Fundamental Frequencies of Cantilever Beams

A simple relationship which predicts the first mode natural frequency of a tapered cantilever beam is presented as a function of the stiffness to mass ratio and a mass distribution parameter for the beam. In this study the mass distribution parameter, obtained using referenced results, is presented as a function of the taper ratio of the beam for the case of beams with linear tapers. Conical truncated beams, truncated wedges with vibration perpendicular to the parallel sides of the taper, and truncated wedges with vibration parallel to the parallel sides of the taper have been investigated.