M. H. Yas, M. Nejati, S. S. Jafari,
Volume 35, Issue 2 (2-2017)
Abstract
In this paper, free vibration of carbon nanotube-reinforced functionally graded circular plates with hole has been
investigated. Distribution of carbon nanotubes are continuous and the gradual and graded changes of materials through the
plate thickness are considered as volume fraction. Considering the linear and non-linear variation of circular plates through the
radial direction and also considering the proposed function for the thickness, the plate thickness can be convex or concave.
Moreover, the motion equations of plate were obtained based on the third-order shear deformation theory. These equations are
coupled differential equations which can convert Ordinary Differential Equations (ODE) using the Trigonometric series
expansion of displacement fields such that they satisfy the axial symmetry condition. Solving the converted ODE equations is too
difficult. For this reason, the differential quadrature method is employed to solve these equations. The obtained results are
compared with the results reported by other researchers and an excellent agreement is observed between them. Finally, the effects
of different geometric parameters as well as different volume fracture of nanotubes on natural frequency have been studied.
M. Mohieddin Ghomshei, Sh. Namazi,
Volume 41, Issue 1 (9-2022)
Abstract
In this article, mechanical buckling analysis of tapered beams having constant width and variable thickness, made of two-dimensional functionally graded materials is studied. The beam is assumed to be made of metal and ceramic, where their volume fractions vary in both longitudinal and thickness directions based on the power law. The beam is generally subjected to combined concentrated and distributed axial loads. The set of governing equations are derived using the Principle of Minimum total Potential Energy (PMPE), and are solved numerically using Differential Quadrature Method (DQM) for clamped-free boundary conditions. Convergence and accuracy of the presented solution are confirmed for both cases of concentrated and distributed axial loads. The effects of different parameters on the critical buckling load of the beam for both load cases are studied including geometrical parameters, gradation indices in longitudinal and thickness directions, and variation of thickness. Also buckling analysis of the beam under a combination of concentrated load and distributed axial loads of linear, quadratic and exponential types are investigated. Numerical results show that the highest values of the critical buckling load belong to the linear distributed load, and the lowest value is owned by exponential load.
