Multi-layered media are one of the most common phenomena in natural or artificial surroundings, and it is considered as a good candidates for biomedical applications. The transversely isotropic characteristic of materials have been widely recognized in elastic multi-layered media. Furthermore, interface conditions between transversely isotropic elastic multi-layered medium layers plays an important role in the medium's performance. Despite many numerical approaches in these analyses, very few theoretical methods are available in dealing with these two important issues. This study presents a method to compute the response of transversely isotropic elastic multi-layered medium subjected to the impact load, i.e. falling weight deflectometer load (FWD) load, when interfacial conditions are considered. Details of the mathematical derivation, implementation and verification of the proposed analytical solution are presented. The absence of positive exponential functions in the solution leads to a considerable improvement in computation efficiency and stability. Subsequent numerical results demonstrate that both transverse isotropy and interface conditions could substantially contribute to the responses of the elastic multi-layered medium.
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