A Complex Mode Superposition Method Based on Hysteretic Damping Model for Mode Static Correction

Due to modal truncation, the dynamic responses calculated by the mode superposition method have some errors. In this paper, the source of truncation error of the complex mode superposition method for hysteretic damped systems with non-proportional characteristics is analyzed. It includes truncation errors of external excitation load and Hilbert transform term. With the increase of mode order, the ratio of excitation frequency to natural frequency gradually approaches zero. Combined with the expression of structural modal response caused by harmonic wave, the corresponding approximate expression of high-order modal response is obtained. Through quasi-static analysis, a complex mode superposition method of non-proportionally damped systems for mode static correction is proposed. Numerical examples show that when the ratios of the domain frequencies of the external excitation to the natural frequency of some high-order modes are small, the complex mode superposition method for mode static correction has a good effect.

Automated summary

This paper analyzes the source of truncation error in the complex mode superposition method for hysteretic damped systems with non-proportional characteristics, including truncation errors of external excitation load and Hilbert transform term. It obtains the approximate expression of high-order modal response and proposes a complex mode superposition method for mode static correction in non-proportionally damped systems.