摘要
基于Biot理论和Bloch理论,研究了反平面波在一维液体饱和多孔声子晶体中的传播特性。求解液体饱和多孔介质中反平面波的波动方程;利用界面应力-位移连续条件得到了相邻单胞的传递矩阵,将传递矩阵和Bloch理论相结合计算了单胞的复能带结构;并且利用刚度矩阵法计算声子晶体的响应谱。分析了液体黏度系数、孔隙率和材料组分比对反平面波传播特性的影响。结果表明:随着黏度系数的增大,复能带的虚部先增大后减小,相应的传输先减弱后增强,复能带的实部在布里渊区边界处先变光滑后又变尖角。这些现象与黏性对快纵波的影响是一致的;随着孔隙率的增大,两种多孔介质的密度差变大,导致带隙变宽,带隙内的衰减增强;与快纵波不同的是高频通带对应的虚部仍然为零,这是由于反平面波和慢纵波之间不会发生相互作用;减小材料组分比发现第一条带隙变宽,带隙内的衰减增强,然而第二条带隙先变宽再变窄,带隙内的衰减先增强后减弱。估算的带隙中心频率值和数值结果基本一致。
Combining Biot and Bloch theories,propagation of the anti-plane wave in one-dimensional fluid-saturated porous phononic crystal(FSPPC)is investigated.The wave equation of anti-plane wave in fluid saturated porous media was solved.The transfer matrix(TM)between adjacent unit cells is derived based on the continuity of stress and displacement at the interface.The complex band structure(CBS)for the unit cell is computed combining the TM and Bloch theory.The stiffness matrix method is employed to calculate the transmission spectrum of a finite PC.Effects of fluid viscosity coefficient,porosity and material composition ratio on propagation characteristics of anti-plane wave were analyzed.The results indicate that with the increase of the viscosity parameter,the imaginary part of CBS firstly increases and then decreases,the corresponding transmission firstly weakens and then increases,and the real part of CBS firstly becomes smooth and then becomes sharp at Brillouin zone boundary;these phenomena are consistent with effects of viscosity on fast longitudinal wave;with increase in porosity,the density difference between two porous media becomes larger to cause widening of band gap and enhancement of attenuation in band gap;being different from fast longitudinal wave,imaginary part corresponding to high-frequency passband is still zero,it is due to no interaction between anti-plane wave and slow longitudinal wave;if decreasing material composition ratio,the first band gap widens and attenuation in this band gap increases,but the second band gap widens firstly and then narrows,and attenuation in this band gap increases firstly and then decreases;the estimated band gap center frequencies are basically consistent with the numerical results.
作者
张书燕
王艳锋
ZHANG Shuyan;WANG Yanfeng(Institute of Engineering Mechanics,Beijing Jiaotong University,Beijing 100040,China;School of Mechanical Engineering,Tianjin University,Tianjin 300350,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2022年第9期283-289,共7页
Journal of Vibration and Shock
基金
国家科学自然基金(11702017)。
关键词
声子晶体
液体饱和多孔介质
反平面波
传递矩阵法
刚度矩阵法
phononic crystal
fluid saturated porous medium
anti-plane wave
transfer matrix method
stiffness matrix method
