Free vibration and buckling analysis of functionally graded deep beam-columns on two-parameter elastic foundations using the differential quadrature method

2009 ◽  
Vol 223 (6) ◽  
pp. 1273-1284 ◽  
Author(s):  
S Sahraee ◽  
A R Saidi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Deep Beam ◽  
Quadrature Method ◽  
Beam Columns ◽  
Two Parameter

In this research, a differential quadrature method is applied for free vibration and buckling analysis of deep beam-columns composed of functionally graded materials on two-parameter elastic foundations. Derivation of equations is based on the unconstrained higher-order shear deformation theory taking into account the complete effects of shear deformation, depth change, and rotary inertia. It is assumed that the effective mechanical properties of functionally graded (FG) beam-columns are temperature dependent and vary continuously throughout the thickness direction according to volume fraction of the constituents defined by power-law function. The accuracy, convergence, and flexibility of the differential quadrature technique for simply supported FG deep beam-columns with complicated governing differential equations and boundary conditions are examined and verified with the known data in the literature.

Free vibration of functionally graded sandwich plates based on nth-order shear deformation theory via differential quadrature method

2018 ◽  
Vol 22 (5) ◽  
pp. 1660-1680 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Zhonglong Wang ◽  
Xiaoxiang Liu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Sandwich Plates ◽  
Numerical Comparison ◽  
Quadrature Method

The present study is concerned with free vibration of functionally graded sandwich plates on elastic foundation based on nth-order shear deformation theory. The material properties of functionally graded plate are assumed to vary according to power law distribution of the volume fraction of the constituents, and two common types of FG sandwich plates are considered. Governing differential equations are derived by means of Hamilton’s principle. The differential quadrature method is developed to formulate the problem, and rapid convergence is observed in this study. A numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. Furthermore, effects of gradient indexes, thickness side ratio, aspect ratio, foundation parameters, boundary condition and different sandwich types on the natural frequency of plates are also studied.

Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method

2010 ◽  
Vol 225 (3) ◽  
pp. 568-583 ◽  
Author(s):  
S H Mirtalaie ◽  
M A Hajabasi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fg Plates ◽  
Annular Sector

In this article, the differential quadrature method (DQM) is used to study the free vibration of functionally graded (FG) thin annular sector plates. The material properties of the FG-plate are assumed to vary continuously through the thickness, according to the power-law distribution. The governing differential equations of motion are derived based on the classical plate theory and solved numerically using DQM. The natural frequencies of thin FG annular sector plates under various combinations of clamped, free, and simply supported boundary conditions are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate. In this case, the result shows very good agreement. For the FG-plates, the effects of boundary conditions, volume fraction exponent, and variation of Poisson's ratio on the free vibrational behaviour of the plate are studied.

Free Vibration Analysis of Functionally Graded Moderately Thick Annular Sector Plates Using Differential Quadrature Method

2011 ◽  
Vol 110-116 ◽  
pp. 2990-2998 ◽  
Author(s):  
S.H. Mirtalaie ◽  
M.A. Hajabasi ◽  
F. Hejripour
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Radius Ratio ◽  
Quadrature Method ◽  
Annular Sector

In this paper, the free vibration of moderately thick annular sector plates made of functionally graded materials is studied using the Differential Quadrature Method (DQM). The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power-law distribution. The governing differential equations of motion are derived based on the First order Shear Deformation plate Theory (FSDT) and then solved numerically using DQM under different boundary conditions. The results for the isotropic plates which are derivable with this approach are presented and compared with the literature and they are in good agreement. The natural frequencies of the functionally graded moderately thick annular sector plates under various combinations of clamped, simple supported and free boundary conditions are presented for the first time. The effects of boundary conditions, sector angle, radius ratio, thickness to outer radius ratio, volume fraction exponent and variation of the Poisson’s ratio on the free vibration behavior of the plate are studied

Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates on Elastic Foundations via State-Space Based Differential Quadrature Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
A. Jodaei ◽  
M. H. Yas
Keyword(s):  
Free Vibration ◽  
State Space ◽  
Present Method ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Elastic Foundations ◽  
Annular Plates

In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

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