Forced oscillations of infinite periodic structures. Applications to railway track dynamics

Forced steady-state oscillations of infinite periodic structures, caused by a moving harmonic force, are considered. One can see two periodicities in railway tracks whose periods are equal to the rail length and sleeper spacing, respectively. The first one causes variations in track pliability near rail joints as well as low frequency oscillations of moving vehicles. This allows one to consider the track as a Euler-Bernoulli beam, resting on uniform visco-elastic foundation. Resilient hinges present rail joints in the track model. The second track periodicity is usually considered dong with high frequency track excitation. Taking this into account, the more precise model, that presents the rail as a discretely supported Timoshenko beam, is considered. Three discrete support models of different complexity are studied. The first one presents the rail support as a concentrated mass on a spring and a dashpot in parallel. In the second model, the support is a uniform unbending beam on uniform visco-elastic foundation. The sleeper bend is considered in the third support model. The power series method is used to account its bend. An influence of the fail sheer deformations and the sleeper bend on the track frequency response is estimated.