A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end

This study deals with the determination of natural frequencies and modal shapes of an elastically restrained-free beam which carries a finite mass, M , at the free end. Numerical results are presented for different concentrated mass/beam mass ratios, M/M v , and a wide range of values of the parameter β EI/L , where β is the coefficient which relates angle of rotation and bending moment at the elastically-restrained end. The variation of the maximum dynamic stress as a function of M/M v and β EI/L also is analyzed for the first mode of vibration.