Vibration analysis of rotating Rayleigh beams at high angular velocity; “BCOP” variational approach

This paper presents a dynamic model for the vibration of rotating Rayleigh beam. The governing differential equations of motion of the beam in free vibration are derived using Lagrange’s equations and include the effect of an arbitrary hub radius. Three linear partial differential equations are derived. Two of the linear differential equations are coupled through the stretch and chordwise deformation. The other equation is an uncoupled one for the flapwise deformation. A method based on the Rayleigh-Ritz solution is proposed to solve the natural frequency of very slender rotating beam at high angular velocity. The parameters for the hub radius, rotational speed, tapered ratio, rotary inertia and slenderness ratio are incorporated into the equation of motion. Finally the resonance frequency of rotating bema is evaluated. The non-dimensional frequency coefficients are given in tabular form. Some numerical examples are presented and the influence of different non-dimensional parameters on frequency values is discussed.