NDLI: Transient response of nonlinear vibro-impact system under Gaussian white noise excitation through complex fractional moments

Content Provider	Springer Nature Link
Author	Xie, Xiufeng Li, Junlin Liu, Di Guo, Rong
Copyright Year	2016
Abstract	The approximate transient response of a nonlinear vibro-impact system under Gaussian white noise excitation is investigated by the methods of stochastic averaging and the Mellin transform. The Zhuravlev nonsmooth transformation is utilized to convert the nonlinear vibro-impact system into an equivalent system without velocity jumps by introducing an impulsive damping term. The Itô stochastic differential equation with respect to the amplitude response and the related Fokker–Plank–Kolmogorov (FPK) equation governing the amplitude response probability density of the vibro-impact system are derived with the stochastic averaging method. The Mellin transform is introduced to solve the FPK equation. The differential relations of complex fractional moments are obtained. The probability density function for transient response of this system constructed by solving a set of differential equations yields complex fractional moments. Two illustrative examples are examined to evaluate the effectiveness of the proposed solution procedure. The effects of restitution factors are investigated on the transient probability density distribution of the vibro-impact systems. At the same time, the convergence and the error analyses for different restitution factors are illustrated. Influences of the truncate term on the convergence and the error are further illustrated. The results obtained from the proposed procedure agree well with the results from Monte Carlo simulations.
Starting Page	1153
Ending Page	1163
Page Count	11
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	228
Issue Number	3
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2016-11-22
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical and Applied Mechanics Classical and Continuum Physics Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Thermodynamics, Heat and Mass Transfer
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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