Lagrange's equation in analytical mechanics is the basis of the mechanical vibration theory and the equation with dissipation function is important to this basis.
分析力学的拉格朗日方程是机械振动理论的基础，含耗散函数的拉格朗日方程又是这个基础的重要方面。
In the present paper, applying the theory of Mathieu s function the analytical solutions for horizontal free and forced vibrations of rigid elliptic liquid-storage-tank are obtained.
本文应用马休函数理论获得了刚性椭圆形储液罐水平自由振动和强迫振动的解析解，并获得了一些有关计算结果。
In terms of stress wave theory and complex function, analytical solution for the interaction between blasting seismic wave and arbitrary shape underground Chambers is deduced.
根据应力波理论和复变函数方法，建立了求解爆破地震波作用下任意形状洞室动态响应的解析方法。
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