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本文以线性广义特征值问题的矩阵摄动法为理论工具,分析了一般振动结构的固有振频和固有振型对结构质量和刚度(包括内部连接刚度和边界约束刚度)修改的灵敏度特性,得到了一系列有实用价值的结论,其中指出了对结构进行摄动修改的最灵敏位置。这些分析结果实际上表明了结构固有振动特性设计的最优动力学修改原理,据此可使大型、复杂结构动态特性灵敏度分析的计算量大大减少,也可使灵敏度分析结果的可靠性和完整性得以改善。它对于有效地进行结构的动态特性优化设计及振动控制等具有重要意义。
In this paper, based on the matrix perturbation method of linear generalized eigenvalue problem, the sensitivity characteristics of the natural vibration frequency and natural vibration mode of the general vibration structure to the modification of structure mass and stiffness (including the internal connection stiffness and the boundary constraint stiffness) are analyzed. A series of practical conclusions were made, pointing out the most sensitive positions perturbed by the structure. The results of these analyzes actually indicate the principle of optimal dynamic modification of the inherent vibration characteristics of the structure, which can greatly reduce the computational complexity of the sensitivity analysis of the dynamic characteristics of large and complex structures, as well as the reliability and completeness of the sensitivity analysis results Be improved. It is important for the effective structural optimization of dynamic characteristics and vibration control.