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Abstract

The integral equation method is developed for vibration analysis of solid circular plates with arbitrary thickness variation along the radius. General boundary conditions are considered. The problem is formulated in terms of displacements. The resulting fourth-order linear hyperbolic equation with variable coefficients is solved using the analogue equation method of Katsikadelis. According to this method the linear governing differential equation is replaced by a linear equation of a substitute beam with unit bending stiffness, under a fictitious load distribution. Numerical examples are presented for plates with various thickness variation laws, which illustrate the method and demonstrate its efficiency and accuracy.

Keywords

circular plate vibrations variable thickness boundary elements integral equation method analogue equation method

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Free vibrations of circular plates with axisymmetric thickness variation

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