【摘要】 通过研究蜂窝材料的弹性波频散关系,分析了其弹性波传播特性.采用基于小波理论的分析方法,将材料参数和位移均展开为双正交周期小波基函数的形式,利用Bloch定理将波动方程转化为特征值方程,求解该方程得到3种典型结构——正方、三角与六角排列的铝(Al)和聚丙烯(PP)蜂窝材料的频散关系,并进行了比较分析.结果显示:结构形式的不同显著地影响其波动特性,而制作材料的不同则没有影响;3种结构形式都不存在完全带隙,但正方和三角形结构在一定的传播方向范围内存在方向带隙,而六角形结构则在任何方向都不存在方向带隙;与正方结构相比,三角结构在相同孔隙率下,在更广的传播方向内和更低的频率下,能产生较宽的方向带隙.更多还原

【Abstract】 In this paper,the elastic wave propagation in honeycomb materials is investigated based on the dispersion relations.The Block waves will be generated due to the periodicity of the honeycomb structure.Con- sequently,the dispersion relation (also called the band structure) is divided into separate bands.The wavelet theory is employed to calculate the band structures of aluminum (Al) and polypropylene (PP) honeycomb ma- terials with three typical lattice structures,namely,square,triangular and hexagonal.The material parameters and the displacements of the honeycomb materials are deduced into the wavelet forms associated with biorthog- onal periodic basis functions.The wave equations are also reduced to Eigenvalue problems characterized by the Bloch theorem and variational theory.The theoretical results show that the significant effect of lattice structures and the little effect of the material types of the honeycomb materials are found on the elastic wave propagation.All three lattice cases do not exhibit the complete band gaps and only the square and triangular cases exhibit the directional band gaps.Furthermore,a wider directional band gap is achieved in the triangular case than in the square case in the wider propagating direction at lower frequencies.更多还原