Vibration analysis of beams with a two degree-of-freedom spring-mass system

In this paper, the natural frequencies and mode shapes of a Bernoulli-Euler beam with a two degree-of-freedom spring-mass system are determined by using Laplace transform with respect to the spatial variable. The deterministic and random vibration responses of the beam are obtained by using model analysis. The various spring constants of the boundary conditions of the beam are considered to model those special structures and machines, also different parameters of the spring-mass system are taken into consideration to study the fundamental natural frequencies of the beam. It should be emphasized that the proposed analysis is quite important for the design of some components of the buildings or machine tools. © 1997 Elsevier Science Ltd.