An improved modal truncation method for responses to harmonic excitation

Determining the steady state responses of a structural system, to a harmonic excitation, is an important problem. The modal superposition method is often used, although it cannot always give an exact solution when the mode truncation is serious or the excitation frequency is larger than the frequencies of the truncated modes. Fast and accurately evaluating the contribution due to the truncated modes to the response of harmonic excitation is put forward in reference by Liu et al. [Modal Anal: Int J Exp Modal Anal 9 (1994) 2] without using the truncated modes. The present paper suggests a modification to the approach of Liu et al., in that, it uses eigenvalue shift approach to enhance convergence when the frequency of the harmonic excitation is larger than the frequency of the truncated modes. Three numerical examples are given to demonstrate the validity and the effectiveness of the present method.