Open AccessStability and approximate solution of a relative-rotation nonlinear dynamical system under harmonic excitation
Author(s) -
Pengfei Shi,
Bin Liu,
Shuang Liu
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.4675
Subject(s) - physics , nonlinear system , excitation , resonance (particle physics) , harmonic , singularity , rotation (mathematics) , lyapunov function , stability (learning theory) , classical mechanics , harmonic oscillator , equations of motion , nonlinear resonance , mathematical analysis , mathematics , quantum mechanics , geometry , computer science , machine learning
The dynamical equation of a relative-rotation nonlinear dynamical system with nonlinear elastic force and common friction and harmonic excitation is deduced. The singularity stability of the autonomous system is studied by constructing the Lyapunov function. The approximate solution of unautonomous equation with different resonance response under harmonic excitation is obtained by the method of multiple scales, and the stability of main resonance stable state of motion is studied.