Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

作     者：B.Tie B.Y.Tian D.Aubry 

作者机构：Laboratory MSSMat(UMR-CNRS 8579)Ecole Centrale ParisGrande Voie des Vignes92295 Chatenay-Malabry CedexFrance 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2013年第29卷第6期

页      面：783-798页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 080102[工学-固体力学] 

主　　题：Elastic wave propagation Periodic beam lattice Bloch wave theory Bandgaps Anisotropy Disper- sion relation 

摘      要：The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane （with respect to the lattice plane） and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding ＂retro-propagating＂ frequency bands.