Reflection of Plane Harmonic Waves At a Plane Interface of a Semi-Infinite Lattice and a Semi-Infinite Continuum

Abstract eng:
Whereas the wave reflection and refraction at an interface of two continua has been studied in detail and has become a matter of text books, the wave reflection at an interface of a lattice and a continuum does not seem to have been systematically studied. The aim of this development is to close this gap. Two semi-infinite elastic media are considered in contact at a plane interface. One of these media is modelled using a rectangular network of identical masses and springs (hereafter called a lattice), whereas the other one is described by the equations of the classical elastic continuum. The wave reflection at the interface with the classical continuum is studied assuming that a plane harmonic wave falls from the lattice on the interface. The reflection coefficients for the reflected compressional and shear waves are found as functions of the wave frequency and of the incidence angle. It is shown that the reflection at low frequencies can be made very small by properly choosing the parameters of the continuum. However, the reflection coefficients inevitably grow with increase of the frequency and can reach the values close to one. This is to be expected as the classical continuum is capable of approximating a lattice only at relatively low frequencies.

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