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CLC number: TU502

On-line Access: 2017-01-03

Received: 2016-02-03

Revision Accepted: 2016-05-24

Crosschecked: 2016-12-19

Cited: 0

Clicked: 1421

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yiu-yin Lee

http://orcid.org/0000-0003-1657-4503

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Journal of Zhejiang University SCIENCE A 2017 Vol.18 No.1 P.75-82

http://doi.org/10.1631/jzus.A1600145


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


Author(s):  Yiu-yin Lee

Affiliation(s):  Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong, China

Corresponding email(s):   bcraylee@cityu.edu.hk

Key Words:  Large amplitude vibration, Elliptic integral method, Noise and vibration


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Yiu-yin Lee. Large amplitude free vibration of a flexible panel coupled with a leaking cavity[J]. Journal of Zhejiang University Science A, 2017, 18(1): 75-82.

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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.

The paper focuses on the vibration of a panel subjected to acoustic pressure: this matter is believed interesting by the writer and important in the field of the Engineering Mechanics. The Mathematics are sound.

与裂缝腔联结的弹性板的大幅自主震动

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。

关键词:大幅自主震动;椭圆积分方法;声音与震动

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Hui, C.K., Lee, Y.Y., Reddy, J.N., 2011. Approximate elliptical integral solution for the large amplitude free vibration of a rectangular single mode plate backed by a multi-acoustic mode cavity. Thin-walled Structures, 49(9):1191-1194.

[2]Lee, Y.Y., 2002. Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate. Applied Acoustics, 63(11):1157-1175.

[3]Lee, Y.Y., 2016a. The effect of leakage on the sound absorption of a nonlinear perforated panel backed by a cavity. International Journal of Mechanical Sciences, 107:242-252.

[4]Lee, Y.Y., 2016b. Free vibration analysis of a nonlinear panel coupled with extended cavity using the multi-level residue harmonic balance method. Thin-walled Structures, 98:332-336.

[5]Lee, Y.Y., Lee, E.W.M., 2007. Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances. International Journal of Mechanical Sciences, 49(8):925-934.

[6]Li, Y.Y., Cheng, L., 2007. Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall. Applied Acoustics, 68(7):739-751.

[7]Pretlove, A.J., 1966. Forced vibration of a rectangular panel backed by a closed rectangular cavity. Journal of Sound and Vibration, 3(3):252-261.

[8]Xie, X., Zhang, H., Zhang, Z.C., 2008. Nonlinear dynamic response of stay cables under axial harmonic excitation. Journal of Zhejiang University-SCIENCE A, 9(9):1193-1200.

[9]Zhang, H., Zhou, C.L., Wang, S.J., et al., 2007. Dynamics analysis of vibration process in particle impact noise detection. Journal of Zhejiang University-SCIENCE A, 8(3):444-448.

[10]Zhu, W.G., Bai, X.Z., 2009. Bifurcation and chaos of a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields. Journal of Zhejiang University-SCIENCE A, 10(1):62-71.

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