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将动力刚度法应用于薄壁杆系结构自由振动的分析.采用常微分方程求解器COLSYS求解薄壁杆件单元动力刚度所满足的常微分方程边值问题获得单元动力刚度的数值精确解,基于COLSYS求解单元动力刚度的网格采用Wittrick-Williams算法获得单元固端频率的计数,调用COLSYS求解单元动力刚度对频率的导数所满足的常微分方程边值问题获得其数值精确解.由此建立起薄壁杆系结构自由振动精确求解的导护型牛顿法,求得精确的频率和振型.本文数值算法的计算结果与文献以及ANSYS软件的计算结果吻合很好,表明本文方法准确、可靠、有效,可进一步推广应用于其他复杂结构自由振动的分析.
The dynamic stiffness method is applied to the analysis of free vibration of thin-walled bar structures.The numerical solution of the element dynamic stiffness is obtained by using the ordinary differential equation solver COLSYS to solve the boundary value problems of ordinary differential equations for the dynamic stiffness of thin-walled bar elements, COLSYS solver unit kinetic stiffness of the grid using Wittrick-Williams algorithm to obtain unit solid end frequency count, call COLSYS unit dynamic stiffness of the derivative of the frequency of the differential equation boundary value problems to obtain its numerical exact solution.Thus set up The exact frequency and mode shape of the thin walled rod structure with free vibration are solved accurately.The calculation results of the numerical algorithm in this paper are in good agreement with those of the ANSYS software and the results show that the proposed method is accurate and reliable, Effective, and can be further popularized and applied to the analysis of free vibration of other complicated structures.