Analytical analysis of vibration isolation of open trench under plane elastic wave incidence

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (9) : 293-303.

ZHOU Fengxi1,2, LIANG Yuwang1, LIU Yunshuai1,2

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Abstract

Based on the complex function theory and conformal mapping method, an analytical solution to the vibration isolation problem of a semi-infinite space trench for plane SH waves and plane P waves has been developed using the wave function expansion method and multi-level coordinate transformation techniques. Firstly, the scattering fields of incident plane SH and P waves in semi-infinite space are given using the imaginary source method and the big arc assumption method, respectively; Then, a system of linear equations of infinite order is established using the stress-free boundary conditions at the boundary of the open trench and the big arc, for which the analytical solution of the scattering of plane SH and plane P waves for the open trench is given by solving the system of equations. Finally, the effect of excitation frequency, trench depth to vibration isolation effect is parametrically analyzed. The results show that the vibration isolation effect of the trench on plane SH and plane P waves increases with the increase of the incident wave frequency and with the rise in the depth of the trench.

Key words

Complex variables / Wave function expansions / Conformal mapping / Open trench / Analytic solutions

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ZHOU Fengxi1,2, LIANG Yuwang1, LIU Yunshuai1,2. Analytical analysis of vibration isolation of open trench under plane elastic wave incidence[J]. Journal of Vibration and Shock, 2023, 42(9): 293-303

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