Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter

In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the mult...

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Autores principales:	Ying Zhang, Xiaxia Duan, Yu Shi, Xiaole Yue
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	uncertain parameter tristable energy harvester Chebyshev polynomial approximation bifurcation chaos Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/cecf96cad8b64ffb95c9f9cd709f8242
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spelling	oai:doaj.org-article:cecf96cad8b64ffb95c9f9cd709f82422021-11-11T15:04:01ZResponse Analysis of the Tristable Energy Harvester with an Uncertain Parameter10.3390/app112199792076-3417https://doaj.org/article/cecf96cad8b64ffb95c9f9cd709f82422021-10-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/9979https://doaj.org/toc/2076-3417In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.Ying ZhangXiaxia DuanYu ShiXiaole YueMDPI AGarticleuncertain parametertristable energy harvesterChebyshev polynomial approximationbifurcationchaosTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 9979, p 9979 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	uncertain parameter tristable energy harvester Chebyshev polynomial approximation bifurcation chaos Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	uncertain parameter tristable energy harvester Chebyshev polynomial approximation bifurcation chaos Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Ying Zhang Xiaxia Duan Yu Shi Xiaole Yue Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
description	In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.
format	article
author	Ying Zhang Xiaxia Duan Yu Shi Xiaole Yue
author_facet	Ying Zhang Xiaxia Duan Yu Shi Xiaole Yue
author_sort	Ying Zhang
title	Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
title_short	Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
title_full	Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
title_fullStr	Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
title_full_unstemmed	Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter
title_sort	response analysis of the tristable energy harvester with an uncertain parameter
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/cecf96cad8b64ffb95c9f9cd709f8242
work_keys_str_mv	AT yingzhang responseanalysisofthetristableenergyharvesterwithanuncertainparameter AT xiaxiaduan responseanalysisofthetristableenergyharvesterwithanuncertainparameter AT yushi responseanalysisofthetristableenergyharvesterwithanuncertainparameter AT xiaoleyue responseanalysisofthetristableenergyharvesterwithanuncertainparameter
_version_	1718437177221709824

Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter

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