Free Axisymmetric Bending Vibration Analysis of two Directional FGM Circular Nano-plate on the Elastic Foundation

Subject Areas : Engineering

M Zarei ¹ (Department of Mechanical Engineering, Tarbiat Modares University (TMU), Tehran, Iran)
Gh Rahimi ² (Department of Mechanical Engineering, Tarbiat Modares University (TMU), Tehran, Iran)

Received: 2018-08-03 Accepted : 2018-10-05 Published : 2018-12-30

Keywords: Free vibration, Differential transform method, Ritz method, Eringen’s theory, FGM nano-plate,

Abstract :

In the following paper, free vibration analysis of two directional FGM circular nano-plate on the elastic medium is investigated. The elastic modulus of plate varies in both radial and thickness directions. Eringen’s theory was employed to the analysis of circular nano-plate with variation in material properties. Simultaneous variations of the material properties in the radial and transverse directions are described by a general function. Ritz functions were utilized to obtain the frequency equations for simply supported and clamped boundary. Differential transform method also used to develop a semi-analytical solution the size-dependent natural frequencies of non-homogenous nano-plates. Both methods reported good results. The validity of solutions was performed by comparing present results with themselves and those of the literature for both classical plate and nano-plate. Effect of non-homogeneity on the nonlocal parameter, geometries, boundary conditions and elastic foundation parameters is examined the paper treats some interesting problems, for the first time.

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