This paper is concerned with a method for solving in-plane vibration problems of thick-walled pipes and rings of arbitrary shape. The solution to the equation of motion based on the theory of elasticity under the plane-strain assumption is obtained exactly by using polar coordinates. The boundary conditions along both the outer and the inner surfaces of the ring of arbitrary shape are satisfied directly by means of the Fourier expansion collocation method which has been developed in the author’s previous reports concerning vibration, dynamic response, and wave propagation problems of plates and rods with various shapes. Numerical calculations have been carried out for a thick elliptical ring, a rectangular ring with rounded corners, and a rectangular ring with a circular inner boundary. To discuss the accuracy of the present analysis, the results of a thick circular ring have also been calculated, and the present results are compared with the previously published ones.

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