In this paper, the large-amplitude oscillation of a triple-well non-natural system, covering both qualitative and quantitative analysis, is investigated. The nonlinear system is governed by a quadratic velocity term and an odd-parity restoring force having cubic and quintic nonlinearities. Many mathematical models in mechanical and structural engineering applications can give rise to this nonlinear problem. In terms of qualitative analysis, the equilibrium points and its trajectories due to the change of the governing parameters are studied. It is interesting that there exist heteroclinic and homoclinic orbits under different equilibrium states. By adjusting the parameter values, the dynamic behavior of this conservative system is shifted accordingly. As exact solutions for this problem expressed in terms of an integral form must be solved numerically, an analytical approximation method can be used to construct accurate solutions to the oscillation around the stable equilibrium points of this system. This method is based on the harmonic balance method incorporated with Newton's method, in which a series of linear algebraic equations can be derived to replace coupled and complicated nonlinear algebraic equations. According to this harmonic balance-based approach, only the use of Fourier series expansions of known functions is required. Accurate analytical approximate solutions can be derived using lower order harmonic balance procedures. The proposed analytical method can offer good agreement with the corresponding numerical results for the whole range of oscillation amplitudes.
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September 2019
Research-Article
Analysis of Large-Amplitude Oscillations in Triple-Well Non-Natural Systems
S. K. Lai,
S. K. Lai
Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China;
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China;
The Hong Kong Polytechnic University
Shenzhen Research Institute,
Nanshan, Shenzhen 518057, China
e-mail: sk.lai@polyu.edu.hk
Shenzhen Research Institute,
Nanshan, Shenzhen 518057, China
e-mail: sk.lai@polyu.edu.hk
1Corresponding author.
Search for other works by this author on:
X. Yang,
X. Yang
Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China
Search for other works by this author on:
F. B. Gao
F. B. Gao
School of Mathematical Science,
Yangzhou University,
Yangzhou 225002, China;
Yangzhou University,
Yangzhou 225002, China;
Departament de Matemàtiques,
Universitat Autònoma de Barcelona,
Bellaterra, Barcelona 08193, Spain
Universitat Autònoma de Barcelona,
Bellaterra, Barcelona 08193, Spain
Search for other works by this author on:
S. K. Lai
Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China;
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China;
The Hong Kong Polytechnic University
Shenzhen Research Institute,
Nanshan, Shenzhen 518057, China
e-mail: sk.lai@polyu.edu.hk
Shenzhen Research Institute,
Nanshan, Shenzhen 518057, China
e-mail: sk.lai@polyu.edu.hk
X. Yang
Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China
Environmental Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon, Hong Kong, China
F. B. Gao
School of Mathematical Science,
Yangzhou University,
Yangzhou 225002, China;
Yangzhou University,
Yangzhou 225002, China;
Departament de Matemàtiques,
Universitat Autònoma de Barcelona,
Bellaterra, Barcelona 08193, Spain
Universitat Autònoma de Barcelona,
Bellaterra, Barcelona 08193, Spain
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 24, 2018; final manuscript received May 18, 2019; published online July 15, 2019. Assoc. Editor: Brian Feeny.
J. Comput. Nonlinear Dynam. Sep 2019, 14(9): 091002 (10 pages)
Published Online: July 15, 2019
Article history
Received:
March 24, 2018
Revised:
May 18, 2019
Citation
Lai, S. K., Yang, X., and Gao, F. B. (July 15, 2019). "Analysis of Large-Amplitude Oscillations in Triple-Well Non-Natural Systems." ASME. J. Comput. Nonlinear Dynam. September 2019; 14(9): 091002. https://doi.org/10.1115/1.4043833
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