Acta Mechanica Sinica

, Volume 33, Issue 1, pp 200–207 | Cite as

Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function

Research Paper


By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.


Bistable piezoelectric cantilever beam Second order Melnikov function Homoclinic bifurcation Basin of attraction 



The project was supported by the National Natural Science Foundation of China (Grant 11172199).


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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 2016

Authors and Affiliations

  1. 1.Department of Mechanics, School of Mechanical EngineeringTianjin UniversityTianjinChina
  2. 2.College of ScienceNorth China University of Science and TechnologyTangshanChina
  3. 3.Tianjin Key Laboratory of Nonlinear Dynamics and Chaos ControlTianjinChina

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