Bending vibration characteristics analysis of a rectangular plate with complex-opening using Chebyshev-variational method

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (2) : 178-187.

LU Bin,CHEN Yuehua,FENG Zhimin,ZHANG Gang,YAN Wei,XU Qiang

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Abstract

A modeling method for the vibration analysis of a rectangular plate with different openings under elastically restrained conditions was proposed based on the Chebyshev-variational theory.Its elastic boundary condition was simulated by introducing boundary constraint factors.The opening portion was regarded as a membrane with zero physical properties.The transverse vibration displacement was expressed in a double Chebyshev series form, based on which the characteristic equation of the plate with opening was obtained by using the variational method.The modal tests of the plate with different openings were carried out.By comparing the experimental results with the corresponding theoretical results and finite element results, the accuracy of the present method was validated.The effects of boundary constraint and opening shape on bending vibration characteristics were analyzed.It is shown that the shape of the opening has little effect on the low-order natural frequencies of the structure, but has a great influence on the high-order natural frequencies.Furthermore, the shape of the opening shows greater influence on odd-order natural frequencies than that on even-order natural frequencies.

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rectangular thin plate with opening / bending vibration / Chebyshev series;variational method

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LU Bin,CHEN Yuehua,FENG Zhimin,ZHANG Gang,YAN Wei,XU Qiang. Bending vibration characteristics analysis of a rectangular plate with complex-opening using Chebyshev-variational method[J]. Journal of Vibration and Shock, 2020, 39(2): 178-187

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