自由—自由结构振动模态的一阶导数

CALCULATING OF FIRST-ORDER DERIVATIVES OF VIBRATION MODE SHAPES FOR FREE-FREE STRUCTURES

空间飞行器和车辆等一大类结构属于自由－自由结构。本文讨论这类结构的振动模态一阶导数计算问题，提出了一种改进的截尾模态展开法，将未知模态对模态导数的贡献用已知模态和系统矩阵来表达。针对刚度阵奇异问题，提出了移位措施，通过选择合适的移位系数，不仅解决了奇异问题，而且加速了算法的收敛速度。给出了一个数值例子，算例表明本文方法十分有效。

There exist a class of structures,such as aricrafts,automobiles and ships,which belong to the free-free structures.This paper addresses the computational problem of the vibration mode shape derivatioves with respect to design parameters.An improved modal superposition method for mode shape derivatives is proposed,in which the contribution due to the unavailable mode shapes to the derivatives of mode shapes under consideration is explicitly and accurately expressed using the available mode shapes and the system matrices.A shift in eigenvalues is introduced to deal with the singularity of the stiffness matrix and a proper shift value can speed the convergence of the algorithm presented in this paper.A numerical example with one rigid mode is given to illustrate the effectiveness of the present method.