DYNAMIC RESPONSE OF A ROTATING FLEXIBLE ARM CARRYING A MOVING MASS

A clamped–free flexible arm rotating in a horizontal plane and carrying a moving mass is studied in this paper. The arm is modelled by the Euler–Bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored. The assumed mode method in conjunction with Hamiltonʹs principle is used to derive the equation of motion of the system which takes into account the effect of centrifugal stiffening due to the rotation of the beam. The eigenfunctions of a cantilever beam which satisfy the prescribed geometric boundary conditions are used as basis functions in the assumed mode method. The equation of motion is expressed in non-dimensional matrix form. Pre-designed transformed cosine profiles are used as trajectory inputs for the hub angle and the moving mass. The equation of motion is solved numerically using the fourth order Runge–Kutta method. Graphical results are presented to show the influence of centrifugal stiffening effect, moving mass values, mass travelling time, hub angle and mass trajectory profile on the deflection of the beam.