The Theory Research Of The Bandgap Structure Of One Dimensional Phononic Crystals

Phononic crystal is the present scientific hot research content, by analogy in the1990s, theconcept of photonic crystal and derived. The researchers found that it will form the elasticwave band gaps when elastic wave propagation in the phononic crystal, which is due to thespecial cycle internal structure that can form special dispersion relations. The elastic wave cannot propagation in the band gap range unless the phonon crystal has defect, and the elasticwave will be localized in the defect or propagation along the defect. Phononic crystal also hasthe characteristics such as negative refraction, sound absorption, directional transmission andfocus of the acoustic. These properties aroused the interests of domestic and foreign scientists,phonon crystal has become a scientific hot topic.In this paper, we deduced the transfer matrixof one-dimensional periodic layered phononic crystal, based on the energy band theory andelastic dynamics theory, starting from the basic equations of continuous state parameters andcombined with the boundary conditions;deduce the transmissivity formula based on transfermatrix theory and analyzes the influence factor of transmittance.A two-component one dimension phononic crystal is designed which is constitute ofepoxy resin and aluminum. Inspired by the thought of mesoscopic piezoresistive effect,phnonic crystal is studied by introducing pressure variable.The transmission spectrumfeatures under stress are studied by transfer matrix method. Through the analysis of thechange of transmission line, we has found a new phenomenon: under the influence of variablepressure, the sonic band gaps can be controlled appearance and disappearance or translation,especially the pass band will reverse to a band gap with the change of pressure. In order todifferent from the acoustic elasticity effect of body material, reference mesoscopic pressureresistance and the effects of the mesoscopic calender, we proposed the mesoscopic soundpressure effect, that is the force coupled with sound phenomenon of phononic crystal, thisinheritanced and maintained the systemic research of mentor. In order to determine this kindof phenomenon is caused by stress, we especially studied the relationship between the cyclenumber and the transmission spectrum of the phononic crystal line, under the constantcondition of pressure. A structure of ABBA composed of aluminum and plastic one dimensional mirror imageDual-periodical Photonic Crystal Hererogeneous was designed. The change of thetemperature parameters are studied by transfer matrix method for the influence of the bandgap of phononic crystal. The results show that when the temperature changes, the phononcrystal not only happened linear expansion, the young’s modulus of the aluminium and plasticwhich composed the phononic crystal is change, also. The transmission line shows that underthe influence of the temperature, the band gaps can be controlled appearance anddisappearance, and with the increase of temperature, the band gap will move towards thedirection of the frequency increases. Especially under the condition of a certain temperature inthe reversal of the band gap, which changed from pass band to band gap. The results showthat temperature has a significant effect on the phonon crystal band gap.