Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

• Published in: Acta mechanica Sinica 2017-08, Vol.33 (4), p.801-822
• Main Authors: Zang, Jian, Chen, Li-Qun
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Complexity; Computational Intelligence; Degrees of freedom; Engineering; Engineering Fluid Dynamics; Excitation; Frequency response; Harmonic excitation; Hopf bifurcation; Hopf分岔; Mathematical models; Nonlinear dynamics; Oscillators; Power spectra; Research Paper; Stiffness; Theoretical and Applied Mechanics; 周期分岔; 和谐; 混沌运动; 简谐激励; 结构耦合; 能量; 非线性行为
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-017-0671-x

Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.