积分型黏弹性土中球形空腔的稳态振动分析

Analysis of Steady State Vibration of a Spherical Cavity in Integral Viscoelastic Soil

在球对称情况下,利用积分型黏弹性本构关系建立了土体的振动微分方程。采用积分型分数阶Kelvin黏弹性本构关系描述土体的应力应变关系,借助Fourier变换和势函数求解了积分型分数阶黏弹性土中球形空腔的稳态振动,考虑边界条件得到了球形空腔的径向位移和应力。研究结果表明:分数导数的阶数、无量纲化的土体阻尼比和土体的模量比,对积分型分数阶黏弹性本构关系描述的土中球形空腔的稳态振动有较大的影响,分数导数的阶数和土体的模量比对球形空腔稳态振动的影响与频率有关。

In the case of spherical symmetry,the dynamic different equations of soil were established and the stress-strain relationship of the soil was described by integral fractional Kelvin viscoelastic constitutive relationship.The steady state vibration of a spherical cavity in soil was solved by Fourier transform and potential function,and the radial displacement and stress of the spherical cavity were obtained by considering boundary conditions.The results indicate that the order of fractional derivative,damping ratio of soil and modulus ratio have great effect on the steady state vibration of a spherical cavity in soil described by integral fractional viscoelastic constitutive relationship.The influences of order of fractional derivative and modulus ratio on the vibration are related with frequency.