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Bifurcations and chaotic thresholds for the spring-pendulum oscillator with irrational and fractional nonlinear restoring forces

Bifurcations and chaotic thresholds for the spring-pendulum oscillator with irrational and fractional nonlinear restoring forces
Bifurcations and chaotic thresholds for the spring-pendulum oscillator with irrational and fractional nonlinear restoring forces
Nonlinear dynamical systems with irrational and fractional nonlinear restoring forces often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational and fractional nonlinear restoring forces avoiding the conventional Taylor’s expansion to retain the natural characteristics of the system. By introducing a particular dimensionless representation and a series of transformations, the two-degree-of-freedom system can be transformed into a perturbed Hamiltonian system. The extended Melnikov method is directly used to detect the chaotic threshold of the perturbed system theoretically, which overcomes the barrier caused by solving theoretical solution for the homoclinic orbit of the unperturbed system. The numerical simulations are carried out to demonstrate the complicated dynamics of the nonlinear spring-pendulum system, which show the efficiency of the criteria for chaotic motion in the system.



2190-5444
1-12
Ruilan, Tian
e328e71b-26d2-449c-ab0c-6107be3ce096
Qiliang, Wu
314d727e-e08b-47c3-84ef-afbd23b9cb10
Yeping, Xiong
51be8714-186e-4d2f-8e03-f44c428a4a49
Xinwei, Yang
89a3fd9f-5fed-48c1-b77b-a12e908a206a
Ruilan, Tian
e328e71b-26d2-449c-ab0c-6107be3ce096
Qiliang, Wu
314d727e-e08b-47c3-84ef-afbd23b9cb10
Yeping, Xiong
51be8714-186e-4d2f-8e03-f44c428a4a49
Xinwei, Yang
89a3fd9f-5fed-48c1-b77b-a12e908a206a

Ruilan, Tian, Qiliang, Wu, Yeping, Xiong and Xinwei, Yang (2014) Bifurcations and chaotic thresholds for the spring-pendulum oscillator with irrational and fractional nonlinear restoring forces. The European Physical Journal Plus, 129 (85), 1-12. (doi:10.1140/epjp/i2014-14085-3).

Record type: Article

Abstract

Nonlinear dynamical systems with irrational and fractional nonlinear restoring forces often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational and fractional nonlinear restoring forces avoiding the conventional Taylor’s expansion to retain the natural characteristics of the system. By introducing a particular dimensionless representation and a series of transformations, the two-degree-of-freedom system can be transformed into a perturbed Hamiltonian system. The extended Melnikov method is directly used to detect the chaotic threshold of the perturbed system theoretically, which overcomes the barrier caused by solving theoretical solution for the homoclinic orbit of the unperturbed system. The numerical simulations are carried out to demonstrate the complicated dynamics of the nonlinear spring-pendulum system, which show the efficiency of the criteria for chaotic motion in the system.



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Published date: May 2014
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 365465
URI: http://eprints.soton.ac.uk/id/eprint/365465
ISSN: 2190-5444
PURE UUID: e6898cac-8758-494d-96f5-328e7b9d74d5
ORCID for Xiong Yeping: ORCID iD orcid.org/0000-0002-0135-8464

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Date deposited: 05 Jun 2014 10:44
Last modified: 20 Jul 2019 01:07

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Contributors

Author: Tian Ruilan
Author: Wu Qiliang
Author: Xiong Yeping ORCID iD
Author: Yang Xinwei

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