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Probabilistic Solutions of the Stretched Beam Systems Formulated by Finite Difference Scheme and Excited by Gaussian White Noise
Er, G. K.; Iu, V. P.; Wang, K.; Du, H. N.
2019-02-01
Source PublicationIUTAM Symposium on Intelligent Multibody Systems - Dynamics, Control, Simulation
PublisherSpringer
Pages99-114
Abstract

The probabilistic solutions of elastic stretched beams are studied when the beam is discretized by finite difference scheme and excited by Gaussian white noise which is fully correlated in space. The nonlinear multi-degree-offreedom system about the random vibration of stretched beam is formulated by finite difference scheme first. Then the relevant Fokker-Planck-Kolmogorov equation is solved for the probabilistic solutions of the system by the state-spacesplit and exponential polynomial closure method. Monte Carlo simulation method and equivalent linearization method are also adopted to analyze the probabilistic solutions of the system responses, respectively. Numerical results obtained with the three methods are presented and compared to show the computational efficiency and numerical accuracy of solving the Fokker-Planck-Kolmogorov equation by the state-space-split and exponential polynomial closure method in analyzing the probabilistic solutions of the beams discretized by finite difference scheme and excited by Gaussian white noise. The techniques of using the state-space-split procedure for dimension reduction of the beam systems are discussed through the given beam systems with different space distributions of excitations.

KeywordStretched Beam Nonlinear Random Vibration Fpk Equation Mdof System Finite Difference Sss-epc Method
DOI10.1007/978-3-030-00527-6_5
URLView the original
Language英語English
ISBN9783030005276
The Source to ArticlePB_Publication
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeBook chapter
CollectionDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
Faculty of Science and Technology
Corresponding AuthorEr, G. K.
Recommended Citation
GB/T 7714
Er, G. K.,Iu, V. P.,Wang, K.,et al. Probabilistic Solutions of the Stretched Beam Systems Formulated by Finite Difference Scheme and Excited by Gaussian White Noise:Springer,2019:99-114.
APA Er, G. K.,Iu, V. P.,Wang, K.,&Du, H. N..(2019).Probabilistic Solutions of the Stretched Beam Systems Formulated by Finite Difference Scheme and Excited by Gaussian White Noise.IUTAM Symposium on Intelligent Multibody Systems - Dynamics, Control, Simulation,99-114.
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