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Dynamics of Systems with Randomly Disordered Periodic Excitations

  • M. Dimentberg
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

A model of a periodic process with random phase modulation, or disorder, is described. It can be easily incorporated into Stochastic Differential Equations Calculus, thereby providing potential for analytical solution to dynamic problems where it represents the forcing function, or excitation. Thus, the corresponding method of moments had been applied to a linear system subject to external and parametric excitation with preliminary reduction of the equation of motion by asymptotic stochastic averaging in the latter case; boundaries for parametric instability had been derived both in the mean square and in the almost sure sense. Solution for a strongly nonlinear system with impacts had also been obtained illustrating potentially strong influence of imperfect periodicity of excitation on response subharmonics. Examples of application from engineering mechanics are presented.

Keywords

Bounded noise Non-Gaussian processes Stochastic differential equations Stochastic mechanics Engineering mechanics Parametric resonance Subharmonics 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringWorcester Polytechnic InstituteWorcesterUSA

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