Free vibration of rotating beam with tip mass

Abstract

The objective of this paper is to investigate the effect of tip mass on the natural frequency of the rotating beam with tip mass. The equations of motion for rotating Euler beam are derived by the d'Alembert principle and the virtual work principle. In order to capture all inertia effect and coupling between extensional and flexural deformation, the consistent linearization of the fully geometrically non-linear beam theory is used in the derivation. A method based on the power series solution is proposed to solve the natural frequency. Numerical examples are studied for the natural frequency of rotating beams with different tip mass, angular velocity, setting angle, and slenderness ratio.