Vibrations of a timoshenko beam clamped at one end and carrying a finite mass at the other

The present paper deals with an exact solution of the title problem. Modal shapes and natural frequency coefficients are determined for a significant range of the mechanical and geometric parameters that come into play. When the parameter I/AL² (where I is cross-sectional moment of inertia, A is cross-sectional area, and L beam length) approaches zero, the beam dynamic characteristics agree with values already available in the open literature.