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STOCHASTIC AVERAGING OF STRONGLY NON-LINEAR OSCILLATORS UNDER COMBINED HARMONIC AND WHITE-NOISE EXCITATIONS

โœ Scribed by Z.L. HUANG; W.Q. ZHU; Y. SUZUKI

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
662 KB
Volume
238
Category
Article
ISSN
0022-460X

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โœฆ Synopsis

A stochastic averaging procedure of strongly non-linear oscillators subject to external and (or) parametric excitations of both harmonic and white-noise forces is developed by using the so-called generalized harmonic functions. The procedure is applied to a Du$ng oscillator with hardening sti!ness under both external harmonic excitation and external and parametric excitations of white noises. The averaged Fokker}Planck}Kolmogrov equation is solved by using the path integration method. Based on the stationary joint probability density of amplitude and phase obtained by using the stochastic averaging and the path integration, the stochastic jump of the Du$ng oscillator under combined harmonic and white-noise excitations and its bifurcation as the system parameters (frequency ratio, strength of the non-linearity, amplitude of harmonic excitation and intensity of white noise) change are examined for the "rst time.

2000 Academic Press

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Non-linear oscillators under harmonic and/or weak stochastic excitations are considered in this paper. Under harmonic excitations alone, an analytical technique based on a set of exponential transformations followed by harmonic balancing is proposed to solve for a variety of one-periodic orbits. The