Dynamics of trains and train-like articulated systems travelling in confined fluid—Part 2: Wave propagation and flow-excited vibration

Wave propagation and response of a train of flexibly interconnected rigid cars travelling in a confined cylindrical “tunnel” subjected to fluid dynamic forces are studied theoretically. For the wave propagation analysis, an infinite-length train represented by a lumped-parameter Timoshenko-beam (LTB) model is employed. The train response is simulated using a travelling sinusoidal aerodynamic force that mimics the features obtained during running experiments on real trains. In addition, the response of the system is examined when the velocity of the force approaches the minimum phase velocity of a travelling wave in the train. The principal aim of this study is to investigate the effect of aerodynamic forces on the dynamics of a high-speed train running in a tunnel, or more generally of a train-like system travelling in a coaxial cylindrical tube. The results of this study show that: (a) when aerodynamic forces act on a train, the frequency bands of the dispersion relation of wave propagation shift, and thus no classical normal modes (standing wave solutions) exist in the system; (b) the wavelength of the travelling sinusoidal force controls the phase differences between cars in the train; and (c) the response of the train can be considerably amplified when the speed of the travelling force coincides with the minimum phase velocity of travelling waves in the train.