Frequency band structures and band-gaps of elastic wave propagation in graphene origami-reinforced Love-Bishop phononic crystals

This paper presents the frequency band structures and band-gaps analysis of elastic wave propagation in a graphene origami-reinforced Love-Bishop phononic crystal (PnCs) using an analytical approach based on the transfer matrix method. The PnCs is assumed to be made of many unit-cells, which each unit-cell is made of two sections. One section is made of pure Cu and other section is made of graphene origami-reinforced Cu material. The constitutive and governing equations of both sections are derived using Love-Bishop elasticity theory. Continuity conditions and the Bloch–Floquet theorem regarding the periodicity of the material constants in periodic materials are satisfied to obtain the frequency dispersion curves versus Bloch wave numbers. A modified micromechanical model is employed to predict the material properties of the graphene origami-reinforced section. The results show that there are two sets of frequency band-gaps, which they are called as partial and complete band-gaps. Effects of two key parameters containing the graphene origami weight fraction and the hydrogen coverage on the partial and complete frequency band-gaps are obtained and studied in detail. Both key parameters influence partial and complete band-gaps, which are created in the graphene origami-reinforced Love-Bishop PnCs.