Self-sustained vibrations in the system of a bi-harmonically driven pendulum
In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, sl...
Ausführliche Beschreibung
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| Autor*in: |
Shaginyan, Sh.A. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Transient response and failure of medium density fibreboard panels subjected to air-blast loading - Langdon, G.S. ELSEVIER, 2021, Amsterdam |
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| Übergeordnetes Werk: |
volume:428 ; year:2022 ; day:14 ; month:03 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.physleta.2022.127943 |
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ELV056703511 |
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| 520 | |a In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. | ||
| 520 | |a In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. | ||
| 650 | 7 | |a Damped-driven pendulum |2 Elsevier | |
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| 650 | 7 | |a Semi-inverse approach |2 Elsevier | |
| 650 | 7 | |a Self-sustained vibrations |2 Elsevier | |
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| 700 | 1 | |a Kovaleva, M.A. |4 oth | |
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10.1016/j.physleta.2022.127943 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001664.pica (DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 DE-627 ger DE-627 rakwb eng 670 VZ 51.75 bkl Shaginyan, Sh.A. verfasserin aut Self-sustained vibrations in the system of a bi-harmonically driven pendulum 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. Damped-driven pendulum Elsevier Bi-harmonic forcing Elsevier Semi-inverse approach Elsevier Self-sustained vibrations Elsevier Manevitch, L.I. oth Kovaleva, M.A. oth Enthalten in North-Holland Publ Langdon, G.S. ELSEVIER Transient response and failure of medium density fibreboard panels subjected to air-blast loading 2021 Amsterdam (DE-627)ELV006407811 volume:428 year:2022 day:14 month:03 pages:0 https://doi.org/10.1016/j.physleta.2022.127943 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.75 Verbundwerkstoffe Schichtstoffe VZ AR 428 2022 14 0314 0 |
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10.1016/j.physleta.2022.127943 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001664.pica (DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 DE-627 ger DE-627 rakwb eng 670 VZ 51.75 bkl Shaginyan, Sh.A. verfasserin aut Self-sustained vibrations in the system of a bi-harmonically driven pendulum 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. Damped-driven pendulum Elsevier Bi-harmonic forcing Elsevier Semi-inverse approach Elsevier Self-sustained vibrations Elsevier Manevitch, L.I. oth Kovaleva, M.A. oth Enthalten in North-Holland Publ Langdon, G.S. ELSEVIER Transient response and failure of medium density fibreboard panels subjected to air-blast loading 2021 Amsterdam (DE-627)ELV006407811 volume:428 year:2022 day:14 month:03 pages:0 https://doi.org/10.1016/j.physleta.2022.127943 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.75 Verbundwerkstoffe Schichtstoffe VZ AR 428 2022 14 0314 0 |
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10.1016/j.physleta.2022.127943 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001664.pica (DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 DE-627 ger DE-627 rakwb eng 670 VZ 51.75 bkl Shaginyan, Sh.A. verfasserin aut Self-sustained vibrations in the system of a bi-harmonically driven pendulum 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. Damped-driven pendulum Elsevier Bi-harmonic forcing Elsevier Semi-inverse approach Elsevier Self-sustained vibrations Elsevier Manevitch, L.I. oth Kovaleva, M.A. oth Enthalten in North-Holland Publ Langdon, G.S. ELSEVIER Transient response and failure of medium density fibreboard panels subjected to air-blast loading 2021 Amsterdam (DE-627)ELV006407811 volume:428 year:2022 day:14 month:03 pages:0 https://doi.org/10.1016/j.physleta.2022.127943 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.75 Verbundwerkstoffe Schichtstoffe VZ AR 428 2022 14 0314 0 |
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10.1016/j.physleta.2022.127943 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001664.pica (DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 DE-627 ger DE-627 rakwb eng 670 VZ 51.75 bkl Shaginyan, Sh.A. verfasserin aut Self-sustained vibrations in the system of a bi-harmonically driven pendulum 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. Damped-driven pendulum Elsevier Bi-harmonic forcing Elsevier Semi-inverse approach Elsevier Self-sustained vibrations Elsevier Manevitch, L.I. oth Kovaleva, M.A. oth Enthalten in North-Holland Publ Langdon, G.S. ELSEVIER Transient response and failure of medium density fibreboard panels subjected to air-blast loading 2021 Amsterdam (DE-627)ELV006407811 volume:428 year:2022 day:14 month:03 pages:0 https://doi.org/10.1016/j.physleta.2022.127943 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.75 Verbundwerkstoffe Schichtstoffe VZ AR 428 2022 14 0314 0 |
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10.1016/j.physleta.2022.127943 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001664.pica (DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 DE-627 ger DE-627 rakwb eng 670 VZ 51.75 bkl Shaginyan, Sh.A. verfasserin aut Self-sustained vibrations in the system of a bi-harmonically driven pendulum 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. Damped-driven pendulum Elsevier Bi-harmonic forcing Elsevier Semi-inverse approach Elsevier Self-sustained vibrations Elsevier Manevitch, L.I. oth Kovaleva, M.A. oth Enthalten in North-Holland Publ Langdon, G.S. ELSEVIER Transient response and failure of medium density fibreboard panels subjected to air-blast loading 2021 Amsterdam (DE-627)ELV006407811 volume:428 year:2022 day:14 month:03 pages:0 https://doi.org/10.1016/j.physleta.2022.127943 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.75 Verbundwerkstoffe Schichtstoffe VZ AR 428 2022 14 0314 0 |
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Transient response and failure of medium density fibreboard panels subjected to air-blast loading |
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Self-sustained vibrations in the system of a bi-harmonically driven pendulum |
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(DE-627)ELV056703511 (ELSEVIER)S0375-9601(22)00025-1 |
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Self-sustained vibrations in the system of a bi-harmonically driven pendulum |
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Shaginyan, Sh.A. |
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Transient response and failure of medium density fibreboard panels subjected to air-blast loading |
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Transient response and failure of medium density fibreboard panels subjected to air-blast loading |
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Shaginyan, Sh.A. |
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Elektronische Aufsätze |
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Shaginyan, Sh.A. |
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10.1016/j.physleta.2022.127943 |
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670 |
| title_sort |
self-sustained vibrations in the system of a bi-harmonically driven pendulum |
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Self-sustained vibrations in the system of a bi-harmonically driven pendulum |
| abstract |
In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. |
| abstractGer |
In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. |
| abstract_unstemmed |
In this paper, we investigate self-sustained oscillations in a weakly damped pendulum system under the action of two harmonic forces with close frequencies. With no limitations on the amplitude of oscillations, we construct an asymptotic procedure; separating the dynamics of the system into fast, slow, and super-slow timescales, we show that the movements of the pendulum on the fast and slow scales are decoupled. The system of equations for the amplitude of the envelope and the phase of the state function in the leading approximation on a slow scale become autonomous when the super-slow time parameter depends rather weakly on slow time. Using this technique, it is possible to analyse relaxation oscillations in a wide frequency range along with their dependence on the friction coefficient. The results obtained are in good agreement with the numerical solution of the original system. |
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| title_short |
Self-sustained vibrations in the system of a bi-harmonically driven pendulum |
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https://doi.org/10.1016/j.physleta.2022.127943 |
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Manevitch, L.I. Kovaleva, M.A. |
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Manevitch, L.I. Kovaleva, M.A. |
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