Research On The Applied Condition Of The Quasi-static Analytical Methods For Elastic Waves Propagating In The Periodic Honeycomb Structures

The lattice material has been widely used in various engineering fields as its feature of light weight, high strength, energy absorption, noise reduction and so on. The study of its dynamic character is divided into two categories. One is the quasi-static analytical methods, such as the representative volume element method, the asymptotic homogenization method, differential medium method, to analyze the quasi-static material parameters under the wprking condition of static load; the other is the dynamic analytical methods, such as the plane wave spectrum method, finite difference time domain method, finite element method, to analyze the dynamic material parameters and Band gap structures. In order to research the applied scope of the two kind methods, a two dimensional analytical model with a large number of honeycomb structures is constructed to study on its quasi-static material parameters and its Band gap properties, the main research includes:Firstly, the quasi-static material parameters of the model are analyzed with the method of representative volume element method and asymptotic homogenization method by using finite element software, and the correctness of the result are verified by comparing the two method. Secondly the viscous boundary condition in the boundary of the model is established to simulate the effects of external unlimited domain to the computational domain, the relationship between simulation accuracy and the angle of incident wave are also analyzed. Thirdly, the Band gap character of the model are analyzed with viscous boundary and the starting frequency of the first Band gap are calculated out with the method of finite element method by using finite element software ANSYS. Lastly, 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 obtained by using the homogenization method and the spectrum analysis method, the condition is discussed for the use of the material parameters evaluated by means of the quasi-static analytical methods, which is described by virtue of the characteristic parameter defined 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 dimensional large model of honeycomb structures, are illustrated when the plane wave frequency gradually approaches the first band gap frequency of honeycomb structures.