Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (5): 1124-1130.

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

SUI Guangyu1, LI Zhengguang1, WU Baisheng2   

  1. 1. College of Mathematics, Jilin University, Changchun 130012, China;
    2. School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China
  • Received:2021-03-25 Online:2021-09-26 Published:2021-09-26

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

CLC Number: 

  • O342