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

  • Guo-Kang ErEmail author
  • Vai Pan Iu
  • Kun Wang
  • Hai-En Du
Conference paper
Part of the IUTAM Bookseries book series (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.

Keywords

Stretched beam Nonlinear random vibration FPK equation MDOF system Finite difference SSS-EPC method 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of MacauMacau SARPeople’s Republic of China

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