Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers

P. H. Tuan, C. P. Wen, P. Y. Chiang, Y. T. Yu, H. C. Liang, Kai-Feng Huang, Yung-Fu Chen*

*此作品的通信作者

研究成果: Article同行評審

37 引文 斯高帕斯(Scopus)

摘要

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

原文English
頁(從 - 到)2113-2123
頁數11
期刊Journal of the Acoustical Society of America
137
發行號4
DOIs
出版狀態Published - 1 4月 2015

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