频率波数域内层状地基动力柔度的精细求解

精细积分法既可得到在计算机精度意义下的精确解,又能够保持哈密顿体系的辛结构。其是求解一阶线性常微分方程组的精确数值方法,既可以用于时间域的初值问题,又可以应用于空间域的两点边值问题。运用精细积分法求解微层区段矩阵,并对微层区段矩阵合并得到整个层状地基的区段矩阵,最终得到层状地基的动力柔度值。运用数值算例验证了本文方法的计算精度。

A Precise Method for Calculating the Dynamic Flexibility of Layered Foundation in the Frequency-wavenumber Domain

The integration method used here is a precise numerical method for solving sets of first order linear ordinary differential equations with specified two-point boundary value conditions for space domain problems,or with specified initial value conditions for time domain problems.It can produce numerical results up to the precision of the computer used and preserve the symplectic structure of the Hamilton system.The segment matrix of micro layer is obtained by using the precise integration method,and then,through merging segment matrix of micro layer,we evaluate the segment matrix of the whole foundation.Finally,the dynamic flexibility of layered elastic foundation is calculated by incorporating the radiation condition of boundary into the segment matrix of the whole foundation.In the end,accuracy of this method is verified by numerical examples.