Author ORCID Identifier

Shahzrad Towfighian -

Document Type


Publication Date



parametric resonator, coupled oscillators, energy harvesting, nonlinear dynamics, nonlinear vibration, parametric resonance, piezoelectric


A parametric resonator for vibration energy harvesting is presented. Despite large responses from parametric resonance, two major drawbacks of parametric resonance harvesters are the high threshold excitation and narrow bandwidth. We addressed these two shortcomings by adding magnetic nonlinearity to the system. The proposed vibration energy harvester consists of two piezoelectric cantilevers beams, each with a magnetic tip. By controlling the distance between the two magnets, the threshold excitation level needed to trigger the parametric resonance decreases. Combining the softening and hardening behavior of the two magnetically coupled beams increases the frequency bandwidth. In addition, the amplitude of the response increases with the merger of the direct and parametric resonances of the two beams. We present a mathematical model of the system consisting of two lumped systems coupled by the magnetic force. The coupled governing equations are solved numerically, analytically, and are verified by experiments. Unique characteristics of wider bandwidth, larger response, and lower threshold excitation occur at the low frequency because of the added magnetic nonlinearity to the two-beam system. These properties can improve the efficiency of vibration energy harvesters.

Publisher Attribution

Journal of Sound and Vibration, published by Elsevier -

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Available for download on Tuesday, January 26, 2021