Wave Propagation in a Periodically Layered Medium, Taking into Account the Effect of Microstructure Size: A Tolerance Modelling Method

The subject of consideration is a medium that is periodically layered along its thickness, H, in the direction of the x3 axis, resting on an undeformable base. It consists of many repeating thin layers of thickness h (small compared to H). Each layer is made up of an even number of ‘sublayers’. In the medium under consideration, it is possible to identify a small repeating element, known as the periodicity cell. In order to account for the influence of the size of this element (the so-called microstructure size effect) in the analysis of the dynamic behaviour of a periodically layered medium, the tolerance modelling method is applied. The derived equations have constant coefficients and take into account the microstructure size effect mainly in dynamic problems of a periodically layered medium. This effect is demonstrated using the example of wave propagation along the x1 axis, parallel to the layers, with a displacement component along the x3 axis, i.e., perpendicular to the layers. Formulas determining the wave propagation speeds in the medium under consideration are derived, and the influence of various parameters related to the medium’s structure is analysed. Furthermore, in the range of lower wave propagation speeds, the results are confirmed using the well-known asymptotic model.