An Accurate Standard Mapping Method for Stochastic Layers in Nonlinear Hamiltonian Systems

Article type: Research Article

Authors: Luo, Albert C.J.^{; 1}

Affiliations: Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA

Correspondence: [1] Address for Correspondence: Dr. Albert C.J. Luo Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805. Tel: (618) 650-5389. Fax: (618) 650-2555. Email: [email protected].

Abstract: An accurate standard mapping approach based on the exact period and energy approximations is developed for prediction of the onset of a new resonance in the stochastic layer. This accurate approach applies to the twin-well Duffing oscillator and a parametrically excited pendulum for prediction of the resonant characteristics in stochastic layers as sample problems. From examples, this accurate approach gives a better prediction than the approximate method, compared to numerical results.

Keywords: Standard mapping method, Stochastic layer, Nonlinear Hamiltonian systems, Resonance

Keywords: 37D45, 37C10, 37J40, 37J35

DOI: 10.3233/JCM-2003-3104

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 1, pp. 41-53, 2003