Comments on “bounds on natural frequencies of composite circular plates: Integral equation method” by W. B. Bickford and S. Y. Wu

1991 ◽  
Vol 144 (1) ◽  
pp. 173-178
Author(s):  
P.A.A. Laura ◽  
E.A. Bambill
Keyword(s):  
Integral Equation ◽  
Natural Frequencies ◽  
Integral Equation Method ◽  
Equation Method ◽  
Circular Plates

A Simple Spline Integral Equation Method for Circular Plates with Variable Thickness

2007 ◽  
Vol 353-358 ◽  
pp. 2687-2690
Author(s):  
Xin Zhu Zhou ◽  
Jian Jun Zheng
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Analytical Solution ◽  
Variable Thickness ◽  
Order Differential Equation ◽  
Spline Interpolation ◽  
Bending Moment ◽  
Integral Equation Method ◽  
Equation Method ◽  
Circular Plates

A simple spline integral equation method is presented in this paper for the axisymmetrical bending of circular plates with variable thickness. Firstly, the fundamental solution of a second-order differential equation is derived. With the slope of the deflection surface taken as an unknown function, an integral equation is then established for circular plates with variable thickness. The integral equation is solved numerically by cubic spline interpolation and the deflection and bending moment at any point within the circular plate are obtained. Finally, the validity of the proposed method is verified with the analytical solution obtained from the literature.

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