中文摘要：

从一维声子晶体的波动方程出发,选用保持晶格对称性的原胞对声子晶体的能带结构进行解析分析。结果表明一维声子晶体带隙边缘的振动模式与其单个对称性原胞的固有振动模式完全一致,从而对一维声子晶体带隙特性的分析可以简化为对其单个对称性原胞固有模式的分析。研究表明,一维声子晶体中的振动模式是其各对称性原胞固有振动模式相互作用的耦合模式,在带隙边缘由于布拉格散射出现解耦效应,振动模式为解耦的驻波模式,从而与单个对称性原胞的固有振动模式一致。以有机玻璃及铝构成的声子晶体细直梁为例,采用振动试验对其振动传输特性进行测试,试验结果同理论分析结果基本吻合。这为声子晶体复杂梁杆结构的带隙特性研究及减振降噪设计提供了新的、简化的思路。

英文摘要：

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.