PLANAR MOTION OF A FLEXIBLE BEAM WITH A TIP MASS DRIVEN BY 2 KINEMATIC ROTATIONAL DEGREES OF FREEDOM

The objective was to model planar motion of a flexible beam with a tip mass that is driven by two kinematic rotational degrees of freedom wh ich are (1) at the center of the hub and (2) at the point the beam is attached to the hub. The equations of motion were derived using Lagran ge's equations and were solved using the finite element method. The re sults for the natural frequencies of the beam especially at high tip m asses and high rotational velocities of the hub were calculated and co mpared to results obtained using the Raleigh-Ritz method. The dynamic response of the beam due to a specified hub rotation was calculated fo r two cases.