【摘要】 得到了地下结构在水平地震作用下的动力运动方程,利用拉普拉斯变换和结构的对接条件,得到了求解待定系数的超越方程。利用拉普拉斯逆变换得到了结构的位移表达式和确定拉普拉斯参数极点的方程。进一步研究发现,拉普拉斯变换参数s与结构频率ω之间存在某种特殊的关系:s2=?ω2。为了避免确定待定系数及拉普拉斯参数极点时求解复杂超越方程的困难,建议通过数值的办法先把结构体系的频率求出来,再通过拉普拉斯逆变换留数定理求解结构的位移和内力。更多还原

【Abstract】 The dynamic motion equations of underground structure under horizontal seismic action are obtained. The transcendental equation for the determination of solution coefficients is deduced by using Laplace integral transform method and linking conditions of structure members. Using inverse Laplace integral transform method the equations for the determination of the displacements of the structure and the poles of the transformation parameters of the Laplace transform are obtained. The further study shows that a special relationship exists between the transformation parameters of Laplace transform s and natural frequency of structure ω : s 2 = ?ω 2. To avoid the difficulty in determining the coefficients of the solution and the poles of the transformation parameters of the Laplace transform in solving the transcendental equation, the authors suggest that the frequency of structural system is figured out firstly by numerical methods; then the structural displacement and internal forces are obtained by using the residue theorem of inverse Laplace transform.更多还原