Parametrically amplified Mathieu-Duffing nonlinear energy harvesters

Karlicic, Danilo; Chatterjee, Tanmoy; Cajić, Milan; Adhikari, Sondipon

doi:10.1016/j.jsv.2020.115677

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Parametrically amplified Mathieu-Duffing nonlinear energy harvesters

Danilo Karlicic

, Tanmoy Chatterjee, Milan Cajić, Sondipon Adhikari

Journal of Sound and Vibration, Volume: 488, Start page: 115677

Swansea University Authors: Danilo Karlicic , Tanmoy Chatterjee, Sondipon Adhikari

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DOI (Published version): 10.1016/j.jsv.2020.115677

Abstract

The steady-state response of a nonlinear piezoelectric energy harvester subjected to external and parametric excitation is investigated based on the Mathieu-Duffing nonlinear oscillator model. The parametric excitation is introduced to amplify the external harmonic excitation and extend the capabili...

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Published in:	Journal of Sound and Vibration
ISSN:	0022-460X
Published:	Elsevier BV 2020
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URI:	https://cronfa.swan.ac.uk/Record/cronfa55103
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The parametric excitation is introduced to amplify the external harmonic excitation and extend the capabilities of the nonlinear piezoelectric energy harvester device. To obtain the approximated solution of the nonlinear periodic responses for displacement and electrical voltage of the energy harvester, the incremental harmonic balance method in combination with the path-following technique is adopted. It is assumed that the proposed nonlinear model consists of cubic and quadratic nonlinearity, where parametric amplification appears in the form of a trigonometric function. The frequency is tuned as one-to-one and the one-to-two ratio between external and parametric excitation. The effects of quadratic and cubic nonlinearity as well as parametric amplification are studied in detail, and their incredible properties to extend harvester application performance is illustrated. It is explicitly demonstrated that for some particular combination of the system parameters, vibration amplitudes and harvested power can be amplified up to three or five times in comparison to the classical broadband nonlinear energy harvester based on the forced Duffing oscillator. This extraordinary amplification shown to be a key motivation to realize the proposed concept in practice. The presence of combined quadratic and cubic nonlinearities resulted in both hardening and softening spring behavior and leading to the appearance of coexisting periodic solutions in the amplitude-frequency responses. Periodic orbits obtained by the proposed methodology are verified with the results from direct numerical integration and fine agreement is demonstrated. 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spelling	2020-11-03T13:52:50.5980592 v2 55103 2020-09-01 Parametrically amplified Mathieu-Duffing nonlinear energy harvesters d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 5e637da3a34c6e97e2b744c2120db04d Tanmoy Chatterjee Tanmoy Chatterjee true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2020-09-01 EEN The steady-state response of a nonlinear piezoelectric energy harvester subjected to external and parametric excitation is investigated based on the Mathieu-Duffing nonlinear oscillator model. The parametric excitation is introduced to amplify the external harmonic excitation and extend the capabilities of the nonlinear piezoelectric energy harvester device. To obtain the approximated solution of the nonlinear periodic responses for displacement and electrical voltage of the energy harvester, the incremental harmonic balance method in combination with the path-following technique is adopted. It is assumed that the proposed nonlinear model consists of cubic and quadratic nonlinearity, where parametric amplification appears in the form of a trigonometric function. The frequency is tuned as one-to-one and the one-to-two ratio between external and parametric excitation. The effects of quadratic and cubic nonlinearity as well as parametric amplification are studied in detail, and their incredible properties to extend harvester application performance is illustrated. It is explicitly demonstrated that for some particular combination of the system parameters, vibration amplitudes and harvested power can be amplified up to three or five times in comparison to the classical broadband nonlinear energy harvester based on the forced Duffing oscillator. This extraordinary amplification shown to be a key motivation to realize the proposed concept in practice. The presence of combined quadratic and cubic nonlinearities resulted in both hardening and softening spring behavior and leading to the appearance of coexisting periodic solutions in the amplitude-frequency responses. Periodic orbits obtained by the proposed methodology are verified with the results from direct numerical integration and fine agreement is demonstrated. Moreover, a significant influence of the parametric amplification on the instantaneous power is revealed in time response diagrams, thus showing better performance of the proposed energy harvester system. Journal Article Journal of Sound and Vibration 488 115677 Elsevier BV 0022-460X Energy harvester, Parametric amplification, Nonlinear response, Mathieu-Duffing oscillator, Incremental harmonic balance method 8 12 2020 2020-12-08 10.1016/j.jsv.2020.115677 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2020-11-03T13:52:50.5980592 2020-09-01T09:43:41.7093879 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Danilo Karlicic 0000-0002-7547-9293 1 Tanmoy Chatterjee 2 Milan Cajić 3 Sondipon Adhikari 4 55103__18090__2e4c31fb72dd424493764f24a58c27e3.pdf 55103.pdf 2020-09-01T09:46:24.9706138 Output 11387086 application/pdf Accepted Manuscript true 2021-08-28T00:00:00.0000000 ©2020 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
spellingShingle	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters Danilo Karlicic Tanmoy Chatterjee Sondipon Adhikari
title_short	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
title_full	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
title_fullStr	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
title_full_unstemmed	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
title_sort	Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
author_id_str_mv	d99ee591771c238aab350833247c8eb9 5e637da3a34c6e97e2b744c2120db04d 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv	d99ee591771c238aab350833247c8eb9_*_Danilo Karlicic 5e637da3a34c6e97e2b744c2120db04d__Tanmoy Chatterjee 4ea84d67c4e414f5ccbd7593a40f04d3_**_Sondipon Adhikari
author	Danilo Karlicic Tanmoy Chatterjee Sondipon Adhikari
author2	Danilo Karlicic Tanmoy Chatterjee Milan Cajić Sondipon Adhikari
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container_title	Journal of Sound and Vibration
container_volume	488
container_start_page	115677
publishDate	2020
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issn	0022-460X
doi_str_mv	10.1016/j.jsv.2020.115677
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college_str	Faculty of Science and Engineering
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description	The steady-state response of a nonlinear piezoelectric energy harvester subjected to external and parametric excitation is investigated based on the Mathieu-Duffing nonlinear oscillator model. The parametric excitation is introduced to amplify the external harmonic excitation and extend the capabilities of the nonlinear piezoelectric energy harvester device. To obtain the approximated solution of the nonlinear periodic responses for displacement and electrical voltage of the energy harvester, the incremental harmonic balance method in combination with the path-following technique is adopted. It is assumed that the proposed nonlinear model consists of cubic and quadratic nonlinearity, where parametric amplification appears in the form of a trigonometric function. The frequency is tuned as one-to-one and the one-to-two ratio between external and parametric excitation. The effects of quadratic and cubic nonlinearity as well as parametric amplification are studied in detail, and their incredible properties to extend harvester application performance is illustrated. It is explicitly demonstrated that for some particular combination of the system parameters, vibration amplitudes and harvested power can be amplified up to three or five times in comparison to the classical broadband nonlinear energy harvester based on the forced Duffing oscillator. This extraordinary amplification shown to be a key motivation to realize the proposed concept in practice. The presence of combined quadratic and cubic nonlinearities resulted in both hardening and softening spring behavior and leading to the appearance of coexisting periodic solutions in the amplitude-frequency responses. Periodic orbits obtained by the proposed methodology are verified with the results from direct numerical integration and fine agreement is demonstrated. Moreover, a significant influence of the parametric amplification on the instantaneous power is revealed in time response diagrams, thus showing better performance of the proposed energy harvester system.
published_date	2020-12-08T04:09:05Z
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score	11.037581

Parametrically amplified Mathieu-Duffing nonlinear energy harvesters

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