A Fourier transform-based method has been developed for calculating the response of a railway track as an infinitely long uniform periodic structure subject to moving or stationary harmonic loads. The track may become a non-uniform periodic structure by, for example, rail dampers which are installed between sleepers to control rolling noise and roughness growth. The period of the structure may become greater than the sleeper spacing. For those new situations, the current version of the method cannot be directly applied; it must be generalized and this is the aim of this paper. Generalization is performed by applying periodic conditions to each type of support and summarizing contributions from all types of support. Responses of the rail, sleeper, and damper are all formulated as an inverse Fourier transform from wavenumber domain to spatial domain. The generalized method is applied to investigate dynamics of a typical track with rail dampers of particular design. It is found that the rail dampers can significantly suppress the pinned–pinned vibration of the original track, widen the stop bands and increase vibration decay rate along the rail. However, it is also found that a new pinned–pinned mode is created by the dampers and between about 450 and 1,300 Hz dampers vibrate stronger than the rail, making noise radiation from the dampers a potential issue. These concerns must be fully investigated in the future. The formulae presented in this paper provide a powerful tool to do that.