An Approximate Method to Determine the Frequencies of Lateral Vibrations of Rotating Bars with Variable Cross Section

Abstract

The problems of lateral vibrations of rotating bars are very important with respect to the tur bine blades, and other revolving parts of high speed machine. The author has tried to solve the fundamental equation by means of the combination of Shrödinger's perturbation method and Baker Cowley-Levy's method. Namely the deflection was expanded in the double series of the square of angular velocity ω, and of the eigenvalues λ. Thus the frequency equations were obtained from the boundary conditions, and the frequencies of variable cross sectional bars were calculated with sufficient accracy.