Nonlinear analysis of flexoelectric energy harvesters under force excitations

  • H. L. Dai
  • Z. YanEmail author
  • L. Wang


This work focuses on theoretical modeling and dynamic analysis of a flexoelectric beam energy harvester with the consideration of geometric nonlinearity. We assume that the beam energy harvester has a thickness at nanoscale and a width and length at microscale. Under a harmonic concentrated force, the proposed energy harvester generates electric power due to the phenomenon of flexoelectricity. Based on the theory of flexoelectricity and Euler–Bernoulli beam assumption, the nonlinear electromechanical coupling equations are derived. Galerkin method is employed to obtain the discrete nonlinear equations, which are then solved numerically. Frequency response curves are plotted to reveal the nonlinear characteristics of the energy harvester and it is found that the frequency response curves of the flexoelectric energy harvester exhibit hardening behaviors. Case studies are provided and we emphasize on the influences of load resistance, tip mass, concentrated force and damping ratio on the output performance of the energy harvester. In addition, it is suggested that the flexoelectric energy harvester has a better output performance under a square waveform force among different forms of the concentrated force. The results obtained are significant for designing optimal flexoelectric energy harvesters.


Flexoelectricity Energy harvester Nonlinear effects Size-dependency Nanoscale 



This work is supported by the National Natural Science Foundation of China (No. 11502084), Natural Science Foundation of Hubei Province (2017CFB429) and the Fundamental Research Funds for the Central Universities, HUST (Nos. 2016YXMS096, 2017KFYXJJ135).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory of Engineering Structural Analysis and Safety AssessmentWuhanChina

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