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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Nonlinear Random Vibration of Micro-Beams Resting on Visco-Elastic Foundation via the Modified Couple Stress Theory

Journal of Applied Nonlinear Dynamics 12(4) (2023) 707--721 | DOI:10.5890/JAND.2023.12.006

Dang Van Hieu, Nguyen Thi Hoa

Department of Mechanics, Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of

Technology, Thainguyen, Vietnam

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Abstract

The aim of this paper is to present an analytical analysis of nonlinear random vibration behaviors of micro-beams resting on a visco-elastic foundation. The modif\`{i}ed couple stress theory and the Euler-Bernoulli beam theory (EBT) with the von-K\'{a}rm\'{a}n's geometrical nonlinearity are employed for this analysis. The equation of motion of the micro-beam is established based on the Hamilton's principle. The input excitation is assumed to be a Gaussian process with zero mean. The mean-square of the micro-beam's displacement is found by the regaluted equivalent linearization method. Comparison of the obtained solutions with the published solutions and the classical solutions shows the accuracy. The influences of the material length scale parameter (MLSP), the spectral density of the input excitation and the coefficients of the visco-elastic foundation on the nonlinear random vibration response of micro-beams are investigated in detail.

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