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

✍ Scribed by S.V. Sorokin; S.G. Kadyrov

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 246 KB
• Volume: 222
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.2084

✦ Synopsis

In a problem of structural acoustics with non-linear formulation of structural dynamics, a linearized compatibility condition at the ¯uid±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 aproach is to formulate a compatibility condition at the moving boundary and solve a nonlinear 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 ¯uid 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 nonlinear structure is calculated by the Bernoulli integral with a quadratic velocity term retained. Two model problems of coupled structural acoustics are consideredÐoscillations of a ¯uid-loaded piston and oscillations of an in®nitely 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 ¯uid's motion. Several speci®c eects of structural vibrations generated by the non-linearity of ¯uid± structure interaction, rather than by structural non-linearity are demonstrated.