The impact of root flexibility on the fundamental frequency of a restrained cantilever beam

This study presents the theoretical and experimental studies of the impact of root flexibility on the fundamental frequency of the free bending vibration of a uniform Euler–Bernoulli cantilever beam elastically restrained at the root. The dispersion relation between the natural frequency and modal number has been derived and solved numerically and approximately using the series method of the expansion in terms of the modal number. It is shown that the approximate solution is reduced to the empirical Dunkerley rule, which is sound not universally true. A commercial force sensor is used for the experimental detection of the effect of root flexibility on the fundamental frequency of bending vibrations of a cantilevered beam. The strip-shape specimen attached to the force sensor forms a cantilever beam restrained at the root against rotation and translation and it fundamental frequency is identified. The results of measurements for a series of industrial materials are compared with exact calculations and thos...