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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1033–1044 | Cite as

Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM

  • A. G. Arani
  • G. S. JafariEmail author
Article

Abstract

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 Kármán 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.

Keywords

nonlinear vibration laminated micro-plate orthotropic Pasternak medium differential quadrature method 

Chinese Library Classification

O322 

2010 Mathematics Subject Classification

74K20 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of KashanKashanIran
  2. 2.Institute of Nanoscience & NanotechnologyUniversity of KashanKashanIran

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