Vibration of a Beam under a Random Stream of Moving Forces*

The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes is considered. Force arrivals at the beam are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. This technique is based on the introduction of two influence functions, one of which satisfies nonhomogeneous, the other homogeneous differential equations for beam response. Explicit expressions for expected value and variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations and discussed. The extension of the approach presented to the case of two-axle vehicles is also outlined