Abstract: Fast and accurately evaluating the contribution due to the truncated modes to the response of harmonic excitation is the objective of this paper without using the truncated modes. By using the series expansion of a matrix function and the theory of spectral representation of a matrix, the contribution due to the truncated modes to the response of a harmonic excitation is expressed exactly and exlicitly, with the available low-frequency modes and the system matrices. Two numerical examples are given to demonstrate the validity and effectiveness of the present method.

Key words: modal superposition, modal truncation, forced vibration, harmonic excitation