亏损阻尼系统的模态灵敏度分析算法

提出了亏损振动系统的模态灵敏度分析的算法。首先将N维向量空间中描述的亏损振动系统转入2N维广义状态空间中，再利用广义状态向量及其伴随向量系的解耦性能，解耦广义状态空间中的灵敏度控制方程，并利用移频技术求解广义状态向量的灵敏度；其次建立了2N维广义状态向量与N维亏损系统模态向量之间的联系；最后将广义状态向量灵敏度算法平移至模态向量，从而建立了亏损振动系统模态向量灵敏度分析的移频算法。该算法可用于拥有各种类型Jordan块的亏损系统，结构紧凑，应用灵活，具有较强的工程应用性。数值算例的结果说明了该算法是可行且有效的。

Mode Sensitivity Analysis for Defective Damping System

The algorithm of mode sensitivity analysis is proposed for defective damping systems. Firstly the defective system considered in state space of dimension N is switched to the generalized state space of dimension 2N. By taking advantage of the decoupling property of generalized state-space vectors with its adjoint vectors controlled equations o[ sensitivity are decoupled, and then the sensitivity algorithm of generalized state-space vectors can be obtained by using for moving-frequency technology. Secondly the relation between generalized state-space vectors of dimension 2N is es- tablished and the mode shapes of dimension N is associated with the defective damping system. Finally the sensitivity analysis algorithm of generalized state-space vectors is brought in the mode sensitivity analysis. Hence an algorithm of mode sensitivity analysis based on moving-frequency technology with respect to defective damping system is presented. The algorithm given here can be applied to defective damping system which processes different kinds of Jordan blocks. The algorithm is brief, concise and better to be applied. The validity and feasibility of the derived expressions are dem- onstrated by considering a two degree-of-freedom damping system.