Prediction of frequencies of free axisymmetric vibration of two-directional functionally graded annular plates on Winkler foundation

2013 ◽  
Vol 42 ◽  
pp. 219-228 ◽  
Author(s):  
Yajuvindra Kumar ◽  
R. Lal
Keyword(s):  
Functionally Graded ◽  
Winkler Foundation ◽  
Axisymmetric Vibration ◽  
Annular Plates

Free Vibration of Two-Directional Functionally Graded Annular Plates Using Chebyshev Collocation Technique and Differential Quadrature Method

2015 ◽  
Vol 15 (06) ◽  
pp. 1450086 ◽  
Author(s):  
Yajuvindra Kumar
Keyword(s):  
Annular Plate ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Axisymmetric Vibration ◽  
Quadrature Method ◽  
Chebyshev Collocation ◽  
Annular Plates ◽  
Collocation Technique

This article deals with the free axisymmetric vibration of two-directional functionally graded annular plates. Ceramic and metal are considered two constituents of the functionally graded material (FGM), which are graded through thickness and radial directions of the plate. The Chebyshev collocation technique and differential quadrature method are employed to derive the frequency equations for an annular plate with both edges clamped and another one with both edges simply supported. The results for nonhomogeneous isotropic annular plates are also presented. The accuracy and efficiency of the present approach are confirmed through comparison of the frequencies obtained for homogeneous isotropic annular plates. Identical results are obtained for the two methods used. The effects of volume fraction index, coefficient of radial variation, exponent of power law, inner to outer radii ratio, and boundary conditions are discussed on the first three natural frequencies. It is found that the frequency of a functionally graded annular plate is greater than that of a homogeneous annular plate.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals On the effects of coupling between in-plane and out-of-plane vibrating modes of smart functionally graded circular/annular plates

2012 ◽  
Vol 36 (3) ◽  
pp. 1132-1147 ◽  
Author(s):  
Sh.H. Hashemi ◽  
K. Khorshidi ◽  
M. Es’haghi ◽  
M. Fadaee ◽  
M. Karimi
Keyword(s):  
Functionally Graded ◽  
Annular Plates ◽  
Out Of Plane
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