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A novel computational modelling approach for prediction of environmental vibration is introduced. The model is formulated in both moving and fixed frames of reference, with a mixed frame of reference formulation introduced to couple the two frames of reference. The resulting system is able to model a vehicle travelling on an infinite railway track, formulated in a moving frame of reference, interacting via the soil with a structure (i.e. building), formulated in a fixed frame of reference. The method utilizes a semi-analytical soil model with the structures modelled using three-dimensional finite elements. Two solution procedures of the full system are proposed: partial coupling, where some secondary effects from reflected waves propagating through soil are disregarded, and full coupling, where the vehicle-track-soil-structure is modelled as a fully coupled system. Both proposed solution procedures offer a one-step approach for solving the whole system in the frequency-spatial domain. The usage of the model is demonstrated in two example cases: one analysing a simple building structure near a railway track, using the partial coupling solution procedure, and another one analysing the behaviour of a vehicle model traversing over a rigid block embedded inside the soil, using the full coupling solution procedure. The introduced modelling approach offers a computationally efficient solution procedure, at the same time being applicable to a wide array of application cases.

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Abstract. Periodic structures are known to produce passbands and stopbands for propagation of vibration energy within the frequency domain. Sources vibrating harmonically at a frequency