In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To verify accuracy of Ritz method, differential transform method (DTM) also used to drive the size dependent natural frequencies of circular nano-plates. The validity of solutions was performed by comparing present results with those of the literature for both classical plate and nano plate. Effect of nonlocal parameter, mode number and taper parameter on the natural frequency are investigated. Results showed that taper parameter has significant effect on the non-dimensional frequency and its effects on the clamped boundary condition is more than simply support. تفاصيل المقالة

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. تفاصيل المقالة