结构固有振动特性设计的最优动力学修改原理

The Optimal Dynamics Modification Principle for Structural Natural Vibration Characteristic Design

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。

The sensitivity characteristics of the natural vibration frequencies andmode shapes of vibration structures with respect to mass and stiffnessmodifications are analysed in this paper by using the matrix perturbation method of the linear generalized eigenvalue problem. Some valuable con-clusions are obtained and the most sensitive positions of the structuralperturbation modifications are shown. These results have really revealedthe optimal dynamics modification principle for structural natural vibr-ation characteristic design. With the aid of the principle, a great compu-tational savings is obtainable especially in the dynamic characteristicsensitivity analysis of large or complex structures, and the reliabilityand completeness of the sensitivity analysis result can be improved. Thisis of importance to structural dynamic characteristic optimization, vibra-tion control, and so forth.