Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads

Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived...
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Autor*in:	Li, Dayang [verfasserIn] Cao, Maosen Manoach, Emil Ragulskis, Minvydas

Format:	Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature B.V. 2021

Übergeordnetes Werk:	Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 107(2021), 1 vom: 13. Nov., Seite 247-267
Übergeordnetes Werk:	volume:107 ; year:2021 ; number:1 ; day:13 ; month:11 ; pages:247-267

Links:	Volltext

DOI / URN:	10.1007/s11071-021-07000-2

Katalog-ID:	OLC2077712686

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520			\|a Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics.
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allfields	10.1007/s11071-021-07000-2 doi (DE-627)OLC2077712686 (DE-He213)s11071-021-07000-2-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Li, Dayang verfasserin aut Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution Cao, Maosen aut Manoach, Emil aut Ragulskis, Minvydas aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 107(2021), 1 vom: 13. Nov., Seite 247-267 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:107 year:2021 number:1 day:13 month:11 pages:247-267 https://doi.org/10.1007/s11071-021-07000-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT AR 107 2021 1 13 11 247-267
spelling	10.1007/s11071-021-07000-2 doi (DE-627)OLC2077712686 (DE-He213)s11071-021-07000-2-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Li, Dayang verfasserin aut Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution Cao, Maosen aut Manoach, Emil aut Ragulskis, Minvydas aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 107(2021), 1 vom: 13. Nov., Seite 247-267 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:107 year:2021 number:1 day:13 month:11 pages:247-267 https://doi.org/10.1007/s11071-021-07000-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT AR 107 2021 1 13 11 247-267
allfields_unstemmed	10.1007/s11071-021-07000-2 doi (DE-627)OLC2077712686 (DE-He213)s11071-021-07000-2-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Li, Dayang verfasserin aut Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution Cao, Maosen aut Manoach, Emil aut Ragulskis, Minvydas aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 107(2021), 1 vom: 13. Nov., Seite 247-267 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:107 year:2021 number:1 day:13 month:11 pages:247-267 https://doi.org/10.1007/s11071-021-07000-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT AR 107 2021 1 13 11 247-267
allfieldsGer	10.1007/s11071-021-07000-2 doi (DE-627)OLC2077712686 (DE-He213)s11071-021-07000-2-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Li, Dayang verfasserin aut Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution Cao, Maosen aut Manoach, Emil aut Ragulskis, Minvydas aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 107(2021), 1 vom: 13. Nov., Seite 247-267 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:107 year:2021 number:1 day:13 month:11 pages:247-267 https://doi.org/10.1007/s11071-021-07000-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT AR 107 2021 1 13 11 247-267
allfieldsSound	10.1007/s11071-021-07000-2 doi (DE-627)OLC2077712686 (DE-He213)s11071-021-07000-2-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Li, Dayang verfasserin aut Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution Cao, Maosen aut Manoach, Emil aut Ragulskis, Minvydas aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 107(2021), 1 vom: 13. Nov., Seite 247-267 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:107 year:2021 number:1 day:13 month:11 pages:247-267 https://doi.org/10.1007/s11071-021-07000-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT AR 107 2021 1 13 11 247-267
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author	Li, Dayang
spellingShingle	Li, Dayang ddc 510 ssgn 11 misc Nonlinear oscillation misc Large amplitude vibration misc Modified line spring model misc Hardening nonlinear frequency response misc Bifurcations misc Chaotic dynamics misc Damage characterization misc Crack evolution Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
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topic_title	510 VZ 11 ssgn Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads Nonlinear oscillation Large amplitude vibration Modified line spring model Hardening nonlinear frequency response Bifurcations Chaotic dynamics Damage characterization Crack evolution
topic	ddc 510 ssgn 11 misc Nonlinear oscillation misc Large amplitude vibration misc Modified line spring model misc Hardening nonlinear frequency response misc Bifurcations misc Chaotic dynamics misc Damage characterization misc Crack evolution
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title	Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
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title_full	Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
author_sort	Li, Dayang
journal	Nonlinear dynamics
journalStr	Nonlinear dynamics
lang_code	eng
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author_browse	Li, Dayang Cao, Maosen Manoach, Emil Ragulskis, Minvydas
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doi_str_mv	10.1007/s11071-021-07000-2
dewey-full	510
title_sort	nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
title_auth	Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
abstract	Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. © The Author(s), under exclusive licence to Springer Nature B.V. 2021
abstractGer	Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. © The Author(s), under exclusive licence to Springer Nature B.V. 2021
abstract_unstemmed	Abstract This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics. © The Author(s), under exclusive licence to Springer Nature B.V. 2021
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title_short	Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads
url	https://doi.org/10.1007/s11071-021-07000-2
remote_bool	false
author2	Cao, Maosen Manoach, Emil Ragulskis, Minvydas
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doi_str	10.1007/s11071-021-07000-2
up_date	2024-07-03T16:56:53.572Z
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