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一维指数形变截面有限周期声子晶体的研究
Investigation of one-dimensional finite phononic crystal with exponential section
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摘要: 本文利用集中质量法对弹性纵波在一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．与一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．Abstract: In this paper, we study the propagation of elastic longitudinal wave in one-dimensional (1D) finite periodic phononic crystal with exponential section, and obtain the expression of frequency response function. Comparing the 1D phononic crystal with constant section, we find that the value of attenuation inside the band gap decreases quickly as the cross-sectional area of output and increases, at the same time, the initial frequency decreases and the cut-off frequency increases, i.e. the width of the band gap will increase. The effects of the lattice constant and the filling fraction on band gap are also analyzed. The change trends of the initial frequency and cut-off frequency are consistent with those of constant section. We hope that the investigation of this paper will be helpful for the phononic crystal in practical application such as vibration shield.
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