Modelling of acoustic waves propagating in nesting Fibonacci super-lattice phononic crystal

Abstract

Herein, we report construction of one kind of nesting-Fibonacci-super-lattice phononic crystal, in which the super-lattice cell is a well-defined Fibonacci generation sequence. We present a comparative study on band-gap structures of acoustic waves propagating in one-dimensional, nesting Fibonacci-periodic structure and simple-periodic structure. We find that there are more band gaps in nesting Fibonacci super-lattice models, and that they present behavior different from the split-up of band gaps with different generation numbers. With the increase of generation number, more band gaps split and occur. Additionally, when generation number becomes larger, Bragg scattering becomes more significant: the characteristic curves become flatter and band gaps become wider. Furthermore, we study the effect of various parameters such as density, thickness and defects on band-gap structures. Our work is significant both for understanding the intrinsic physical properties of nesting Fibonacci sequences and for providing flexible choices to meet real engineering requirements.