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Plane wave perturbation method for calculating effective sound velocity of one-dimensional phononic crystals

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Document pages: 9 pages

Abstract: A method for calculating the effective sound velocity of one-dimensional phononic crystals is proposed; This method is effective when the lattice constant is much less than the length of the sound wave; Therefore, periodic media can be regarded as homogeneous media. The method is based on the expansion of displacement field to plane wave and satisfies Bloch s theorem. Through the expansion, we can obtain the wave equation of the amplitude of the macro displacement field. According to the form of the equation, we determine the effective parameters of the transverse and longitudinal macroscopic displacement in the homogenized one-dimensional phononic crystal, that is, the effective sound velocity. The results show that the explicit expression of the effective sound velocity is related to the isotropic include parameterions in the unit cell are obtained: mass density and elastic moduli. These expressions are used for studying the dependence of the effective, transverse and longitudinal, sound velocities for a binary 1D phononic crystal upon the inclusion filling fraction. A particular case is presented for 1D phononic crystals composed of W-Al and Polyethylene-Si, extending for a case solid-fluid.

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