Vibrations of a Multi-Span Beam Structure Carrying Many Moving Oscillators

A beam structure carrying multiple moving oscillators is a mathematical model for various engineering applications, including rapid transit systems. With many moving oscillators having different speeds and varying inter-distances, the number of oscillators on the structure is time-varying, which inevitably complicates the beam–oscillator interactions. Consequently, the order of a mathematical model for the coupled beam–oscillator system changes with time, with many possibilities. Because of this, it is extremely difficult, if not impossible, for a conventional method to determine the dynamic response of a beam structure carrying many moving oscillators. In the literature, previous investigations have been limited to a beam structure with only one moving oscillator, which may not totally capture the physical behaviors of a structure with many moving oscillators, as seen in certain engineering applications. Developed in this work is a new semi-analytical method that can systematically handle arbitrarily many moving oscillators in both modeling and solution. In the development, an extended solution domain (ESD) is defined and based on the ESD a generalized assumed-mode method is devised. This modeling method completely resolves the issue of changing order in mathematical modeling. Because the proposed method makes use of the exact eigenfunctions of the beam structure (instead of traditional admissible functions), it renders determination of the dynamic response of a coupled beam–oscillator system highly accurate and efficient. The proposed method is demonstrated in several numerical examples. Furthermore, in a benchmark problem, it is shown that for the same accuracy in computation, the elapsed computation time used by the proposed method is just 3.3% of the time required by the finite element method.