关键词: 特征灵敏度, 重频, 对称阻尼, 二次特征值

Abstract: 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.

Key words: eigensensitivity, repeated frequencies, symmetric damping, quadratic eigenvalue