MODELLING OF NON-LINEAR OSCILLATIONS OF ELASTIC STRUCTURES IN HEAVY FLUID LOADING CONDITIONS

Abstract

In a problem of structural acoustics with non-liner formulation of structural dynamics, a linearized compatibility condition at the fluid–structure interface is used along with the linear wave equation for the acoustic medium [1–7]. This approach is referred to as a light acoustic loading limit. Another approach is to formulate a compatibility condition at the moving boundary and solve a non-linear wave equation in a volume. As it is shown in references [3–5], a solution for this problem predicts shock wave formation at a certain distance from a vibrating surface. In the present paper, one more model of interaction between an acoustic medium and a non-linear structure is suggested for heavy fluid loading conditions. In this model, propagation of acoustic waves is described by a linear wave equation, but the continuity condition is formulated at the moving boundary and the contact acoustic pressure acting at the vibrating non-linear structure is calculated by the Bernoulli integral with a quadratic velocity term retained. Two model problems of coupled structural acoustics are considered—oscillations of a fluid-loaded piston and oscillations of an infinitely long periodically supported elastic plate. A method of multiple scales is used for analysis of the local non-linear dynamics of the model systems, whilst matched asymptotic expansions are used to model the fluid's motion. Several specific effects of structural vibrations generated by the non-linearity of fluid-structure interaction, rather than by structural non-linearity are demonstrated.