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Secondary Resonance Energy Harvesting with Quadratic Nonlinearity

Piezoelectric energy harvesters can transform the mechanical strain into electrical energy. The microelectromechanical transformation device is often composed of piezoelectric cantilevers and has been largely experimented. Most resonances have been developed to harvest nonlinear vibratory energy exc...

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Detalles Bibliográficos
Autores principales: Zhang, Guoce, Zhang, Bo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7435918/
https://www.ncbi.nlm.nih.gov/pubmed/32751856
http://dx.doi.org/10.3390/ma13153389
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author Zhang, Guoce
Zhang, Bo
author_facet Zhang, Guoce
Zhang, Bo
author_sort Zhang, Guoce
collection PubMed
description Piezoelectric energy harvesters can transform the mechanical strain into electrical energy. The microelectromechanical transformation device is often composed of piezoelectric cantilevers and has been largely experimented. Most resonances have been developed to harvest nonlinear vibratory energy except for combination resonances. This paper is to analyze several secondary resonances of a cantilever-type piezoelectric energy harvester with a tip magnet. The conventional Galerkin method is improved to truncate the continuous model, an integro-partial differential equation with time-dependent boundary conditions. Then, more resonances on higher-order vibration modes can be obtained. The stable steady-state response is formulated approximately but analytically for the first two subharmonic and combination resonances. The instability boundaries are discussed for these secondary resonances from quadratic nonlinearity. A small damping and a large excitation readily result in an unstable response, including the period-doubling and quasiperiodic motions that can be employed to enhance the voltage output around a wider band of working frequency. Runge–Kutta method is employed to numerically compute the time history for stable and unstable motions. The stable steady-state responses from two different methods agree well with each other. The outcome enriches structural dynamic theory on nonlinear vibration.
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spelling pubmed-74359182020-08-24 Secondary Resonance Energy Harvesting with Quadratic Nonlinearity Zhang, Guoce Zhang, Bo Materials (Basel) Article Piezoelectric energy harvesters can transform the mechanical strain into electrical energy. The microelectromechanical transformation device is often composed of piezoelectric cantilevers and has been largely experimented. Most resonances have been developed to harvest nonlinear vibratory energy except for combination resonances. This paper is to analyze several secondary resonances of a cantilever-type piezoelectric energy harvester with a tip magnet. The conventional Galerkin method is improved to truncate the continuous model, an integro-partial differential equation with time-dependent boundary conditions. Then, more resonances on higher-order vibration modes can be obtained. The stable steady-state response is formulated approximately but analytically for the first two subharmonic and combination resonances. The instability boundaries are discussed for these secondary resonances from quadratic nonlinearity. A small damping and a large excitation readily result in an unstable response, including the period-doubling and quasiperiodic motions that can be employed to enhance the voltage output around a wider band of working frequency. Runge–Kutta method is employed to numerically compute the time history for stable and unstable motions. The stable steady-state responses from two different methods agree well with each other. The outcome enriches structural dynamic theory on nonlinear vibration. MDPI 2020-07-31 /pmc/articles/PMC7435918/ /pubmed/32751856 http://dx.doi.org/10.3390/ma13153389 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Zhang, Guoce
Zhang, Bo
Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title_full Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title_fullStr Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title_full_unstemmed Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title_short Secondary Resonance Energy Harvesting with Quadratic Nonlinearity
title_sort secondary resonance energy harvesting with quadratic nonlinearity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7435918/
https://www.ncbi.nlm.nih.gov/pubmed/32751856
http://dx.doi.org/10.3390/ma13153389
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