指数函数剪切模量的成层土地震反应解析解

General solution to earthquake response of stratified foundations with exponential function shear modulus

基于改进的一维剪切梁模型,对剪切模量是其深度的某一指数函数的成层非均质场地,推导了确定自振频率、振型函数、参与系数及稳态动力响应的封闭型解析表达式。证明了这种土层振型函数的正交性。最后应用本解析解对一个算例进行了计算,得到了土层的最大地震反应值(位移、加速度、剪应力)。

Based on a generalized nonhomogeneous shearbeam model,closedform analytical expressions were derived for natural frequencies,modal displacements,participation factors and steady state response function.In this model,the shear modulus of the stratified foundations is assumed to be exponential function varying with the depth,and different layer has different exponential funcion.The orthogonality property of the modal displacements is proved. Using the general solution,the maximum seismic responses(including the displacement,the acceleration,and shear stress) were obtained.