Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Authors

  • Hien Ta Duy University of Transport and Communications, Vietnam
  • Nguyen Dang Diem Campus in Ho Chi Minh City, University of Transport and Communications, Vietnam
  • Giap Van Tan Hanoi Architectural University, Vietnam
  • Vu Van Hiep University of Transport and Communications, Vietnam
  • Nguyen Van Thuan Nha Trang University, Vietnam
Volume: 13 | Issue: 1 | Pages: 9985-9990 | February 2023 | https://doi.org/10.48084/etasr.5456

Abstract

This paper deals with a continuous beam resting on elastic support with elastic modulus derived from a random process. Governing equations of the stochastic higher-order finite element method of the free vibration of the continuous beam were derived from Hamilton's principle. The random process of elastic modulus was discretized by averaging random variables in each element. A solution for the stochastic eigenvalue problem for the free vibration of the continuous beam was obtained by using the perturbation technique, in conjunction with the finite element method. Spectral representation was used to generate a random process and employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

Keywords:

SFEM, free vibration, continuous beam, random field

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[1]
H. Ta Duy, N. D. Diem, G. V. Tan, V. V. Hiep, and N. V. Thuan, “Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus”, Eng. Technol. Appl. Sci. Res., vol. 13, no. 1, pp. 9985–9990, Feb. 2023.

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