Nonlinear Vibration of the Cantilever FGM Plate Based on the Third-order Shear Deformation Plate Theory

This paper thoroughly examines the singularity of stress resultants of the form r−ξFθ for 0<ξ⩽1 as r→0 (Williams-type singularity) at the vertex of an isotropic thick plate; the singularity is caused by homogeneous boundary conditions around the vertex. An eigenfunction expansion is applied to derive the first known asymptotic solution for displacement components, from the equilibrium equations of Reddy’s third-order shear deformation plate theory. The characteristic equations for determining the singularities of stress resultants are presented for ten sets of boundary conditions. These characteristic equations are independent of the thickness of the plate, Young’s modulus, and shear modulus, but some do depend on Poisson’s ratio. The singularity orders of stress resultants for various boundary conditions are expressed in graphic form as a function of the vertex angle. The characteristic equations obtained herein are compared with those from classic plate theory and first-order shear deformation plate theory. Comparison results indicate that different plate theories yield different singular behavior for stress resultants. Only the vertex with simply supported radial edges (S(I)_S(I) boundary condition) exhibits the same singular behavior according to all these three plate theories.

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Reply to the comments of M.E. Golmakani and J. Rezatalab, Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates” (by R. Aghababaei and J.N. Reddy, Journal of Sound and Vibration 326 (2009) 277–289), Journal of Sound Vibration, 333 (2014) 3831–3835

Journal of Sound and Vibration ◽

10.1016/j.jsv.2014.06.005 ◽

2014 ◽

Vol 333 (21) ◽

pp. 5654-5656 ◽

Cited By ~ 1

Author(s):

Noël Challamel ◽

J.N. Reddy

Keyword(s):

Shear Deformation ◽

Plate Theory ◽

Third Order ◽

Shear Deformation Plate Theory ◽

Sound Vibration

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Thermoelastic Stability of Imperfect Functionally Graded Plates Based on the Third Order Shear Deformation Theory

Volume 1: Advanced Energy Systems, Advanced Materials, Aerospace, Automation and Robotics, Noise Control and Acoustics, and Systems Engineering ◽

10.1115/esda2006-95018 ◽

2006 ◽

Author(s):

B. Samsam Shariat ◽

M. R. Eslami ◽

A. Bagri

Keyword(s):

Shear Deformation ◽

Plate Theory ◽

Closed Form Solution ◽

Shear Deformation Theory ◽

Form Solution ◽

Functionally Graded ◽

Functionally Graded Plates ◽

Equilibrium Equations ◽

Third Order ◽

The Third

Thermal buckling analysis of rectangular functionally graded plates with initial geometric imperfections is presented in this paper. It is assumed that the non-homogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under various types of thermal loadings, such as the uniform temperature rise and nonlinear temperature gradient through the thickness. A double-sine function for the geometric imperfection along the x and y-directions is considered. The equilibrium equations are derived using the third order shear deformation plate theory. Using a suitable method, equilibrium equations are reduced from 5 to 2 equations. The corresponding stability equations are established. Using these equations accompanied by the compatibility equation yield to the buckling loads in a closed form solution for each loading case. The results are compared with the known data in the literature.

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