中厚圆柱壳自由振动的动力刚度法分析  

ANALYSIS OF FREE VIBRATION OF MODERATELY THICK CIRCULAR CYLINDRICAL SHELLS USING THE DYNAMIC STIFFNESS METHOD

作　　者：陈旭东[1] 叶康生[2] 

机构地区：[1]江苏科技大学张家港校区船舶与建筑工程学院,江苏张家港215600 [2]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2016年第9期40-48,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(51078198);清华大学自主科研计划项目(2011THZ03)

摘　　要：该文阐述了将动力刚度法应用于中厚圆柱壳的自由振动分析。从考虑横向剪切变形和转动惯量的中厚壳理论出发,将圆柱壳的振动分解为一系列确定环向波数下的一维振动问题。用常微分方程求解器COLSYS求解该一维问题的动力刚度,通过Wittrick-Williams算法及导护型牛顿法求得该环向波数下结构的频率和振型。由于求解动力刚度时使用COLSYS对控制方程进行了精确求解,所以该文方法是精确方法。数值算例验证了中厚圆柱壳壳段固端频率计数J0计算方法的可靠性。综合表明:应用动力刚度法对中厚圆柱壳自由振动进行分析是可靠、精确的。This paper extends the dynamic stiffness method to the free vibration analysis of moderately thick circular cylindrical shells. Starting from the shell theory with the consideration of the transverse shear deformation and rotational inertia, the free vibration of circular cylindrical shells is decomposed into a series of one-dimensional free vibration problems with definite sinusoidal waves in the circumferential direction. This one-dimensional problem is solved by the ODE solver COLSYS to obtain the element dynamic stiffness. Natural frequencies and modes are found by applying the Wittrick-Williams algorithm and the recursive Newton＇s method. Since the governing equations are solved exactly when calculating the dynamic stiffness, the proposed method is exact. In the section of numerical examples, the counting method of segment clamped-ends natural frequencies J0 is verified. In general, the application of the dynamic stiffness method for the free vibration analysis of moderately thick circular cylindrical shells is reliable and accurate.

关 键 词：中厚圆柱壳 自由振动 动力刚度法 Wittrick-Williams算法 Hamilton形式 

分 类 号：TU311.3[建筑科学—结构工程]