Acta Mechanica Sinica

, Volume 35, Issue 4, pp 912–925 | Cite as

Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

  • Tian-Chen Yuan
  • Jian Yang
  • Li-Qun ChenEmail author
Research Paper


A lumped parameter transverse vibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectric circular composite clamped by two steel rings and a proof mass on the plate. The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. A harmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. An incremental harmonic balance approach is also developed for the lumped parameter model. The two approaches yield the same results. The amplitude-frequency responses produced by the harmonic balance approach are validated by the numerical integrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with the coexistence of hardening and softening nonlinearities can outperform not only linear energy harvesters, but also typical hardening nonlinear energy harvesters.


Piezoelectric energy harvester Circular composite plate Transverse nonlinear vibration Harmonic balance Arc-length continuation 



This work was supported by the National Natural Science Foundation of China (Grants 51575334 and 11802170), the State Key Program of National Natural Science Foundation of China (Grant 11232009), the Key Research Projects of Shanghai Science and Technology Commission (Grant 18010500100), and the Innovation Program of Shanghai Municipal Education Commission (Grant 2017-01-07-00-09-E00019).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.School of Urban Railway TransportationShanghai University of Engineering ScienceShanghaiChina
  3. 3.Department of MechanicsShanghai UniversityShanghaiChina
  4. 4.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina

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