An approximate solution to transverse vibration of a rectangular plate with 4 free edges and its experimental verification

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (5) : 92-97.

FU Jiang-song 1 XU Jian 1

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Abstract

Aiming at no exact solution to transverse vibration of a rectangular plate with 4 free edges, an approximate solution to transverse vibration mode functions of this plate was proposed here. Following the fact that transverse vibration of a rectangular plate induces various standing waves, trying to combine them and approach the exact solution to mode functions of the rectangular plate, then an approximate solution to transverse vibration mode functions of this plate was formed. In order to verify the validity of the approximate solution, an experimental platform for the transverse vibration of a rectangular plate with 4 free edges was designed and made. The experimental results showed that a series of two-dimensional standing wave patterns (Chladni patterns) of the plate are obtained within the simple harmonic excitation frequency range of 0 to 2000Hz. Comparing the experiment results (Chladni patterns) to the standing wave patterns in the approximate solution, it was shown that they agree well each other qualitatively and quantitatively, so the correctness of the approximate solution is verified.

Key words

rectangular plate with 4 free edges / Chladni pattern / standing wave / vibration mode function / approximate solution

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FU Jiang-song 1 XU Jian 1. An approximate solution to transverse vibration of a rectangular plate with 4 free edges and its experimental verification[J]. Journal of Vibration and Shock, 2018, 37(5): 92-97

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