Vibrations of a mass-loaded clamped-free Timoshenko beam

The purpose of this study is to determine the influence of rotary inertia and shear deformation on the motion of a flexible robot arm modelled as a cantilevered Timoshenko beam with a lumped moment of inertia at the free end. The first five natural frequencies and modal shapes of this Timoshenko beam are determined. The frequency results are presented graphically in three-dimensional plots as a function of the (tip mass)/(beam mass) ratio and the (radius of gyration of the tip mass)/(beam length) ratio.