Large amplitude free vibration of a flexible panel coupled with a leaking cavity

Abstract

This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic governing equations are employed to study this nonlinear problem. An elliptical integral method, which was recently developed for the nonlinear panel cavity problem, is introduced here to solve for the structural-acoustics responses. The present results agree reasonably well with those obtained from the classical harmonic balance method. Modal convergences of the nonlinear solutions are performed to verify the proposed method. The effects of vibration amplitude and leakage size are studied and discussed. It is found that (1) the edge leakages in a panel cavity system significantly affect the natural frequency properties, and (2) the edge leakages induce a low frequency acoustic resonance.

抽象

目 的

板腔系统中的裂缝会导致共振特性发生变化。本文旨在探讨裂缝的影响, 推导其中的关系与相关公式, 并控制计算精确的程度。

创新点

1. 通过椭圆积分方法破解控制方程, 推导裂缝腔联结的弹性板的共振频率; 2. 建立理论模型, 成功计算不同情况下弹性板的共振频率。

方 法

1. 通过理论推导, 计算裂缝腔大小、震动幅度与共振频率之间的关系(公式(10)~(12)); 2. 与其它方法得到的数据进行比较, 验证所提方法的可行性和有效性(图3 和4); 3. 通过仿真模拟, 推导裂缝腔对弹性板共振频率的影响(图5a~5c)。

结 论

1. 板腔系统中的裂缝会导致共振频率出现重大变化; 2. 裂缝会导致一个额外的低频率共振点。