The natural frequency estimation for a system composed of a beam and a spring-mass system

This study presents an approximate method for determining the natural frequency of a system composed of a beam and a two-degree-of-freedom spring-mass system. The expression for estimating the natural frequency is derived following the standard procedures of the forced vibration analysis of a beam. The results obtained using the current method are in good agreement with those obtained through the dynamic stiffness method, especially when the spring stiffness is large. The innovativeness of the current method is that it reveals the relevance between the natural frequency of the system, the natural frequency of the beam, and the mode shape data at the positions where the spring-mass system is attached to the beam. The method is potentially useful in the dynamic wheel-track interaction analysis because the train wheel is normally simplified as a spring-mass system with high spring stiffness. It may also be applied to natural frequency-based damage detection where an auxiliary spring-mass system is used. When the spring-mass system roves on the beam, the curve of natural frequency versus spring-mass system location would be relevant to the mode shape square which is sensitive to local damage.