Postbuckling and free nonlinear vibration of microbeams based on nonlinear elastic foundation
type: Item
instance of: scholarly article
title: Postbuckling and free nonlinear vibration of microbeams based on nonlinear elastic foundation
zbMATH Open document ID: 1426.74153
DOI: 10.1155/2018/1031237
author: Dang Van Hieu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: In this paper, post-buckling and free nonlinear vibration of microbeams resting on nonlinear elastic foundation subjected to axial force are investigated. The equations of motion of microbeams are derived by using the modified couple stress theory. Using Galerkin's method, the equation of motion of microbeams is reduced to the nonlinear ordinary differential equation. By using the equivalent linearization in which the averaging value is calculated in a new way called the weighted averaging value, approximate analytical expressions for the nonlinear frequency of microbeams with pinned-pinned and clamped-clamped end conditions are obtained in closed-forms. Comparisons with previous solutions are showed accuracy of the present solutions. Effects of the material length scale parameter and the axial compressive force on the frequency ratios of microbeams; and effect of the material length scale parameter on the buckling load ratios of microbeams are investigated in this paper.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 7018444
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1031237
OpenAlex ID: W2898725448
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Wikidata QID: Q129009572
description: scientific article; zbMATH DE number 7018444