系统移频动柔度式与特征向量导数

Computation of eigenvector derivatives using a shift-system dynamic flexibility

本文针对作者过去建立的两种动柔度混合幂级数用于自由结构的很多特征向量导数计算时 ,求解待定矩阵 A0 ,A1…的支配方程的系数阵为奇异刚度阵 K。为求解这些方程必须补充若干独立方程 ,这便导致 K阵之带状特点的破坏。为此 ,本文利用“移频”建立了一种系统移频动柔度式 ,其中A0 ,A1…的支配方程之系数阵为移频刚度阵 K*,它总是非奇异的 ,可它却具有原 K阵的带状特征。这样 ,本文移频动柔度法的计算效率便明显提高。

HT5SS]When two dynamic flexibility formulae proposed early by author are used in the analysis of eigen derivative for free structure with rigid\|body motion, the coefficient matrix of governing equation for solving matrices A\-0, A\-1,… to be determined in the power series is singular stiffness matrix K. To solve matrices A\-0, A\-1,… one has to complement some independent equations associated with rigid\|body motion, so that the band\|state characteristic of matrix K is broken. In order to improve computational efficiency, a shift\|system dynamic flexibility expression is developed by using shifting frequency in this paper. The coefficient matrix of governing equation for solving matrices A\-0,A\-1,… in the shift\|system dynamic flexibility expression is a shifted stiffness matrix K\+* that always is non\|singular and possesses the band\|state characteristic of original matrix K. Thus the computational efficiency of the method presented in this paper is obviously better than that of early methods.