Acta Mechanica Sinica

, Volume 35, Issue 4, pp 894–911 | Cite as

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environments

  • Dongxing CaoEmail author
  • Yanhui Gao
  • Wenhua Hu
Research Paper


A novel oscillator structure consisting of a bimorph piezoelectric cantilever beam with two steps of different thicknesses is proposed to improve the energy harvesting performance of a vibration energy harvester (VEH) for use in low-frequency vibration environments. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler–Bernoulli beam assumptions, then the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the coupled electromechanical equations governing the piezoelectric energy harvester are introduced by means of the Lagrange equations. Furthermore, expressions for the steady-state response are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed, and the effects of the ratio of lengths, ratio of thicknesses, end thickness, and load resistance on the output voltage, harvested power, and power density are discussed. Moreover, to verify the analytical results, finite element method simulations are also conducted to analyze the performance of the proposed VEH, showing good agreement. All the results show that the present oscillator structure is more efficient than the conventional, uniform beam structure, specifically for vibration energy harvesting in low-frequency environments.


Vibration energy harvesting Piezoelectric cantilever beam Stepped variable thicknesses Finite element method simulation 



The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grants 11672008 and 11272016).


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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.College of Mechanical EngineeringBeijing University of TechnologyBeijingChina
  2. 2.Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical StructuresBeijingChina
  3. 3.School of Mechanical EngineeringTianjin University of TechnologyTianjinChina

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