Based on the harmonic balance method, a solution procedure of residue harmonic was developed for studying the system in which the motion of a particle is a rotating parabola.Firstly, the higher-order analytical vibration frequency and steady state response were obtained.Secondly, we study the change trend of vibration frequency as nonlinear coefficient, initial amplitude, linear stiffness coefficient of the system in steady state, the effects of initial amplitude, nonlinear coefficient on vibration frequency response were presented.The results show that the presented second-order residue harmonic balance approximations to vibration frequency and steady response are more accurate than some existing results, and that the relative error of the solution is greatly reduced, which are in good agreement with the exact ones.The vibration frequency is decreased with the increase of the nonlinear coefficient and the initial amplitude, but it increased with the increase of the linear stiffness coefficient.
Key words
Particle vibration system /
residue harmonic balance /
higher-order approximation /
frequency response
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