Dynamic analysis of piezoelectric energy harvester under combination parametric and internal resonance: a theoretical an
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ORIGINAL PAPER
Dynamic analysis of piezoelectric energy harvester under combination parametric and internal resonance: a theoretical and experimental study Anshul Garg
· Santosha K. Dwivedy
Received: 1 February 2020 / Accepted: 29 August 2020 © Springer Nature B.V. 2020
Abstract In this work, theoretical and experimental analysis of a piezoelectric energy harvester with parametric base excitation is presented under combination parametric resonance condition. The harvester consists of a cantilever beam with a piezoelectric patch and an attached mass, which is positioned in such a way that the system exhibits 1:3 internal resonance. The generalized Galerkin’s method up to two modes is used to obtain the temporal form of the nonlinear electromechanical governing equation of motion. The method of multiple scales is used to reduce the equations of motion into a set of first-order differential equations. The fixed-point response and the stability of the system under combination parametric resonance are studied. The multi-branched non-trivial response exhibits bifurcations such as turning point and Hopf bifurcations. Experiments are performed under various resonance conditions. This study on the parametric excitation along with combination and internal resonances will help to harvest energy for a wider frequency range from ambient vibrations. Keywords Nonlinear dynamics · Piezoelectric energy harvester · Internal resonance · Combination A. Garg (B)· S. K. Dwivedy Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India e-mail: [email protected] S. K. Dwivedy e-mail: [email protected]
parametric resonance · Bifurcation · Method of multiple scales 1 Introduction The low-powered microelectronic systems [1], which are used as sensors and actuators, need to be self-reliant in the energy front for remote operations. The ambient kinetic energy available from sources such as winds and vibrating structures can be utilized to convert into electricity by several mechanisms. These transduction mechanisms [2,3] are piezoelectric, electromagnetic, and electrostatic, which are extensively utilized for energy harvesting purposes mostly in the linear range of oscillations. The combination of these three transduction mechanisms is also explored as hybrid energy harvesters [4–6]. Among them, the piezoelectric-based energy harvesting has been the most attractive one due to its energy extracting capabilities over a wide range of available frequencies. Researchers started with linear vibration-based harvesters [7,8], but the limitations of having limited frequency bandwidth and very few resonance conditions lead to shift their focus on nonlinear vibration-based harvesters [9–17]. The term bandwidth is defined as the range of frequency that is available for energy transduction. Wider bandwidth means a higher range of ambient frequency over which energy transfer is possible. Rich dynamical behavior (e.g., multiple resonances, bifurcation, internal resonance, and chaos) [18,19] of nonlinear vibrat
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