求解结构振动非线性特征值问题的一个方法

本研究结构分析中动态有限元引起的非线性特征值问题。中提出将动态有限元法与Ｒｉｃａａｔｉ传递矩阵法相结合求解振动非线性特征值问题。该方法减少了普通动态有限元法中结构划分所需的节点数，大大扩大了在微型机上的求解问题的规模；对传递矩阵引入Ｒｉｃｃａｔｉ变换，从而比标准传递托 阵法减少了误差传递，提高了计算效率；采用Ｎｅｕｔｏｎ－Ｒｑｐｈｓｏｎ法代替行列式值试凑法计算频率值简单高效。最后，本给出了两

A METHOD FOR SOLVING NON - LINEAR EIGENPROBLEMS OF STRUCTURAL VIBRATION

This paper deals with the non - linear eigenvalue problems arising from dynamic finite element in structural analysis. A combination of dynamic finite element and riccati transfer matrix methods is proposed for solving non - linear eigenvalues of vibrations. This method minimizes the propagation of round off errors occurred in the standard transfer matrix method and yields the value of the frequency by Newton - Raphson method. By using this technique, the nodes required in the regular finite element method is reduced and therefore a microcomputer Can be used. Besides, no plotting of the values of the determinant versus the assumed frequency i necessary. As an application of this method, numerical examples are given. The results show that this method proves to be effective.