet, and an acoustic-dominated regime, in which the dynamics are controlled by compressible modes of the gas. These results provide a framework for understanding how compressibility influences confined fluid-structure interactions.