实模态灵敏度分析的2种模态算法及其应用

Two modal algorithms with the application for computing the sensitivity of real mode

文章利用一种简单而易于操作的实模态规范化方法,推导实模态的一阶、二阶灵敏度及其梯度向量和海森矩阵的全模态算法公式,并提出一种实用的模态截断准则,形成全新的实模态灵敏度的截模态算法,从而成功构建实模态的一阶、二阶泰勒近似式,为灵敏度分析在结构优化与控制、损伤识别和模型修正等工程领域中的应用提供高精度的算法支撑。最后利用数值算例说明该文算法是正确的和有效的,并且具有较高的精度。

An efficient full-mode algorithm by using a concise normalization condition which is easy to implement is derived for the computation of the modal first-and second-order sensitivities with the gradient and Hessian matrices for the real symmetrical eigenvalue problem.Meanwhile,a truncated criterion in full-mode algorithm is presented.And then the new truncated modal algorithm can be formed while conducting expressions for the first and second degree of Taylor approximations of real mode.For many application areas of the eigensolution sensitivity,e.g.optimization and controlling of the dynamic structure,damage detection and modal updating,it is indicated that the second degree of Taylor approximation has higher accuracy and the truncated modal algorithm can be utilized in practice.A numerical example is given to illustrate the effectiveness and correctness of the full-mode algorithm.The numerical accuracy of the truncated modal algorithm is also examined by considering the 7-DOF non-proportionally damped system.