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本文利用集中质量法对弹性纵波在—维指数形截面有限周期声子晶体中的传播进行了研究,得到了频率响应函数的表达式.与—维等截面的声子晶体相比,指数形变截面声子晶体带隙内的衰减值随着输出端截面积的增大而减小,同时带隙的起始频率降低而截止频率升高,也即带隙的宽度会得到拓展.晶格常数和材料组份比变化时,变截面声子晶体带隙的起始频率和截止频率的变化趋势与等截面时的声子晶体相同.希望本文的研究能够推动声子晶体在减振降噪等领域中的应用.
In this paper, we study the propagation of elastic longitudinal waves in phononic crystals with finite periodicity in a - dimensional exponential cross-section and obtain the expression of frequency response function by using the mass method. Compared with the phononic crystals with - The attenuation value in the phononic crystal band gap decreases with the increase of the cross-sectional area of the output end, meanwhile the initial frequency of the band gap decreases and the cut-off frequency increases, that is, the width of the bandgap will be expanded. When the material composition ratio changes, the change trend of the initial frequency and the cutoff frequency of the band gap of the phononic crystals with the same cross section is the same as that of the phonon crystals with the same cross-section. It is hoped that this study can promote the application of phononic crystals in the fields of vibration reduction and noise reduction In the application.