Vibration Characteristics of Functionally Graded Plates with Non-Ideal Boundary Conditions

2012 ◽  
Vol 19 (7) ◽  
pp. 543-550 ◽  
Author(s):  
M. M. Najafizadeh ◽  
J. Mohammadi ◽  
P. Khazaeinejad
Keyword(s):  
Boundary Conditions ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Ideal Boundary ◽  
Functionally Graded Plates

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

scholarly journals Thermal Free Vibration Analysis of Temperature-Dependent Functionally Graded Plates Using Second Order Shear Deformation

2011 ◽  
Vol 471-472 ◽  
pp. 133-139 ◽  
Author(s):  
Ali Shahrjerdi ◽  
Faizal Mustapha ◽  
S.M. Sapuan ◽  
M. Bayat ◽  
Dayang Laila Abang Abdul Majid ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Second Order ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Functionally Graded Plates ◽  
Temperature Dependent

This research has been conducted to approach second-order shear deformation theory (SSDT) to analysis vibration characteristics of Functionally Graded Plates (FGP’s). Material properties in FGP's were assumed to be temperature dependent and graded along the thickness using a simple power law distribution in term of the volume fractions of the constituents. FGP was subjected to a linear and nonlinear temperature rise. The energy method was chosen to derive the equilibrium equations. The solution was based on the Fourier series that satisfy the simply supported boundary condition (Navier's method). Numerical results indicated the effect of material composition, plate geometry, and temperature fields on the vibration characteristics and mode shapes. The results revealed that, the temperature field and volume fraction distribution had significant effect on the vibration of FGPs. It was observed the second order theory was very close to the other shear deformation theorem as reported in the literature.

Thermo-mechanical induced vibration characteristics of shear deformable functionally graded ceramic—metal plates using finite element method

2010 ◽  
Vol 225 (1) ◽  
pp. 50-65 ◽  
Author(s):  
M Talha ◽  
B N Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Temperature Field ◽  
Boundary Conditions ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Aspect Ratios ◽  
Shear Deformable ◽  
Element Method

This paper deals with the thermomechanical-induced vibration characteristics of shear deformable functionally graded material (FGM) plates. Theoretical formulations are based on higher-order shear deformation theory with a significant improvement in the transverse displacement using finite-element method. The mechanical properties of the plate are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The temperature field is ascertained to be a uniform distribution over the plate surface and varied in the thickness direction only. The fundamental equations for FGM plates are derived using variational approach by considering traction-free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite-element with 13 degrees of freedom (DOF) per node have been used to accomplish the results. Convergence and comparison studies have been performed for square plates to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index, and temperature rise with different boundary conditions. The results reveal that the temperature field and the gradient in the material properties have significant effect on the vibration characteristics of the FGM plates.

Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions

2015 ◽  
Vol 38 (6) ◽  
pp. 630-650 ◽  
Author(s):  
Abdelhakim Bouhadra ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Fabrice Bernard ◽  
Rabbab Bachir Bouiadjra ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Functionally Graded Plates
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