Study Of Band-gap Structure In Nesting-Fibonacci Super-lattice Phononic Crystal

Phononic Crystals are periodic composite materials with band-gap property. As elastic waves can’t propagate in forbidden band, Phononic Crystal can be used for sound-proofing, vibration attenuation and new acoustic function device. The band-gap structure of Phononic Crystal can be affected by some parameters, such as materials parameters, structure parameters of crystal and phononic defection. Generally, large difference of material parameters in Phononic Crystal compositions can enhance the Bragg scattering, as a result band gaps occur more easily. In this paper, Tungsten and Silicon are used as the compositions of Phononic Crystal. We introduce the complete formulations of plane wave expansion method and transfer matrix method. By these methods, we compute and analysis the dispersion curves and transmission spectra of one dimensional Phononic Crystal, the dispersion curves of two dimensional Phononic Crystal and the dispersion curves of Lamb waves in one dimensional Phononic Crystal plates, respectively. The nesting-Fibonacci-super-lattice Phononic Crystals are mainly studied, in which the super-lattice cell is a well-defined Fibonacci generation sequence. The dispersion curves and transmission spectra of nesting-Fibonacci Phononic Crystals are calculated. By a comparative study with the simple periodic structure, we find that there are more band gaps in nesting-Fibonacci super-lattice structure. This is because the Fibonacci super-lattice can cause band-gap splitting. With the increase of Fibonacci generation, more band gaps split and occur. Meanwhile, periodic super-lattice array enhances the Bragg scattering so that the characteristic curves of nesting-Fibonacci Phononic Crystal become flatter. Further, we study the band-gap structure of Lamb waves in one dimensional nesting-Fibonacci super-lattice thin plates. Compared with the periodic thin plates, we find that there are more band gaps split and occur in nesting-Fibonacci super-lattice structure. With the growth of generation numbers, the number of band gaps increases.Our works are significant not only for understanding intrinsic physical property of the nesting Fibonacci sequences, but also for designing the special structures to adjust the width of band gaps and the frequency ranges of Phononic Crystals in applications. It provides flexible choices for real engineering requirement.