多层粘弹性半空间轴对称问题的理论解

摘要

By means of transfer matrix and integral transformation, the solution for solving axisym-metrical problems in multilayered viscoelastic half space is derived, F. Durbin's numerical inversiontransform of Laplace is used. An example shows that deflection in the beginning intervals is ingood agreement with that in elastic solution, with time passing, the surface deflection in multilay-ered viscoelastic body increases, which explains that the viscidity of material plays greater part. Thesolution in this paper can easily be used to solve dynamic question of multilayered viscoelastic halfspace.%利用积分变换和传递矩阵的方法推导了多层粘弹半空间轴对称问题的理论解，引入F．Durbin的方法实现Laplace逆变换，通过实例计算路表弯沉表明初始时段所得结果与弹性解基本一致，随着时间的推移，多层粘弹体系表面弯沉增大，这种现象说明随时间的推移，材料的粘性起到更大的作用，与实际情况相附。本文的方法可以很容易推广到多层粘弹体系的动力学问题之中。