平面弹性波入射下空沟隔振的解析分析

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (9) : 293-303.

论文

平面弹性波入射下空沟隔振的解析分析

周凤玺1,2，梁玉旺1，刘云帅1,2

作者信息 +

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

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

Author information +

文章历史 +

摘要

基于复变函数理论和保角映射方法，采用波函数展开法及多级坐标变换技术，解析求解了半无限空间中空沟对平面SH波和平面P波的隔振问题。首先，通过设虚源法和大圆弧假定法分别给出了平面SH波和平面P波入射半无限空间时的散射场。然后由空沟边界及大圆弧边界处的应力自由边界条件建立无穷阶线性方程组，并通过对该方程组的求解给出了空沟对平面SH波和平面P波散射的解析解答。最后，参数分析了激励频率、空沟深度等因素对隔振效果的影响规律。结果表明：空沟对平面SH波和平面P波的隔振效果随着入射波频率的增大而增大，随着空沟深度增大而增大。

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.

导出引用

周凤玺1,2，梁玉旺1，刘云帅1,2. 平面弹性波入射下空沟隔振的解析分析[J]. 振动与冲击, 2023, 42(9): 293-303

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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