不同声子晶体模型的轨道结构振动带隙对比分析

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摘要为从弹性波角度准确分析轨道结构的振动特性，采用传递矩阵法建立单层欧拉梁、单层铁木辛柯梁，双层欧拉梁、双层铁木辛柯梁四种轨道结构声子晶体理论分析模型，分析结果表明，不考虑阻尼影响时，单层欧拉梁模型与单层铁木辛柯梁模型在0-250Hz内带隙位置无明显差异，在1000Hz以上时二者的带隙位置则显著不同；双层欧拉梁模型和双层铁木辛柯梁模型0-250Hz内带隙位置有较大不同，而在250Hz以上频段内的“带隙”位置基本相同，且与单层梁模型带隙位置有显著不同。考虑阻尼影响时，各模型均存在通带变为不完全带隙，以及禁带的频带宽度会有微小展宽的现象，禁带的中心位置受阻尼的影响可忽略不计。在低频（0-250Hz）内的现场测试结果与理论分析结果基本吻合，因此建议采用声子晶体理论分析钢轨振动噪声控制时，250Hz以上的中高频振动分析采用铁木辛柯梁模型更为准确，分析250Hz以下低频振动时，无砟轨道可用单层欧拉梁模型或铁木辛柯梁模型，有砟轨道应采用双层铁木辛柯梁模型。

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	梁玉雄1
	冯青松1
	陆建飞2
	杨舟1
	雷晓燕1

关键词 ：弹性波传播, 带隙;声子晶体理论模型;有砟轨道;无砟轨道

Abstract：In order to analyze the vibration characteristics of track structure accurately from the perspective of elastic wave, the transfer matrix method was used to establish 4 kinds of phononic crystal theoretical analysis models, single-layer Euler beam, single-layer Timoshenko beam, double-layer Euler beam and double-layer Timoshenko beam. The energy bands and transmission characteristics of track vibration was studied in 0-3500 Hz. The results showed that without considering the influence of damping there is no obvious difference between the single-layer Euler beam model and the single-layer Timoshenko beam model in 0-250 Hz，while the band gap position is significantly different above 1000 Hz. The band gap position in the low frequency during 0-250 Hz was different between the double-layer Euler beam model and the double-layer Timoshenko beam model, when the frequency increases to more than 250 Hz, the double-layer beam model is basically the same, but significantly different from that of the single-layer beam model. When considering the damping affection, the passband changed into incomplete band gap, the width of the forbidden band appeared a small broadening, and the center position of the forbidden band is negligible affected by the damping. Site tests results show that at low frequencies (0-250 Hz) The band gap is basically consistent with the theoretical analysis results. Therefore, in order to study the track vibration and noise controlling with the phononic crystal theory, the Timoshenko beam model was more accurate to analyze the medium and high frequency vibration of more than 250 Hz, the single-layer support Euler beam model and single-layer support Timoshenko beam model can be chosen in ballastless track, while when the analysis frequency range was below 250 Hz, the double-layer support Timoshenko beam model should be chosen.

Key words： elastic wave propagation band gap phononic models ballast track ballastless track

收稿日期: 2020-10-12 出版日期: 2022-03-15

引用本文:

梁玉雄1，冯青松1，陆建飞2，杨舟1，雷晓燕1. 不同声子晶体模型的轨道结构振动带隙对比分析[J]. 振动与冲击, 2022, 41(5): 131-140.
LIANG Yuxiong1, FENG Qingsong1, LU Jianfei2, YANG Zhou1, LEI Xiaoyan1. Comparative analysis of vibration band gap of track structure with different phononic crystal models. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(5): 131-140.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I5/131

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