Vibration analysis of a tip-loaded beam attached to a rotating joint

Abstract

This paper presents a vibration analysis of a rotating beam system. The beam is uniform in cross-section and carrying a tip mass at its proximal end. The other end of the beam is attached to a rotating hub which has compliance in its linear and angular directions. The system equations of motion and the associated boundary conditions were derived by using Hamilton's principle. The frequency equation in dimensionless form is solved by using the secant method. Also the eigenfunctions of the eigenvalue problem are obtained by using the boundary conditions and the orthogonality property of the mode shape functions. In the analysis, the relationship between the frequency and speed ratios are evaluated for the effect of changes in the offset ratio (χ), mass ratio (σ), inertia ratio (γ), hub ratio (δ) and torsional ratio (κ). The effect of centrifugal force is also considered in the beam vibrations. It is confirmed that the frequency increases as the rotation speed for the beams studied becomes higher. The effect of changes in the ratios (χ, σ, γ, δ and κ) on the qualitative behaviour of the dynamic responses is also observed.