AN ANALYTIC SOLUTION FOR A BEAM WITH ARBITRARILY DISTRIBUTED SPRING-MASS SYSTEMS UNDER ELASTIC BOUNDARY CONDITION

An analytic solution for a beam with arbitrarily distributed spring-mass systems under elastic boundary condition is obtained by using sine expansion method. It is applied to solving free vibration of a beam carrying uniformly distributed sprung masses, and results compared with those in reference show good agreement, which validates the methodology. Additional, effects of five different distributions of spring-mass system on dimensionless natural frequencies of beam are studied. Considering modes of beam without spring-mass, it is concluded that the higher the density and the wider the distribution of spring-mass system locating at the largest magnitude of a mode, the greater influences the spring-mass system has on the dimensionless natural frequencies of that mode.