Free vibrations of a cantilever beam with a spring-mass system attached to the free end

Abstract

An exact solution for the title problem is obtained using the Bernoulli-Euler theory of beam vibrations. Natural frequencies are obtained for a wide range of the intervening physical parameters. The problem is of interest in naval and ocean engineering systems since in order to avoid dangerous resonance conditions the designer must be able to predict natural frequencies of the overall mechanical system: structure-motor and its elastic mounting.