Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142315
Title: Frequency equations of nonlocal elastic micro/nanobeams with the consideration of the surface effects
Authors: Zhao, Haisheng
Zhang, Yao
Lie, Seng Tjhen
Keywords: Engineering::Civil engineering
Issue Date: 2018
Source: Zhao, H., Zhang, Y., & Lie, S. T. (2018). Frequency equations of nonlocal elastic micro/nanobeams with the consideration of the surface effects. Applied Mathematics and Mechanics, 39(8), 1089–1102. doi:10.1007/s10483-018-2358-6
Journal: Applied Mathematics and Mechanics
Abstract: A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia, in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.
URI: https://hdl.handle.net/10356/142315
ISSN: 0253-4827
DOI: 10.1007/s10483-018-2358-6
Rights: © 2018 Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:CEE Journal Articles

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