功能梯度材料声子晶体低频带隙特性研究

Study on Low Frequency Band Gap Characteristics of Phonon Crystals of Functionally Graded Materials

声子晶体作为一种减振降噪的结构已经在建筑、土木等领域被广泛应用。基于局域共振声子晶体理论在前期研究的基础上对一种含二维变化功能梯度材料的声子晶体进行优化设计,并通过有限元数值仿真研究该声子晶体的减振性能。结果表明:功能梯度材料声子晶体能带结构在0~1000Hz内共有3条完全带隙,其第一禁带的起始频率约为0,第三禁带截止频率为991.36Hz,总禁带宽度为990.85 Hz,在该带隙范围内占比为99.08%,并且在X方向上对该声子晶体10×5个周期进行传输特性分析,分析结果完全验证了禁带的存在,证明含二维变化功能梯度材料的声子晶体能有效抑制0~1000 Hz的弹性波,最后将含功能梯度材料声子晶体与传统声子晶体进行对比分析,验证了功能梯度材料声子晶体的减振性能。研究结果可为土木交通工程减振降噪提供一种新的设计方法。

Phonon crystal,as a kind of vibration and noise reduction structure,has been widely used in architecture,civil engineering and some other fields.Based on the local resonance phonon crystal theory,a phonon crystal containing two-dimensional variable functionally gradient materials is optimized and designed in this paper.The vibration damping performance of the phonon crystal is studied by finite element numerical simulation.The results show that the band structure of phonon crystal of functionally graded materials has three complete band gaps within 0-1000 Hz.The initial frequency of the first band gap is 0,the cut-off frequency of the third band gap is 991.36 Hz,and the total band gap width is 990.85 Hz,accounting for 99.08%in the band gap range.Moreover,transmission characteristics of the 10×5 cycles of the phonon crystal are analyzed in the X-direction,and the results of the analysis completely verify the existence of band gap and prove that the phonon crystal containing the functionally gradient material with two-dimensional variation can effectively suppress the elastic wave of 0-1000 Hz.Finally,the phonon crystal containing the functionally gradient material is compared with the traditional phonon crystal,and the vibration damping performance of phonon crystals with functionally graded materials is verified.The research results provide a new design method for vibration and noise reduction in civil traffic engineering.