薄壁杆系结构自由振动精确求解的动力刚度法  

Dynamic stiffness method for free vibration analysis of thin-walled skeletal structures

作　　者：叶康生[1,2] 李博[1,2] 

机构地区：[1]清华大学土木工程系,北京100084 [2]土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《空间结构》2015年第1期19-25,共7页Spatial Structures

基　　金：国家自然科学基金项目(51078198)

摘　　要：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.This paper extends the dynamic stiffness method to the free vibration analysis of thin-walled skeletal structures. The ordinary differential equations （ODEs） which governs element＇s dynamic stiffnesses are set up and solved by ODE solver COLSYS to get the numerical exact values of element＇s dynamic stiffnesses. The mesh generated by COLSYS in solving such ODEs is used to calculate the counting of element＇s fixed-end frequency by using Wittrick-Williams algorithm. The derivatives of the dynamic stiffnes- ses to the frequency are reduced to solve corresponding （）DEs by using COI.SYS. Thus the guided and guarded Newton method is set up and structure＇s exact frequencies and vibration modes can be obtained. The numerical results which are consistent with results of other articles and ANSYS, demonstrate that this method is accurate, reliable and effective and can be applied to free vibration analysis of other complex structures.

关 键 词：动力刚度法 Wittrick-Williams算法 导护型牛顿法 弯扭耦合 翘曲刚度 

分 类 号：TU323[建筑科学—结构工程] TU311.3