周期蜂窝结构准静态参数分析方法适用条件探讨

摘要

对于具有周期结构的复合材料动力学特性研究，或采用均匀化等方法分析其准静态材料参数，或采用平面波谱等方法分析其动态材料参数和带隙特性。为界定这两类方法的适用范围，针对蜂窝周期结构，建立了二维大模型，施加吸收边界条件，采用瞬态动力响应分析的时程积分方法，分析了不同频率波在周期蜂窝结构中的传播；并与模型的准静态均匀化分析结果和谐响应谱分析结果加以比较，探讨了准静态分析方法的适用范围，且以周期结构单胞的特征尺寸与传播波在材料中的特征波长之比ζ为参量来描述；同时，给出了传播波频率达到第一带隙频率前，平面波在二维周期蜂窝结构中传播的幅值衰减特性。结果表明：对于单胞角度α≤120°的蜂窝周期结构，当ζ≤0．1时，可采用静态均匀化方法等分析其材料参数，当ζ≥0．3时，可采用平面波谱法、有限差分时域法和多重散射法等分析其带隙特性。%There are two kinds of analytical methods for investigating the material characteristics of composites with periodic mi-crostructures,such as honeycomb structures.One is the quasi-static analytical methods,such as the homogenization method,to analyze the quasi-static material parameters,and the other is the dynamic analytical methods,such as the plane wave spectrum method,to analyze the dynamic material parameters and band gap structures.In order to distinguish the applied scope of the two kind methods,a two dimensional analytical model with a large number of honeycomb structures is firstly constructed,and the transient behaves of waves which propagate in the model of honeycomb structures are simulated by using the time-integration method for transient dynamic analyses with the absorbing boundary condition.Comparing the numerical results with those ob-tained by using the homogenization method and the spectrum analysis method,the condition is discussed for the use of the materi-al parameters evaluated by means of the quasi-static analytical methods,which is described by virtue of the characteristic parame-terζdefined as the ratio of the feature size of periodic structures to the characteristic wavelength of the plane wave propagating in the solid materials.Meanwhile,the amplitude attenuation characteristics of the plane wave,which transmits in the two dimen-sional large model of honeycomb structures,are illustrated when the plane wave frequency gradually approaches the first band gap frequency of honeycomb structures.Results show that for the honeycomb structures with the angle of unit cellα≤120°,the qua-si-static analytical methods can be used to analyze the material parameters whenζ≤0.1,and the dynamic analytical methods can be used to analyze the band gap whenζ≥0.3.