Design and Analysis of Lattice-Tunable Phononic Crystals for Broadband Acoustic Stopband Control

Abstract

A new type of tunable phononic crystals is proposed. The proposed phononic crystals can form acoustic stopbands of a wide frequency range by using two different physical phenomena of the Brag gap and local resonances. Since the frequency band of the stopband is inversely proportional to the lattice size, a method to increase the lattice size up to by a factor of 2 is proposed, covering quite low frequency range. To make a tunable stopband below the Bragg gap without increase in overall crystals size, the concept of an acoustically-resonant phononic crystal system is used, which utilize acoustic resonances. The system resembles a Helmholtz resonator so that the resulting stopband is independent of the lattice periodicity of the phononic crystal system. The finite element simulations for two- dimensional infinite and finite periodic structures are carried out to investigate various dynamic characteristics of the proposed tunable phononic crystals. The transmission analysis with finite periodic structures is used to investigate wave stop phenomena that may not be seen directly from their dispersion diagrams. Individual stopbands of phononic crystals may not be sufficiently wide to cover a large frequency range and also passbands between stopbands are inevitable even if a wide frequency range is realized by stopband tuning. This physical restriction may be avoided if a finite periodic or semi-periodic phononic crystal structure is properly engineered. The proposed finite phononic crystal structure can be constructed either by tuning the structure as a whole or finding the proper configurations of each of the unit cell forming the structure separately by an iterative optimization algorithm. By these two methods, a large frequency range of stopped or significantly-reduced transmission is realized. All these findings are confirmed by a number of numerical simulations.