Modeling of Elastic Waves in a Rotating Disc of Polygonal Cross-Sections

Abstract

In this paper, modeling of elastic waves in a rotating disc of polygonal cross-section is studied using the Fourier expansion collocation method. The equations of motion are derived based on two-dimensional theory of elasticity under the assumption of plane strain rotating disc of polygonal cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the disc using Fourier expansion collocation method. The triangular, square, pentagonal and hexagonal cross sectional discs are computed numerically for Copper material. Dispersion curves are drawn for wave number for longitudinal and flexural (symmetric and antisymmetric) modes of vibration with rotational speed.