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A Study of Band Gap for Two Dimensional Phononic Crystal with Square Lattices Based on Plane Wave Algorithm

Zheng Hui-ming

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Abstract

Phononic crystal can give rise to complete acoustic band gaps within which sound and vibrations are forbidden. In this paper, we use plane wave algorithm to study the band gap structure of 2D phononic crystal with square lattices. The results show that a giant full band gap is found in the CH3OH /Hg system. And in other solid or liquid system, the same width and quantity full band gaps have not been found so far. The influence of different cross section shapes of the scatter pole in 2D phononic crystal for forming full band gap is also studied. From the results, we get the relation of the first(total) relative frequency width with the filling ratio.

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Phononic crystal can give rise to complete acoustic band gaps within which sound and vibrations are forbidden. In this paper, we use plane wave algorithm to study the band gap structure of 2D phononic crystal with square lattices. The results show that a giant full band gap is found in the CH3OH /Hg system. And in other solid or liquid system, the same width and quantity full band gaps have not been found so far. The influence of different cross section shapes of the scatter pole in 2D phononic crystal for forming full band gap is also studied. From the results, we get the relation of the first(total) relative frequency width with the filling ratio.

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Available abstract

Phononic crystal can give rise to complete acoustic band gaps within which sound and vibrations are forbidden. In this paper, we use plane wave algorithm to study the band gap structure of 2D phononic crystal with square lattices. The results show that a giant full band gap is found in the CH3OH /Hg system. And in other solid or liquid system, the same width and quantity full band gaps have not been found so far. The influence of different cross section shapes of the scatter pole in 2D phononic crystal for forming full band gap is also studied. From the results, we get the relation of the first(total) relative frequency width with the filling ratio.

Key concepts: Band gap, Plane wave expansion method, Crystal (programming language), Acoustic metamaterials, Square (algebra), Vibration, Plane (geometry), Materials science

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