平面弹性波入射下空沟隔振的解析分析

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

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。

Here,based on complex variable function theory and conformal mapping method,wave function expansion method and multi-level coordinate transformation technique were used to solve vibration isolation problem of open trench in semi-infinite space against plane SH wave and plane P wave.Firstly,scattering fields of plane SH wave and plane P wave incident into semi-infinite space were given with the virtual source method and the large arc assumption method,respectively.Then,infinite order linear equations were established under stress free boundary conditions at open trench boundary and large arc boundary,and analytical solutions of scatterings of open trench to plane SH wave and plane P wave were obtained by solving these linear equations.Finally,effects of excitation frequency,trench depth and other factors on vibration isolation effect were parametrically analyzed.The results showed that vibration isolation effects of open trench on plane SH wave and plane P wave increase with increase in incident wave frequency and open trench depth.