Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink |
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| Authors: | Jian Zang Li-Qun Chen |
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| Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China;Department of Mechanics, Shanghai University, Shanghai 200444, China |
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| Abstract: | Nonlinear behaviors are investigated for a struc-ture 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 numer-ical 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 peri-odic 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. |
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| Keywords: | Nonlinear energy sink Global bifurcation Chaos Harmonic balance method Stability |
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