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

doi:10.1007/s10483-015-1969-7

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (8): 1033-1044.doi: https://doi.org/10.1007/s10483-015-1969-7

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

A. G. ARANI^1,2, G. S. JAFARI¹

1. Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran;
2. Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan 87317-51167, Iran

收稿日期:2015-03-25 修回日期:2015-05-07 出版日期:2015-08-01 发布日期:2015-08-01
通讯作者: G. S. JAFARI E-mail:soleimani.kashan@gmail.com

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

A. G. ARANI^1,2, G. S. JAFARI¹

1. Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran;
2. Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan 87317-51167, Iran

Received:2015-03-25 Revised:2015-05-07 Online:2015-08-01 Published:2015-08-01
Contact: G. S. JAFARI E-mail:soleimani.kashan@gmail.com

摘要/Abstract

摘要：

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.

关键词: nonlinear vibration, differential quadrature method, orthotropic Pasternak medium, laminated micro-plate

Abstract:

Key words: nonlinear vibration, orthotropic Pasternak medium, differential quadrature method, laminated micro-plate

中图分类号:

O322

A. G. ARANI, G. S. JAFARI. Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 1033-1044.

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

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

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