Abstract: Based on the wave equation of one-dimensional phononic crystal, a study is performed for the band gap characteristics through the analysis of the symmetrical primitive cells in phononic crystal. It is found that the band-edge mode is the same as the natural vibration mode of symmetrical primitive cells. Therefore the analysis on the band gap characteristics of 1D phononic crystal can be simplified to the analysis on the natural mode of its single symmetrical primitive cell. The study shows that the vibration mode of the 1D phononic crystal is the coupling mode of interaction of the natural vibration modes of various symmetrical primitive cells. There is uncoupling effects at the edge of the band gap due to Bragg scattering. The vibration mode is an uncoupling standing-wave mode, thus being consistent with the natural vibration mode of the single symmetrical primitive cell. The conclusions are examined by vibration test of a phononic crystal thin-beam composed of Al and organic glass. The test result is basically in agreement with the result of theoretical analysis. This provides a new and simplified idea for the research on band gap characteristics and for the design of vibration and noise reduction of complex beam structure of phononic crystal.

Key words: Crystal lattice, Phononic crystals, Primitive cell, Symmetry, Vibration band gap