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Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals
Advances in Materials Science and Engineering
A method for calculating the effective sound velocities for a 1D phononic crystal is presented; it is valid when the lattice constant is much smaller than the acoustic wave length; therefore, the periodic medium could be regarded as a homogeneous one. The method is based on the expansion of the displacements field into plane waves, satisfying the Bloch theorem. The expansion allows us to obtain a wave equation for the amplitude of the macroscopic displacements field. From the form of thisdoi:10.1155/2016/3017835 fatcat:ghjlqnlvrjgqhebymo5z7nzfey