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Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

# International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2018026293
pages 163-186

## FREE VIBRATION PROPERTY ANALYSIS OF COMPOSITE LAMINATED MICROPLATES BASED ON DIFFERENT HYPOTHESES IN COUPLE STRESS CONSTITUTIVE EQUATIONS

Shengqi Yang
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China
Shutian Liu
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

### Краткое описание

The free vibration property of composite laminated microplates is analyzed analytically and numerically based on two kinds of couple stress plate models. The laminated microplates are composed of orthotropic plies with different ply angles which are modeled as orthotropic couple stress media. The two kinds of plates models are called as the Simplifiedmodel which is based on simplification hypotheses on the rotation and curvatures (ωz = 0, χxz =0, χyz = 0) in couple stress constitutive equations, and the Complete model without any hypotheses. Hamilton principle is employed to derive the governing equations of free vibration based on the hypotheses on the rotation and/or the curvatures in the couple stress theory and the assumption on the displacements in the plate theory. A kind of finite element is constructed for couple stress microplates, and its convergence and precision are verified through typical examples. Solutions for typical examples with different boundary conditions are obtained in closed form using Navier’s technique and by solving the eigenvalue equation, and/or by the finite element method. The application scope of the Simplified model is investigated through comparing the results with the Complete model’s. It is noted that, although the simplified model can give accurate free vibration modes for Kirchhoff and Mindlin plates, but for Reddy plates, large errors may occur. Thus, it is needed to use the complete model for free vibration analysis of high order theory of microplates.