DYNAMIC STABILITY OF A BEAM LOADED BY A SEQUENCE OF MOVING, MULTI-AXLE, MASS VEHICLES

An approximate method is presented for determining the dynamic stability of the lateral response for a finite Bernoulli-Euler beam loaded by a continuous sequence of vehicles traveling at a constant speed. The beam, which can also be loaded by a constant axial force, is uniform and simply supported & rests on a massless, uniform elastic foundation. Damping for the beam and foundation is provided by a combined uniform viscous damping coefficient. The vehicles, which are identical, equally spaced, and attached to the beam, each consist of a rigid body mass supported by two separate axles or wheel masses. Consequantly, the vehicles can rotate (or pitch) and translate laterally. The Galerkin method is used to generate a set of approximate equations of motion which contain periodic coefficients. Hence, multiple regions of dynamic instability can occur. The coupled equations are simplified by using a one-term Galerkin approximation which, under certain conditions, reduces to a Mathieu equation. Thus, the critical vehicle speeds, which correspond to dynamic instability, are predicted in terms of the physical system parameters by simple algebraic expressions. The principal conclusion which results from the one-term Galerkin approximation is that the critical vehicle speeds are increased by increasing the system stiffness.