Abstract
AbstractIn this paper, the wave propagation in a rotating disc of polygonal cross-section immersed in an inviscid fluid 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 non-dimensional wave number and relative frequency shift for longitudinal and flexural (symmetric and anti-symmetric) modes. This work may find applications in navigation and rotating gyroscope .
Highlights
The rotating disc of polygonal cross-section is the important structural component in construction of gyroscope to measure the angular velocity of a rotating body
This article presents the propagation in a rotating disc of polygonal cross-section immersed in an inviscid fluid using the Fourier expansion collocation method
An analytical method for solving the wave propagation problem of rotating polygonal cross-sectional disc immersed in an inviscid fluid has been presented
Summary
The rotating disc of polygonal cross-section is the important structural component in construction of gyroscope to measure the angular velocity of a rotating body. This article presents the propagation in a rotating disc of polygonal cross-section immersed in an inviscid fluid using the Fourier expansion collocation method. The boundary conditions along both outer and inner free surface of the arbitrary cross-section are satisfied by means of Fourier expansion collocation method. Venkatesan and Ponnusamy (2002) have obtained frequency equation of the free vibration of a solid cylinder of arbitrary cross-section immersed in fluid using the Fourier expansion collocation method. Ponnusamy (2011) studied the wave propagation in thermoelastic plate of arbitrary cross-sections using the Fourier expansion Collocations Method. The wave propagation in rotating disc of polygonal cross-section immersed in an invicid fluid is analysed. 5. Boundary conditions and frequency equations In this problem, the vibration of a polygonal cross-sectional rotating disc immersed in fluid is considered. The solution for the anti symmetric mode n is obtained by replacing cos n by sin n in Equation 34
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