非均匀地基与均匀地基解答之间的相似关系:弹性波速

Analogous relationship between the solutions of non-homogeneous foundation and homogeneous foundation:elastic wave velocity

考虑物理力学特性沿深度连续变化的非均匀地基,研究了非均匀弹性体波相速度和群速度与相应均匀弹性地基解答之间的转换关系。首先,基于弹性动力学基本方程,获得了任意非均匀变化的地基中平面弹性体波相速度以及群速度的解析表达式;与均匀地基弹性波相速度的经典解答进行了比较,发现可将非均匀地基的解答用均匀地基解答线性表示,从而获得了两种解答之间的相似转换关系;最后,作为数值算例,考虑材料特性沿厚度按幂律连续变化的非均匀地基,分析了地基非均匀程度、泊松比以及相位角等对相似转换系数的影响。研究表明,借助于均匀地基中弹性波速的经典解答,可将非均匀地基中波速的求解转化为对相似转换系数的计算,从而使得求解过程得以简化。

Considering the physical and mechanical properties change continuously along the depth in non-homogeneous foundation,the linear transformative relationship is analyzed between the phase velocity and group velocity of the inhomogeneous elastic body waves and the solution of corresponding homogeneous elastic foundation.Firstly,based on the basic equations of elastodynamics,the analytical expressions for the phase velocity and group velocity of the planar elastic body waves in any non-uniformly changing foundation are obtained.Compared with the classical solution of the elastic wave phase velocity of the homogeneous foundation,it is found that the solution of the non-homogeneous foundation can be expressed linearly with the solution of the homogeneous foundation,thus the similarity conversion between the two solutions is obtained.At last,as a numerical example,considering the power law relationship of material properties change continuously along the thickness in the non-homogeneous foundation,the influence of foundation non-uniformity,Poisson’s ratio and phase angle on the similarity conversion coefficients is analyzed.The calculation results show that,with the help of the classical solution of elastic wave velocity in homogeneous foundation,the solution of wave velocity in non-homogeneous foundation can be converted into the calculation of the similarity conversion coefficients,thereby simplifying the solution process.