Research On The Band Gap Mechanism And Its Applicaton Basis Of Phononic Crystals With Slit Characteristic

Phononic crystal is a new functional materials.The unique characteristics of elastic wave band gaps and rich physical connotations such as localized states and negative refraction,lead to the phononic crystal significant potential application in the noise and vibration control area and the design of new acoustical functional devices.Researches on phononic crystal has become one of the focuses concerned by domestic and foreign scholars.Based on supports of the National Basic Research Program,the Project of National Natural Science Foundation of China and the Specialized Research Fund for the Doctoral Program of Higher Education,this dissertation committed on the expansion of the new study method,the exploration of new band gap mechanism and the structure design of new phononic crystal.The related research results have a certain value on enriching the physical meaning of phononic crystals and guiding the practical structure design of phononic crystals.Firstly,aim to investigate the band gap mechanism and generation course of different phononic crystals more deeply,a new visualization method is proposed based on the perspective of elastic wave energy distribution.Starting from the wave equations,the finite element theory bases for the implementation of every aspect of the visualization method are derived.Typical examples are adopted to verify the reliability of the visualization method in investigating different type of phononic crystals.Results show that the method is accurate and reliable for the calculations of both the Bragg scattering and locally resonance phononic crystals and its convergence is fine.Secondly,with the visualization method mentioned above,the generation mechanism of wide band gap in the low frequency range in the phononic crystal with slit characteristics is deeply investigated.By calculating the dispersion relations and analyzing the transmission characteristics of the phononic crystal,the effects of the slit characteristic on the band gaps are studied.Furthermore,the microscopic views of the cell modes and the macro view of time and frequency domains are investigated to explore the interaction course and mechanism between the acoustic wave and the phononic crystal,and the flow and distribution of the acoustic wave energy.The modal inhibition mechanism of the band gap generation and the pipeline model for Bragg band gap calculation are proposed.Thirdly,as an independent concept,the “slit characteristics” is introduced into the design of gas-based phononic crystal structures to explore the effect of slit characteristics on the band gap and noise properties of the phononic crystals.By adding two parallel boards inside the internal cavity of the slotted scatterers,the internal rib phononic crystal is designed.Results show that this structure can lower the band gaps as the resonance characteristics changed,caused by the introduction of the channel and slits between the ribs;the cross-like board phononic crystal is designed,in which the “slit” and the “cavity” are constituted between the adjacent scatterers.The band gap properties of this phononic crystal are studied and the concept of “real-time modulating” is proposed;Through adding traditional sound-absorbing material,the glass wool,into the cavity of the phononic crystal,the material coupled phononic crystal is designed and the band gap properties and noise performance are investigated with the theoretical and experimental methods.Fourthly,the “slit characteristics” concept is further introduced into the design of solid-based phononic crystal structures to explore the effect of slit characteristics on the band gap and vibration properties of the phononic crystals.By setting arc slits between the scatterers and the solid matrix,the two-dimensional phononic crystal with “neck” structures is designed.With the visualization method the gap properties of the structure are studied and the effects of the neck on the band gap modulation are also discussed;furthermore,the neck structure is introduced into the phononic crystal slab with finite thickness and its effect on the lamb wave band gap properties is investigated.Results show that,the introduction of slit in one hand decreases the stiffness of the entire cell,and in other hand it forms new locally resonance unit,resulting in the occurrence of the large band gaps with low frequencies in the phononic crystal.Finally,the “slit characteristics” is introduced into defect state phononic crystal as a new defect source to explore the principle feasibility of defect phononic crystal on the realization of “real-time modulating” acoustic functional devices.Through changing the slit parameter of specific scatterers,the defect phononic crystals with point defect and line defect are formed.The local state characteristics and the wave guiding property of the defect phononic crystal are studied and the variable slit parameters are investigated for their effects on the modulation of defect stats frequencies.The line defect phononic crystal experimental platform is designed and fabricated to verify the existence of wave guiding in the slotted phononic crystal.Results show that the defect phononic crystal formed with “slit characteristics” can yield point(line)defect state in the locally resonance band gap and the variable slit parameters such as the slit width and slit angle can modulate the defect frequencies in almost all the band gap frequency range.The research in this dissertation not only enrich the theoretical connotation of the phononic crystal and laid foundation for the further study,but also provide new ideas and direction for the structure design of new phononic crystals and its application exploration.