Calculation of complex modes of non-proportionally damped systems using real modes
In this paper,a new method for calculating complex modes of non-proportionally damped systems using real modes is proposed.First,an embedded parameter is introduced to directly connect the undamped system with the damped system,and then the modal normalization condition is constructed.The eigenvalues and eigenvectors of the non-proportionally damped system are expanded as the power series of this parameter to obtain the governing equations of the expansion coefficients.The eigenvector expansion coefficients can be determined by solving systems of equations with the same symmetric real-coefficient matrix by Nelson's method for each eigenpair.The proposed approach involves only the modes of interest,no modal truncation,but no generalized inversion,and no matrix expansion.Two numerical examples are given to illustrate the effectiveness of the proposed method.
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