Free vibration analysis of circular plates with multiple circular holes using indirect BIEMs

Abstract

In this paper, a semi-analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and

Independent Coordinate Coupling Method for Free Vibration Analysis of a Plate With Holes

“…Cheng et al(2003) used the finite element analysis code, Nastran, to analyze the effects of the hole eccentricity, hole size and boundary condition on the vibration modes of annular-like plates. Lee et al(2007) used an indirect formulation in conjunction with degenerate kernels and Fourier series to solve for the natural frequencies and modes of circular plates with multiple circular holes and verified the finite element solution by using ABAQUS. Zhong and Yu(2007) formulated a weak-form quadrature element method to study the flexural vibrations of an eccentric annular Mindlin plate.…”

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

“…Recently some researchers intended to extend an annular plate [7,8] to the plate with an eccentric hole. Lee et al [9,10] proposed a semi-analytical approach to solve the free vibration analysis of a circular plate with multiple holes and pointed out some insufficient accurate results in [8] after careful comparisons.…”

“…One is the improper integral in the boundary integral equation; the other is that both field point and source point are located on different circular boundaries. These problems have been treated by using the degenerate kernel and tensor transformation [9,10], respectively. But tensor transformation accompanied with the higher order derivative increases the complexity of computation and then affect the accuracy of its solution [9].…”

“…These problems have been treated by using the degenerate kernel and tensor transformation [9,10], respectively. But tensor transformation accompanied with the higher order derivative increases the complexity of computation and then affect the accuracy of its solution [9]. In addition, the collocation method in [9,10] belongs to point-matching approach instead of analytical derivation.…”

“…But tensor transformation accompanied with the higher order derivative increases the complexity of computation and then affect the accuracy of its solution [9]. In addition, the collocation method in [9,10] belongs to point-matching approach instead of analytical derivation. It also increases the effort of computation since boundary nodes for collocation are required.…”