Free Vibration Analysis of Nonlinear Structural-Acoustic System with Non-Rigid Boundaries Using the Elliptic Integral Approach

Abstract

This study addresses the free vibration analysis of nonlinear structural-acoustic system with non-rigid boundaries. In practice, the boundaries of a panel–cavity system are usually imperfectly rigid. Therefore, this study examines the effect of cavity boundary on the resonant frequencies of the nonlinear system. It is the first work of employing the elliptic integral approach for solving this problem, which is involved with the nonlinear multi-mode governing equations of a large amplitude panel coupled with a cavity. The main advantage of this approach is that less nonlinear algebraic equations are generated in the solution steps. The present elliptic integral solution agrees reasonably well with the results obtained from a finite element harmonic balance method. The effects of other parameters such as vibration amplitude, cavity depth, aspect ratio, etc., are also investigated.

Keywords

• nonlinear panel vibration
• structural dynamics
• wave equation
• elliptical integral
• structural-acoustic interaction