Investigations of Stochastic Layers in Nonlinear Dynamics

[+] Author and Article Information
Albert C. J. Luo

Department of Mechanical & Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805

Ray P. S. Han

Department of Mechanical Engineering, University of Iowa, Iowa City, Iowa 52242-1527

J. Vib. Acoust 122(1), 36-41 (Aug 01, 1999) (6 pages) doi:10.1115/1.568439 History: Received August 01, 1999
Copyright © 2000 by ASME
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Grahic Jump Location
The first-order librational resonance in a stochastic layer in the periodically-driven pendulum (α=1, Ω=0.70, Q0=0.0375)
Grahic Jump Location
The excitation strength Q0 for the onset of a new resonance in the librational layer (upper) and the rotational layer (lower) in the periodically driven-pendulum at α=1 through the incremental energy. –(analytic), -○-○- (numerical).
Grahic Jump Location
Poincaré mapping section for the stochastic layer: the second-order resonance in the inner layer and the fifth-order resonance in the outer layer (Ω=1.8, Q0=0.01,α12=1)
Grahic Jump Location
Strengths of excitation for inner layer (upper) and outer layer (lower) of the Duffing oscillator (α12=1). -□-□- (Chirikov overlap), -▵-▵- (renormalization), -○-○- (numerical)
Grahic Jump Location
Excitation strength for the inner layer (upper) with max|Eα−E0|=0.055 and the outer layer (lower) with max|Eβ−E0|=0.076 in the Duffing oscillator (α12=1.0) through the standard maps. –(accurate), –⋅⋅–⋅ (approximate), -○-○- (numerical)
Grahic Jump Location
Excitation strength for the inner layer (upper) with maxα|Eα−E0|=0.055 and the outer layer (lower) with maxβ|Eβ−E0|=0.076 in the Duffing oscillator α12=1.0 through the incremental energy approach. –(analytic), -○-○- (numerical)
Grahic Jump Location
Minimum and maximum energy spectra for the stochastic layer in the twin-well Duffing oscillator at Q0=0.2 and α12=1.0



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