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应用Hamilton变分原理推导出变截面Timoshenko悬臂梁在谐波位移激励下强迫振动的控制微分方程及相应的边界条件,并用常微分方程求解器(Ordinary Differential Equation Solver)进行求解,同时求得等截面及变截面Timoshenko悬臂梁自由振动的前三阶振动频率和相应的振型,计算结果通过解析解以及SAP2000有限元程序进行校核。数值算例表明:该方法具有收敛速度快、精度高等特点,从而为工程中塔式结构的动力特性分析提供理论参考。
The governing differential equations and corresponding boundary conditions of forced vibration of a Timoshenko cantilever beam with varying cross-section under harmonic displacement excitation are deduced by using the principle of Hamilton variational principle. Ordinary differential equation solver (ESDE) And the first three order vibrational frequencies and the corresponding modes of free vibration of the variable section Timoshenko cantilever were calculated. The calculation results were verified by the analytical solution and the finite element program SAP2000. The numerical example shows that the proposed method has the characteristics of fast convergence and high accuracy, and thus provides a theoretical reference for the analysis of dynamic characteristics of tower structures in engineering.