Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form
The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived f...
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Gespeichert in:
| Autor*in: |
Mohamadi, Arash [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021transfer abstract |
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| Übergeordnetes Werk: |
Enthalten in: Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation - Malki, Mounia ELSEVIER, 2018, Amsterdam |
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| Übergeordnetes Werk: |
volume:134 ; year:2021 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.ijnonlinmec.2021.103733 |
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| 520 | |a The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. | ||
| 520 | |a The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. | ||
| 650 | 7 | |a Nonlinear vibration |2 Elsevier | |
| 650 | 7 | |a Bifurcation analysis |2 Elsevier | |
| 650 | 7 | |a Normal form |2 Elsevier | |
| 650 | 7 | |a Nanocomposite shell |2 Elsevier | |
| 700 | 1 | |a Ashenai Ghasemi, Faramarz |4 oth | |
| 700 | 1 | |a Shahgholi, Majid |4 oth | |
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10.1016/j.ijnonlinmec.2021.103733 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001419.pica (DE-627)ELV054368812 (ELSEVIER)S0020-7462(21)00067-6 DE-627 ger DE-627 rakwb eng 530 VZ 51.32 bkl Mohamadi, Arash verfasserin aut Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. Nonlinear vibration Elsevier Bifurcation analysis Elsevier Normal form Elsevier Nanocomposite shell Elsevier Ashenai Ghasemi, Faramarz oth Shahgholi, Majid oth Enthalten in Elsevier Science Malki, Mounia ELSEVIER Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation 2018 Amsterdam (DE-627)ELV001315986 volume:134 year:2021 pages:0 https://doi.org/10.1016/j.ijnonlinmec.2021.103733 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.32 Werkstoffmechanik VZ AR 134 2021 0 |
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10.1016/j.ijnonlinmec.2021.103733 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001419.pica (DE-627)ELV054368812 (ELSEVIER)S0020-7462(21)00067-6 DE-627 ger DE-627 rakwb eng 530 VZ 51.32 bkl Mohamadi, Arash verfasserin aut Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. Nonlinear vibration Elsevier Bifurcation analysis Elsevier Normal form Elsevier Nanocomposite shell Elsevier Ashenai Ghasemi, Faramarz oth Shahgholi, Majid oth Enthalten in Elsevier Science Malki, Mounia ELSEVIER Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation 2018 Amsterdam (DE-627)ELV001315986 volume:134 year:2021 pages:0 https://doi.org/10.1016/j.ijnonlinmec.2021.103733 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.32 Werkstoffmechanik VZ AR 134 2021 0 |
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10.1016/j.ijnonlinmec.2021.103733 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001419.pica (DE-627)ELV054368812 (ELSEVIER)S0020-7462(21)00067-6 DE-627 ger DE-627 rakwb eng 530 VZ 51.32 bkl Mohamadi, Arash verfasserin aut Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. Nonlinear vibration Elsevier Bifurcation analysis Elsevier Normal form Elsevier Nanocomposite shell Elsevier Ashenai Ghasemi, Faramarz oth Shahgholi, Majid oth Enthalten in Elsevier Science Malki, Mounia ELSEVIER Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation 2018 Amsterdam (DE-627)ELV001315986 volume:134 year:2021 pages:0 https://doi.org/10.1016/j.ijnonlinmec.2021.103733 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.32 Werkstoffmechanik VZ AR 134 2021 0 |
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10.1016/j.ijnonlinmec.2021.103733 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001419.pica (DE-627)ELV054368812 (ELSEVIER)S0020-7462(21)00067-6 DE-627 ger DE-627 rakwb eng 530 VZ 51.32 bkl Mohamadi, Arash verfasserin aut Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. Nonlinear vibration Elsevier Bifurcation analysis Elsevier Normal form Elsevier Nanocomposite shell Elsevier Ashenai Ghasemi, Faramarz oth Shahgholi, Majid oth Enthalten in Elsevier Science Malki, Mounia ELSEVIER Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation 2018 Amsterdam (DE-627)ELV001315986 volume:134 year:2021 pages:0 https://doi.org/10.1016/j.ijnonlinmec.2021.103733 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.32 Werkstoffmechanik VZ AR 134 2021 0 |
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10.1016/j.ijnonlinmec.2021.103733 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001419.pica (DE-627)ELV054368812 (ELSEVIER)S0020-7462(21)00067-6 DE-627 ger DE-627 rakwb eng 530 VZ 51.32 bkl Mohamadi, Arash verfasserin aut Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form 2021transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. Nonlinear vibration Elsevier Bifurcation analysis Elsevier Normal form Elsevier Nanocomposite shell Elsevier Ashenai Ghasemi, Faramarz oth Shahgholi, Majid oth Enthalten in Elsevier Science Malki, Mounia ELSEVIER Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation 2018 Amsterdam (DE-627)ELV001315986 volume:134 year:2021 pages:0 https://doi.org/10.1016/j.ijnonlinmec.2021.103733 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.32 Werkstoffmechanik VZ AR 134 2021 0 |
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Enthalten in Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation Amsterdam volume:134 year:2021 pages:0 |
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Enthalten in Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation Amsterdam volume:134 year:2021 pages:0 |
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Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation |
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The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. 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Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation |
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Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation |
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forced nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form |
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Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form |
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The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. |
| abstractGer |
The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. |
| abstract_unstemmed |
The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton principle in cylindrical coordinate employing a classical nonlinear shell theory. The considered 1:1 internal resonance between asymmetric driven and companion vibration modes profoundly influences the frequency responses’ nonlinear characteristics. Then by the aids of the Airy stress function and the Galerkin method, the motion equations turn into several nonlinear nonhomogeneous ODEs. Finally, the bifurcation analysis is carried out based on various parameters using the normal form method. Three stable, unstable, and quasi-period regions concerning the locations of saddle nodes, pitchfork bifurcation, and torus points at the limit cycle around the resonance condition would differ due to change the structure of the nanocomposite shells, viscous damping coefficient, and the amplitude of the concentrated external force. The perturbation method’s accuracy is compared against the Runge–Kutta 4th order method’s results validated by available data. |
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Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form |
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