In this paper, an analytical solution is found for a cantilever beam carrying an elastically mounted mass at its free end, based on Euler-Bernoulli bending theory. The analysis method is established on the wave vibration approach, in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external forces applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam and single degree-of-freedom spring-mass system, the vibrating discrete spring-mass system injects waves into the distributed beam through spring force at the spring attached point on the beam. Numerical examples are presented with accuracy validated through comparisons to available results.
Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.
