doi:10.1016/j.jsv.2004.11.027 
Copyright © 2004 Elsevier Ltd All rights reserved.
Generalized hypergeometric function solutions for transverse vibration of a class of non-uniform annular plates
W.H. Duana, S.T. Queka, 
, 
and Q. Wangb
aDepartment of Civil Engineering, National University of Singapore, 1 Engineering Drive 2, # E1A-07-03, Singapore 117576, Singapore
bMechanical, Materials & Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816-2450, USA
Received 27 November 2003;
revised 18 June 2004;
accepted 30 November 2004.
Available online 29 January 2005.
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Abstract
Free vibration analysis of thin annular plate with thickness varying monotonically in arbitrary power form is presented. Transformation of variable is introduced to translate the governing equation for the free vibration of thin annular plate into a fourth-order generalized hypergeometric equation. The analytical solutions in terms of generalized hypergeometric function taking either logarithmic or non-logarithmic forms are proposed, which encompass existing published solutions as special cases. To illustrate the use of the closed form solutions presented, free vibration analyses of a thin annular ultra-high-molecular weight polyethylene and a steel plate with linear and nonlinear thickness variation are performed. The results are compared with those from FE analysis based on Kirchhoff thin plate theory and 3D elasticity theory indicating good agreement.
Fig. 1. Geometry of annular plate with m=1,1/2,-1/2,6/5.
Fig. 2. Frequency ratio (varying thickness to uniform plate) for different m.
Fig. 3. Convergence conditions for different m and p (where g1=γ2-γ1,g2=γ3-γ1,g3=γ4-γ1).
Table 1.
Material and geometrical properties of annular plate
Table 2.
Comparison of frequencies (Hz) of annular plate under C–C, F–C boundary conditions between CPT FEM and proposed results for UHMWPE plate
p=number of nodal diameters; n=number of nodal circles; C=clamped, F=free.
a The first letter denotes the condition at the inner edge.
Table 3.
Comparison of frequencies (Hz) of annular plate under C–C, F–C boundary conditions between 3D FEM and proposed results for m=1 (linear increasing)
p=number of nodal diameters; n=number of nodal circles; C=clamped, F=free.
a The first letter denotes the condition at the inner edge.
Table 4.
Comparison of frequencies (Hz) of annular plate under C–C, F–C boundary conditions between 3D FEM and proposed results for m=1/2 (nonlinear increasing)
p=number of nodal diameters; n=number of nodal circles; C=clamped, F=free.
a The first letter denotes the condition at the inner edge.
Table 5.
Comparison of frequencies (Hz) of annular plate under C–C, C–F boundary conditions between 3D FEM and proposed results for m=-1/2 (nonlinear decreasing)
p=number of nodal diameters; n=number of nodal circles; C=clamped, F=free.
a The first letter denotes the condition at the inner edge.
Abstract
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