Journal
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
Volume 36, Issue 8, Pages 1033-1044Publisher
SHANGHAI UNIV
DOI: 10.1007/s10483-015-1969-7
Keywords
nonlinear vibration; laminated micro-plate; orthotropic Pasternak medium; differential quadrature method
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The nonlocal nonlinear vibration analysis of embedded laminated microplates resting on an elastic matrix as an orthotropic Pasternak medium is investigated. The small size effects of micro/nano-plate are considered based on the Eringen nonlocal theory. Based on the orthotropic Mindlin plate theory along with the von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. The differential quadrature method (DQM) is applied for obtaining the nonlinear frequency of system. The effects of different parameters such as nonlocal parameters, elastic media, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate. Results show that considering elastic medium increases the nonlinear frequency of system. Furthermore, the effect of boundary conditions becomes lower at higher nonlocal parameters.
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