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Probabilistic Solutions of the Stretched Beam Systems Formulated by Finite Difference Scheme and Excited by Gaussian White Noise

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IUTAM Symposium on Intelligent Multibody Systems – Dynamics, Control, Simulation

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 33))

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-of-freedom 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-space-split 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.

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Acknowledgement

The results presented in this paper were obtained under the supports of the Science and Technology Development Fund of Macau (Grant No. 042/2017/A1) and the Research Committee of University of Macau (Grant No. MYRG2018-00116-FST).

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Authors and Affiliations

  1. University of Macau, Macau SAR, People’s Republic of China

    Guo-Kang Er, Vai Pan Iu, Kun Wang & Hai-En Du

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  1. Guo-Kang Er
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  2. Vai Pan Iu
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  3. Kun Wang
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  4. Hai-En Du
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Correspondence to Guo-Kang Er .

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Editors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Evtim Zahariev

  2. Laboratory of Mechanical Engineering, University of La Coruña, Ferrol, Spain

    Javier Cuadrado

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Er, GK., Iu, V.P., Wang, K., Du, HE. (2019). Probabilistic Solutions of the Stretched Beam Systems Formulated by Finite Difference Scheme and Excited by Gaussian White Noise. In: Zahariev, E., Cuadrado, J. (eds) IUTAM Symposium on Intelligent Multibody Systems – Dynamics, Control, Simulation. IUTAM Bookseries, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-00527-6_5

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  • DOI: https://doi.org/10.1007/978-3-030-00527-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00526-9

  • Online ISBN: 978-3-030-00527-6

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