Nonlinear Dynamics

, Volume 85, Issue 4, pp 2507–2520 | Cite as

Internal resonance in axially loaded beam energy harvesters with an oscillator to enhance the bandwidth

  • Wen-An Jiang
  • Li-Qun Chen
  • Hu Ding
Original Paper


Internal resonance is explored as a possible mechanism to enhance the bandwidth of vibratory energy harvesters. To demonstrate the improved performance, an axially loaded beam energy harvester with an oscillator is considered. Based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude–frequency response relationships of the voltage and the power in the first primary resonances with a two-to-one internal resonance. The optimal resistance is determined to achieve the maximum of the power. The amplitude–frequency response curves of the voltage and the power under the optimal load resistance have two peaks bending to the left and the right, respectively. The amplitude–frequency response curves bend more to the right, indicating hardening-type nonlinearity. The numerical simulations support the analytical results. The results demonstrate that the internal resonance design can improve bandwidth of the energy harvester. Numerical simulations indicate the appearance of chaos under sufficiently strong excitation.


Internal resonance Double-jumping Buckled beam Energy harvesting Nonlinearity 



This work was supported by the State Key Program of National Natural Science of China (No. 11232009) and the National Natural Science Foundation of China (Nos. 11422214 and 11572182).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina

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