Effective speed of shear waves in phononic crystals
Résumé
The paper is concerned with the analytical and numerical study of quasistatic (effective) speed of shear waves in phononic crystals. The study involves the plane wave expansion (PWE) and the new method based on the monodromy matrix (MM). It is introduced as a multiplicative integral, taken with respect to one coordinate, of the matrix with components defined as operators acting on the functions of the other coordinates. Using these two approaches, we derive closed-form estimates and develop efficient numerical procedures. It is shown that the MM method provides the best accuracy both of the estimates and of the numerical calculation.
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