Direct numerical procedure for solution of moving oscillator problems

In this paper, the problem of a 1D elastic distributed system coupled with a moving linear oscillator, often referred to as the 'moving oscillator' problem, is studied. The problem is formulated using a 'relative displacement' model, which shows that, in the limiting case of infinite oscillator stiffness, the moving mass problem is recovered. The coupled equations of motion are recast into an integral equation that is amenable to solution by a direct numerical procedure. Both the integral equation and the numerical procedure show that the response of the elastic system at the current time depends only on the time history of its response at the positions of the oscillator. Numerical results are presented for the examples of a string and simply supported beam and are compared to the moving force solutions. It is shown that the oscillator, with its stiffness suitably tuned, can excite the elastic structure into resonance.