Showing 7 results for Functionally Graded
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.
N. Cheraghi, M. Miri, M. Rashki,
Volume 39, Issue 1 (8-2020)
Abstract
This paper presents a probabilistic assessment on the free vibration analysis of functionally graded material plates, including layers with magneto-electro-elastic properties, using the 3D solution and surrogate models. The plate is located on an elastic foundation and the intra-layer slipping effect is also considered in the analysis by employing the generalized intra-layer spring model. Due to the high computational cost of the 3D solution in calculating the free vibration frequency of the plate, surrogate models are used. The meta models including kriging method, radial fundamental function method and polynomial response surface method are used to construct the surrogate model. For surrogate models training, the results of the three-dimensional solving method are used. The elastic foundation hardness, the intra-layer slipping effect, the material properties index, and the layer densities are considered as the variables with uncertainty. The three-dimensional solution method is validated through a comparison with other available reference. The results obtained through the surrogate models have been compared to those of the 3D solution formulation, showing a good agreement. The effects of some parameters including the elastic foundation hardness, the intra-layer slipping effect, the density of each layer, and the material properties index on the fundamental frequency of functionally graded material plates are investigated. By using three-dimensional solution method and Kriging Surrogate Model, it is shown that the shear and transverse components of elastic foundation hardness and the density of each layer have the greatest effect on the fundamental frequency of the functionally graded material plates.
M. Hashemian, M. Jabbarzadeh,
Volume 40, Issue 1 (9-2021)
Abstract
In this paper, nonlinear bending analysis of functionally graded rectangular and sectorial micro/nano plates is investigated using the modified couple stress theory. For this purpose, a higher-order shear deformation theory and von Kármán geometrically nonlinear theory are employed. The equilibrium equations and the boundary conditions for rectangular and annular sector plates are derived from the principle of minimum total potential energy and solved using the Semi-Analytical Polynomial Method (SAPM). One of the advantages of the implemented shear deformation theory is removing the defects of higher order shear deformation theory, and obtaining the response of the first and the third-order shear deformation theories at the same time. Afterwards, beside investigating the benefits of this theory compared with other ones, the results are verified with those by other researches. At the end, the effects of length scale parameter, boundary conditions, power law index, and geometrical dimensions are investigated
A. Panjebashi Naghsh, K. K. Esmaeili. Torkanpouri ,
Volume 40, Issue 2 (1-2022)
Abstract
One of the new methods for powering low power electronic devices is the use of mechanical energies due to vibrations. In this method, the piezoelectric material is employed for converting the mechanical energy of vibration into the electrical energy. The advantage of this method is needlessness of using the battery charging system. In this paper, the functionally graded (FG) cantilever with the piezoelectric layer is considered as energy harvester system. The mathematical model of the system is constructed and the governing equation for electromechanical coupling is presented. Then the effects of the system parameters on the generated power is studied. Finally, by considering uncertainties in energy harvester parameters, the effect of uncertainties on the produced energy is investigated by Monte-Carlo simulation method for the first time. The results show that although the amount of generated power in the first natural frequency is higher than the other frequencies, but around the first natural frequency, the effect of uncertainties is increased and thus, the reliability of the energy harvester will be decreased.
H. Salehipour,
Volume 41, Issue 1 (9-2022)
Abstract
In this paper, static buckling of homogeneous beams coated by a functionally graded porous layer with different boundary conditions is investigated based on the Timoshenko beam theory. The principle of virtual work has been used to obtain the governing equations. Two different methods, namely analyticalsolution and numerical solution are used to solve the governing equations and extract the buckling force. The governing equations are coupled as a series of ordinary differential equations. In the analytical solution, these equations are first uncoupled using a series of mathematical operations, and are then solved. The obtained solution has a series of parameters and unknown constants. Using the boundary conditions at the boundaries of the beam, a homogeneous system of equations is extracted, from which the axial buckling force is obtained. In the numerical solution, the generalized differential quadrature method is used to solve the static equations. Finally, the numerical results are presented and the effects of various parameters such as thickness to beam length ratio, porous layer thickness, porosity parameter, etc. on the buckling of the beam are investigated. Comparison of the results obtained from the two analytical and numerical solution methods confirms the accuracy and validity of both methods.
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.
M. Ghomeshi Bozorg,
Volume 41, Issue 1 (9-2022)
Abstract
In this paper, dynamic instability due to parametric and external resonances of moderately thick functionally graded rectangular plates, under successive moving masses, is examined. Plate mass per unit volume and Young’s modulus are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituent. The considered rectangular plates have two opposite simply supported edges while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The governing coupled partial differential equations of the plate are derived based on the first-order shear deformation theory with consideration of the rotational inertial effects and the transverse shear stresses. All inertial components of the moving masses are considered in the dynamic formulation. Using the Galerkin procedure, the partial differential equations are transformed into a set of ordinary differential equations with time-dependent coefficients. The Homotopy Analysis Method (HAM) is implemented as a semi-analytical method to obtain stable and unstable zones and external resonance curves in a parameters space. The effects of the index of volume fraction, thickness to length ratio, and different combinations of the boundary conditions on the dynamic stability of the system are also investigated. The results indicate that decreasing the index of volume fraction, increasing thickness to length ratio, and higher degree of edge constraints (respectively from free to simply-supported to clamped) applied to the other two edges of the plate shift up the instability region and resonance curves in the parameters plane and, from a physical point of view, the system becomes more stable. In addition to using numerical simulations of the plate midpoint displacement, Floquet theory is also employed to validate the HAM results. Finally, the results of this study, in a particular case, are compared and validated with the results of other works.
