任意荷载下黏弹性饱和土体中球壳的动力响应研究

工程实践中经常需要解决无限大弹性体内球壳的动力响应问题.采用Biot波动理论，对黏弹性饱和
土体中球壳的动力响应问题进行研究分析.利用Helmholtz分解原理，通过引入势函数，在Laplace变换域
中得到任意响应模式下球壳的动力响应解答.最后利用Laplace数值逆变换得到时间域中的数值结果，讨
论了在球壳内作用有轴对称荷载和流体压力两种情况时不同响应模式条件下球壳动力响应.球壳内作用有
轴对称荷载时接触面上的径向位移随n值的增大而减小，孔隙水压力开始有较大振荡；球壳内作用有流体
压力时在瞬时响应模式下位移趋近于零，而孔隙水压力变化相对平缓.结果表明,对于黏弹性饱和土体中
的球壳在不同的边界条件和响应模式下动力响应差别很大.

Dynamic response of spherical shell in viscoelastic saturated soil under arbitrary loads

Dynamical response of spherical shell contained in infinite elastic body is a common problem in engineering practice.Based on Biot's wave equation,the dynamic response of spherical shell in viscoelastic saturated soil was investigated.By introducing scalar potential functions and applying Helmholtz decomposition theorem,the analytical solutions of dynamic response of shell were derived in Laplace transform domain.Numerical results obtained by inverse Laplace transformation were used to discuss the difference of the dynamic responses of shell under different response modes by respectively applying axial symmetry load and fluid load.In the case of axial symmetry load the radial displacement decreases when n increases,and the porewater pressure oscillates dramatically in the beginning.In the case of fluid load the radial displacement in transient response mode tends to zero,and the porewater pressure varies relatively smoothly.Results showed that dynamical responses of spherical shell in viscoelastic saturated soil vary dramatically in different boundary conditions and response modes.