饱和土一维简谐响应解析解的求解和应用:I求解

对于饱和土一维简谐响应的u-w和u-p方程，通过消元分别将二阶微分方程组变为一个四阶的微分方程。求解此微分方程则得到一维简谐响应的通解。对于特定的边值问题，通过求解描述边界条件的线性方程组得到满足边界条件的解析解。此解析解可用于饱和土动力响应研究的诸多方面。

Analytical solution of 1-D harmonic response in saturated soil

For the u-w and u-p formulations of 1-D harmonic response in saturated soil, a fourth order equation can be derived through these second order equations by elimination. General solution can be derived by solving this fourth order equation. For a special boundary value problem, analytical solution, which satisfies the boundary conditions, can be reached by solving the linear equations that include these boundary conditions. This analytical solution can be used in several research aspects of dynamic response in saturated soil.