Differential Quadrature Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates in Thermal Environments

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. H. Mirtalaie
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Annular Sector

In this paper, the free vibration behavior of functionally graded (FG) thin annular sector plates in thermal environment is studied using the differential quadrature method (DQM). The material properties of the FG plate are assumed to be temperature dependent and vary continuously through the thickness, according to the power-law distribution of the volume fraction of the constituents. The nonlinear temperature distribution along the thickness direction of the plate is considered. Based on the classical plate theory, the governing differential equations of motion of the plate are derived and solved numerically using DQM. The natural frequencies of thin FG annular sector plates in thermal environment under various combinations of clamped, free, and simply supported boundary conditions (BCs) 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 where the results are in good agreement. The effects of temperature field, BCs, volume fraction exponent, radius ratio, and the sector angle on the free vibrations of the FG-plate are examined.

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

Free Vibration Analysis of Functionally Graded Beams Resting on Elastic Foundation in Thermal Environment

2016 ◽  
Vol 16 (07) ◽  
pp. 1550029 ◽  
Author(s):  
P. Zahedinejad
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Various Boundary Conditions

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

Large Amplitude Free Vibration Analysis of Thin Annular Sector Plates Using Differential Quadrature Method

2010 ◽  
Author(s):  
S. H. Mirtalaie ◽  
M. A. Hajabasi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Large Amplitude ◽  
Plate Theory ◽  
Nonlinear Eigenvalue Problem ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Annular Sector

In this paper, the Differential Quadrature Method (DQM) is used to study the large amplitude free vibration of thin annular sector plates. The geometrical nonlinear governing equations of motion are derived based on the classical plate theory and using the von Karman nonlinear strain-displacement relationships. Following the DQ-procedure and employing the concept of new degrees of freedom a nonlinear eigenvalue problem is obtained which is solved iteratively and nonlinear natural frequencies of the plate are obtained. The results show a very good convergence and they are compared with the available literature for the clamped boundary conditions to demonstrate the validity of the work. The effects of boundary conditions, inner to outer radius ratio and sector angle on the large amplitude free vibration of thin plate are studied.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

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