计算结构稳态强迫振动的有限元传递矩阵法

对结构稳态强迫振动的有限元传递矩阵法进行了研究 .建立了结构在简谐激励力作用下稳态强迫振动的有限元运动方程 ,将普通有限元传递矩阵法中状态向量从左至右的传递改变为子结构界面刚度方程从左至右的传递 ,从而有效地减小了因矩阵多次相乘而产生的舍入误差积累 ,且克服了普通有限元传递矩阵法仅适用于链式结构 ,要求所有子结构边界自由度数相等的限制 数值算例表明该方法具有较高的计算精确度及较广泛的适用范围

A Combined finite element-transfer matrix method for steady state forced vibration of structures

An extended finite element transfer matrix method, in combination with stiffness equation transfer, is applied to dynamic response analysis of the structures under periodic excitations. In the present method, the transfer of state vectors from left to right in a combined finite element transfer matrix method (FE TM) is changed into the transfer of general stiffness equations of every section from left to right. This offers the advantages to reduce the order of standard transfer equation systems and, to minimize the propagation of round off errors occurring in recursive multiplication of transfer and point matrices. Furthermore, the drawback that in the ordinary FE TM, the number of degrees of freedom on the left boundary must be the same as on the right, is avoided. A FESET program based on this method using microcomputers is developed. Finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures.