Transition radiation excited by a surface load that moves over the interface of two elastic layers

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Transition radiation is emitted when a perturbation source such as an electric charge or mechanical load, which has no inherent frequency, moves along a straight line at constant velocity in or near an inhomogeneous medium. Transition radiation of elastic waves is emitted, for example, by the wheels of a train due to track inhomogeneities such as non-uniform subsoil. This type of radiation was analyzed in the framework of several 1-D and 2-D elastic systems, but very few studies focus on elastic continua. Here, we consider a continuum consisting of two elastic layers (i.e., waveguides) that are coupled at a vertical interface. Both layers are in plane strain, have a free surface and are fixed to a rigid bottom, while the load is assumed to move along the free surface and over the layer interface. The response in each layer consists of the stationary eigenfield that moves with the load and a free field that propagates independently. The latter is expanded into a set of propagating and evanescent guided modes, while all fields are coupled at the interface. Orthogonality relations are employed to find the modal coefficients. Results show that the transition radiation energy (i.e., the energy flux through a surface far away from the layer interface) becomes powerful for load velocities approaching the critical velocity or for high contrast in material parameters. Furthermore, the free-field contribution to the energy flux through a circular surface close to the layer interface exhibits peculiar directivities. Depending on the contrast in material parameters and the load velocity, it can be extreme along the free surface, along the layer interface or into the medium. The free-field contribution can dominate that of the eigenfield for high load velocities, as is the case for the transition radiation energy. To study the features of the generated wave field in pure form, we take the load velocity sub-critical throughout the paper, excluding other radiation effects. However, the adopted solution is not restricted to that and is expected to work also for layered media, even when connected to other elastic structures like beams.