Dc. Winfield et Bc. Soriano, PLANAR MOTION OF A FLEXIBLE BEAM WITH A TIP MASS DRIVEN BY 2 KINEMATIC ROTATIONAL DEGREES OF FREEDOM, Journal of vibration and acoustics, 120(1), 1998, pp. 206-213
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.