The Optimization Of Acoustic Band Gaps Between Any Bands In Two-dimensional Phononic Crystals

Phononic crystal (PC) is a kind of periodic-structure material, in which there exists acoustic or elastic wave band-gaps. The sound and vibration are forbidden during band-gaps. Since most applications of the PCs rely on the existence of acoustic band-gaps (ABGs), we would design the PCs structures to create ABGs with a desired width in particular frequencies, basing on the idea, we commit ourselves to the optimization of ABGs between any bands in two-dimensional PCs. Which will help the applications of PCs.First, we introduced concept, properties and calculation method of band structure of PCs from the theory of energy band and photonic crystals, and given the importance, actuality, research direction of PCs.Then, elastic wave equation of PCs is given from basis of elasticity. And the equations of plane-wave expansion (PWE) method for kinds of PCs are given in detail. And we introduced kinds of common structure functions and common arrays of phononic crystals.Third, the concept of group is introduced, which is a mathematical tool for analyzing symmetry of the crystal structure. And the crystallographic point groups and group of symmetry are shown particularly.Forth, we study the ABGs between any bands tuned by configuration of atom rods. As a comparison, we have examined the normalized gap width of gaps between 1-2 bands,2-3 bands,3-4 bands and 4-5 bands varies with the radius of a single rod atom, find out the maximum of every band gap. Then we insert an additional rod atom in the arbitrary position of unit cell with the radiuses of two atom rods being 0.1a, find out the positions which the ABGs can obtain the maximum, then tuned the radiuses of the two atom rods with their position fixed. The numerical results show that the ABGs between any bands except 1-2 bands could be enlarged and reach the maximum by configuration at a suitable position of the second rod atom and preferable radiuses of the two atom rods . The results also show that the symmetry reduction of the system is more efficient to create the ABGs between the bands in higher frequency. This kind of approach will be proved useful in designing phononic band gaps of a variety of phononic crystals.We find that ABGs between any bands can be tuned by configuration of atom rod, and could obtain larger ABGs, this is the innovation of the paper.