Acta Mechanica Sinica

, Volume 33, Issue 4, pp 801–822 | Cite as

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

Research Paper


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.


Nonlinear energy sink Global bifurcation Chaos Harmonic balance method Stability 



This work was supported by the National Natural Science Foundation of China (Grants 11402151 and 11572182).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghaiChina
  3. 3.Department of MechanicsShanghai UniversityShanghaiChina

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