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Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates

Published online by Cambridge University Press:  04 April 2016

R. Ansari ,
R. Gholami  and
A. Shahabodini
R. Ansari*
Affiliation:
Department of Mechanical Engineering University of Guilan Rasht, Iran
R. Gholami*
Affiliation:
Department of Mechanical Engineering Lahijan Branch Islamic Azad University Lahijan, Iran
A. Shahabodini
Affiliation:
Department of Mechanical Engineering University of Guilan Rasht, Iran
*
**Corresponding author (r_ansari@guilan.ac.ir)
*Corresponding author (gholami_r@liau.ac.ir)
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Abstract

In this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

Keywords

Nonlinear forced vibration of FG microplateModified couple stress theoryGDQPseudoarc length method
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 539 - 554
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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