ABSTRACT
Application of Floquet's theorem has enabled solution of problems of free and forced vibrations of a periodic railway track. The problem of travelling wave propagation in the continuous structure has been studied at first. This chapter deals with the dynamics of a periodic structure by means of which such a mechanical system as a railway track can be modelled. The structure considered consists of an infinite Bernoulli–Euler beam resting on periodically spaced spring–damper–mass elements. At first, the case of free wave propagation in a pure elastic structure is considered. Then the steady–state system dynamic response to a moving harmonic force is studied. In both cases a procerure is used which bases on Floquet's theorem. The analysis of dispersion relations makes it possible to determine passing and stopping bands and the eigenforms corresponding to cut–off frequencies. The chapter discusses the theory of wave propagation in continuous periodic systems which are considered in mechanical engineering.
