Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (...

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Autores principales:	Zharilkassin Iskakov, Kuatbay Bissembayev, Nutpulla Jamalov, Azizbek Abduraimov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	modeling of dynamics gyroscopic rotor non-linear stiffness linear damping non-linear damping Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/9d8cd89ea1be471798be2a456dd7d5c6
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spelling	oai:doaj.org-article:9d8cd89ea1be471798be2a456dd7d5c62021-11-25T18:12:13ZModeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support10.3390/machines91102762075-1702https://doaj.org/article/9d8cd89ea1be471798be2a456dd7d5c62021-11-01T00:00:00Zhttps://www.mdpi.com/2075-1702/9/11/276https://doaj.org/toc/2075-1702This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.Zharilkassin IskakovKuatbay BissembayevNutpulla JamalovAzizbek AbduraimovMDPI AGarticlemodeling of dynamicsgyroscopic rotornon-linear stiffnesslinear dampingnon-linear dampingMechanical engineering and machineryTJ1-1570ENMachines, Vol 9, Iss 276, p 276 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	modeling of dynamics gyroscopic rotor non-linear stiffness linear damping non-linear damping Mechanical engineering and machinery TJ1-1570
spellingShingle	modeling of dynamics gyroscopic rotor non-linear stiffness linear damping non-linear damping Mechanical engineering and machinery TJ1-1570 Zharilkassin Iskakov Kuatbay Bissembayev Nutpulla Jamalov Azizbek Abduraimov Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
description	This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.
format	article
author	Zharilkassin Iskakov Kuatbay Bissembayev Nutpulla Jamalov Azizbek Abduraimov
author_facet	Zharilkassin Iskakov Kuatbay Bissembayev Nutpulla Jamalov Azizbek Abduraimov
author_sort	Zharilkassin Iskakov
title	Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
title_short	Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
title_full	Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
title_fullStr	Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
title_full_unstemmed	Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support
title_sort	modeling the dynamics of a gyroscopic rigid rotor with linear and nonlinear damping and nonlinear stiffness of the elastic support
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9d8cd89ea1be471798be2a456dd7d5c6
work_keys_str_mv	AT zharilkassiniskakov modelingthedynamicsofagyroscopicrigidrotorwithlinearandnonlineardampingandnonlinearstiffnessoftheelasticsupport AT kuatbaybissembayev modelingthedynamicsofagyroscopicrigidrotorwithlinearandnonlineardampingandnonlinearstiffnessoftheelasticsupport AT nutpullajamalov modelingthedynamicsofagyroscopicrigidrotorwithlinearandnonlineardampingandnonlinearstiffnessoftheelasticsupport AT azizbekabduraimov modelingthedynamicsofagyroscopicrigidrotorwithlinearandnonlineardampingandnonlinearstiffnessoftheelasticsupport
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Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

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