scholarly journals Free vibration analysis of a circular plate with multiple circular holes by using the addition theorem and direct BIEM

2009 ◽  
Author(s):  
W. M. Lee ◽  
J. T. Chen
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Addition Theorem ◽  
Circular Holes

Free Vibration Analysis of a Circular Plate With Multiple Circular Holes by Using Indirect BIEM and Addition Theorem

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
W. M. Lee ◽  
J. T. Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Free Vibration Analysis ◽  
Addition Theorem ◽  
Boundary Integral ◽  
Kernel Functions ◽  
Mode Shapes ◽  
Linear Algebraic Equations ◽  
Circular Holes

In this paper, natural frequencies and natural modes of a circular plate with multiple circular holes are theoretically derived and numerically determined by using the indirect boundary integral formulation, the addition theorem, and the complex Fourier series. Owing to the addition theorem, all kernel functions are expanded into degenerate forms and further expressed in the same polar coordinates centered at one circle where the boundary conditions are specified. Not only the computation of the principal value is avoided but also the calculation of higher-order derivatives can be easily determined. By matching boundary conditions, a coupled infinite system of linear algebraic equations is derived as an analytical model for the free vibration of a circular plate with multiple circular holes. The direct-searching approach is utilized in the truncated finite system to determine the natural frequency through singular value decomposition. After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the indirect boundary integral formulations. Some numerical eigensolutions are presented and then utilized to explain some physical phenomenon such as the beating and the dynamic stress concentration. Good accuracy and fast rate of convergence are the main features of the present method, thanks to the analytical approach.

scholarly journals FREE VIBRATION ANALYSIS OF CIRCULAR PLATE WITH ECCENTRIC HOLE SUBMERGED IN FLUID

2009 ◽  
Vol 41 (3) ◽  
pp. 355-364 ◽  
Author(s):  
Myung-Jo Jhung ◽  
Young-Hwan Choi ◽  
Yong-Ho Ryu
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Vibration Analysis ◽  
Free Vibration Analysis

Free vibration analysis of a circular plate partially in contact with a liquid

2009 ◽  
Vol 324 (1-2) ◽  
pp. 194-208 ◽  
Author(s):  
Kyeong-Hoon Jeong ◽  
Gyu-Mahn Lee ◽  
Tae-Wan Kim
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Vibration Analysis ◽  
Free Vibration Analysis
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