Effects of boundary flexibility on the vibration of a continuum with a moving oscillator

In this paper, the problem of an oscillator traversing an elastically supported continuum is studied. The flexibility in the boundaries of the continuum is modeled by linear, transverse springs. The response of the continuum and the dynamic interaction force between the moving oscillator and the continuum are evaluated by an eigenfunction expansion series. To circumvent convergence difficulties associated with the jump in the shear force due to the moving interaction force, an improved series expansion employing the static Green’s function is derived. The coupled governing equations of motion are solved numerically and results are obtained to examine the effects of the boundary flexibility on the response, the dynamic interaction force, the shear force spatial and temporal distributions, as well as the convergence properties of the expansion series. It is found that high order modal terms contribute significantly to the shear force expansion series in the elastically supported model. The presence of large amplitude and high frequency components in the shear force is critical in understanding the cumulative fatigue failure of the structure. A useful and compact formula estimating the value of the support stiffness above which a boundary may be modeled as simply supported is also derived.