Elastic wave propagation in honeycomb materials

In this paper, the elastic wave propagation in honeycombmaterials is investigated based on the dispersion relations. The Block waveswill be generated due to the periodicity of the honeycomb structure.Consequently, the dispersion relation (also called the band structure) isdivided into separate bands. The wavelet theory is employed to calculate theband structures of aluminum (Al) and polypropylene (PP) honeycomb materialswith three typical lattice structures, namely, square, triangular andhexagonal. The material parameters and the displacements of the honeycombmaterials are deduced into the wavelet forms associated with biorthogonalperiodic basis functions. The wave equations are also reduced to Eigenvalueproblems characterized by the Bloch theorem and variational theory. Thetheoretical results show that the significant effect of lattice structuresand the little effect of the material types of the honeycomb materials arefound on the elastic wave propagation. All three lattice cases do notexhibit the complete band gaps and only the square and triangular casesexhibit the directional band gaps. Furthermore, a wider directional band gapis achieved in the triangular case than in the square case in the widerpropagating direction at lower frequencies.