Generalized hypergeometric function solutions for transverse vibration of a class of non-uniform annular plates

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.