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

An exact solution for the title problem is obtained using the Bernoulli-Eul er theory of beam vibrations. Natural frequencies are obtained for a wide r ange of the intervening physical parameters. The problem is of interest in naval and ocean engineering systems since in order to avoid dangerous reson ance conditions the designer must be able to predict natural frequencies of the overall mechanical system: structure-motor and its elastic mounting. ( C) 2001 Elsevier Science Ltd. All rights reserved.