On the eigenfrequencies of a combined system consisting of a simply supported beam and in-span helical spring-mass with mass of the helical spring considered

Abstract

The present study deals with the determination of the frequency equation of a Bernoulli-Euler beam simply supported at both ends, to which is attached in-span a longitudinally vibrating elastic rod with a tip mass, representing a helical spring-mass system with mass of the helical spring considered. The principal aim is to underline once more the importance of the consideration of the mass of the helical spring for some parameter combinations and to supply the design engineers working in this area with the "exact" frequency equation of the combined system under investigation which can be thought of, for example, as a simple model of an engine elastically mounted on a structural element. Further, the frequency equation of the reduced system is established in which the free end of the longitudinally vibrating rod is fixed. Frequency equations obtained are solved for various non-dimensional mass and spring parameters and the results are compared with the massless spring case as well as with FE solutions and Dunkerley estimations. The "errors" are tabulated in Tables. It is seen that not taking into account the mass of the helical spring can lead to considerable errors for some parameter combinations.