阻尼结构重频特征灵敏度计算的扩展Nelson方法

考虑求解阻尼结构重频特征灵敏度计算问题, 针对传统Nelson方法无法计算重频特征灵敏度的问题, 提出一种新的扩展Nelson方法. 通过构造新的灵敏度特解控制方程, 并证明其系数矩阵的非奇异性, 使其可以计算结构重频复模态振型灵敏度， 扩展了Nelson方法. 该方法保持了传统Nelson方法的优点, 仅利用重频频率对应的模态振型求解, 无需扩大方程求解规模和矩阵重排. 数值实例验证了该方法的有效性.

Extended Nelson's Method for Calculating Eigensensitivity of Damped Structures with Repeated Frequencies

The problem of  calculating the eigensensitivity  of damped structures. Aiming at the problem that the traditional Nelson’s method could not  calculate the eigensensitivity with repeated frequency, we proposed a new extended Nelson’s method. The non-singularity of its coefficient matrix was proved by constructing a new particular solution control equation of  sensitivity. It could be used to calculate the sensitivity of repeated frequency complex mode shapes in structures, and the Nelson’s method was extended. The method kept the advantages of the traditional Nelson’s method and only used the mode shape corresponding to the repeated frequencies to solve the equation, and there was no need to expand the scale  of solving the equation  and rearrange the matrix. Numerical examples verify  the effectiveness of the method.