An efficient method for vibration equations with time varying coefficients and nonlinearities

An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the mode...

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Autores principales:	Jinsong Yang, Jingsong Xie, Gaige Chen, Jinglong Chen
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246
Acceso en línea:	https://doaj.org/article/25360c165a50452493a7cc7121860e04
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spelling	oai:doaj.org-article:25360c165a50452493a7cc7121860e042021-12-02T02:34:40ZAn efficient method for vibration equations with time varying coefficients and nonlinearities1461-34842048-404610.1177/14613484211025151https://doaj.org/article/25360c165a50452493a7cc7121860e042021-12-01T00:00:00Zhttps://doi.org/10.1177/14613484211025151https://doaj.org/toc/1461-3484https://doaj.org/toc/2048-4046An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.Jinsong YangJingsong XieGaige ChenJinglong ChenSAGE PublishingarticleControl engineering systems. Automatic machinery (General)TJ212-225Acoustics. SoundQC221-246ENJournal of Low Frequency Noise, Vibration and Active Control, Vol 40 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246
spellingShingle	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246 Jinsong Yang Jingsong Xie Gaige Chen Jinglong Chen An efficient method for vibration equations with time varying coefficients and nonlinearities
description	An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.
format	article
author	Jinsong Yang Jingsong Xie Gaige Chen Jinglong Chen
author_facet	Jinsong Yang Jingsong Xie Gaige Chen Jinglong Chen
author_sort	Jinsong Yang
title	An efficient method for vibration equations with time varying coefficients and nonlinearities
title_short	An efficient method for vibration equations with time varying coefficients and nonlinearities
title_full	An efficient method for vibration equations with time varying coefficients and nonlinearities
title_fullStr	An efficient method for vibration equations with time varying coefficients and nonlinearities
title_full_unstemmed	An efficient method for vibration equations with time varying coefficients and nonlinearities
title_sort	efficient method for vibration equations with time varying coefficients and nonlinearities
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/25360c165a50452493a7cc7121860e04
work_keys_str_mv	AT jinsongyang anefficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT jingsongxie anefficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT gaigechen anefficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT jinglongchen anefficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT jinsongyang efficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT jingsongxie efficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT gaigechen efficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities AT jinglongchen efficientmethodforvibrationequationswithtimevaryingcoefficientsandnonlinearities
_version_	1718402335451906048

An efficient method for vibration equations with time varying coefficients and nonlinearities

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