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

Journal of Solid Mechanics

مقاله 13، دوره 10، شماره 4، اسفند 2018، صفحه 874-893   

نوع مقاله: Research Paper

نویسندگان

M Zarei^* ؛ Gh Rahimi

Department of Mechanical Engineering, Tarbiat Modares University (TMU), Tehran, Iran

چکیده

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.                      

کلیدواژه‌ها

Eringen’s theory؛ Free vibration؛ FGM nano-plate؛ Ritz method؛ Differential transform method

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