Theoretical Study On Transmission Spectrum Of1D Phononic Crystal

The study of the transmission spectrum is the most basic and the most attractive partin phononic crystal research. Application prospect of the Band gap characteristics inphononic crystal has being attracting the attention of more and more people,studying inphysics，materials and mechanics or other related scientific researchers. The study ofphononic crystal has been gradually changed from theory to experiments. As the acousticdevices，such as the surface acoustic wave filter devices,the acoustic surface waveresonator and acoustic wave guide, was being to production and use for us, application ofphononic crystal was becoming more and more widespread in the military and life.This paper mainly uses the transfer matrix method to study the transmissioncharacteristics of elastic wave which transmit in1D periodic phononic crystal. Using theanalytical method to deduce one-dimensional phononic crystal transmittance formula inthe cases of incident longitudinal wave, using the numerical simulation to get transmissionspectrum under the same situation, the results of transmission coefficient match each otherwith two kinds of methods and are precise. The law could be found by analysising thetransmission formula, researching the transmission appearing position of peaks and themost important influence factors of transmission coefficient. Research shows that, if thecomponents material of phononic crystal was not changed, the appearing position oftransmission peaks mainly are related to the period number and the lattice constant, andthe maximum position of the transmission peaks do change along with phononic crystalcycle number. If the period and lattice constant of phononic crystals are invariable, bandgap width would become large with the increasing acoustic impedance of betweenelements. Further research on the band structure can obtain main factors which are relatedwith the group velocity and phase velocity of elastic wave in the phononic crystal. Theobtained results can provide theoretical basis for developing acoustic device design andideal phononic crystal materials based on forbidden band characteristic of phononiccrystal.Phononic crystal is the full vector wave of coupled transverse wave and longitudinalwave, so that it has many unique properties. This article introduced tunneling effect of phononic crystals and theoretical explanation briefly. Adjusting the parameters attemptedto find the rule of transmission spectrum of one-dimensional phononic crystal withtunneling effect. Through the analysis of phononic crystals of phase difference ofinterfacial elastic wave, the reason of transmission peaks was given for a relativelydetailed theoretical interpretation. These researches have a guiding significance for newacoustic filter design and manufacturing.