On the wave propagation in a beam-string model subjected to a moving harmonic excitation

Abstract

The vibration of an infinitely long beam with a large axial tension under a point harmonic load moving at a uniform speed is studied to find out the importance of bending rigidity of the beam. It is found analytically that the effect of bending stiffness of the beam does not play any significant role in the dynamics of the continuum beyond a certain distance away from the point of application of the load. The beam-string system simply acts as a taut string in those regions. However, the bending of the beam-string plays a major part in the vicinity of the load. It is shown that the beam model neglecting the inertia term is sufficient to capture the real scenario with negligible error in the close proximity of the load. The string model also becomes insufficient, especially at the upstream side when the speed of the load approaches the critical speed. In that case the bending and the inertia terms cannot be ignored in the Euler–Bernoulli beam model. It is seen from the response that, when the speed of the load is near the critical speed, one of the four propagating waves traverses with high phase speed, high frequency and low amplitude in the portion of the beam lying upstream of the load. This phenomenon cannot be captured in a simple string model. Comparison between the string model and the complete beam model in determining loading point displacement shows that the former can only be used at low frequencies in the subcritical speed regime.