Non-linear oscillations of an elastic shell controlled by the interface pressure

Abstract

In the present work, we study analytically and numerically the non-linear radial oscillations and unitary deformations of a thin elastic shell surroundings a perfect gas under an external ultrasound pressure field. The model comprehends a Rayleigh–Plesset kind equation (RP) to predict the liquid radius, which in turn surrounds the elastic shell. In this manner, both media are coupled through the boundary conditions and the resulting governing equations are solved simultaneously. Using dimensionless variables, we use basically three main parameters: β which represents the quasi steady-state deformations of the solid, π x is the ratio between the ambient pressure and the elasticity modulus of the shell and β A that represents the competition between the driving pressure and the dynamic pressure. The numerical results predict the oscillations of the liquid and the pressure, also. For the solid, we have obtained a weak oscillatory and irregular behavior which can conduct to the final collapse of the solid. The most relevant physical variables of the problem such as the displacement of the shell, interface pressure, deformation rate and radius of the shell are obtained as functions of time and different values of the above dimensionless parameters.