Lattice Resonance Phononic Crystals And Supercell Lattice Studies

Phononic crystals are an functional materials whose elastic constant and density are periodically distributed in space.Its special structure makes it difficult for elastic waves of a certain frequency range to pass through,resulting in elastic wave band gaps.There are currently well-known two phononic crystal band gap generation mechanisms:local resonance mechanism(This mechanism produces sub-wavelength band gaps)and Bragg scattering mechanism(This mechanism can only produce non sub-wavelength band gaps).On the basis of these two mechanisms,the band gap designs of phononic crystals has been fully developed.In this thesis,a new sub-wavelength band gap generation mechanism(lattice resonance mechanism)is proposed.Both it and the local resonance mechanism belong to the resonance type mechanism of producing sub-wavelength band gaps.The former is not explicitly mentioned in the literature,but the latter is widely known.The physical view of localization degree is proposed.The generation mechanism of sub-wavelength band gaps of lattice resonance and its difference from local resonance and Bragg scattering mechanism are studied.The lattice resonance 3×3 supercell structures are constructed,and the effects of the removal of the scatterer,the translation of the intermediate scatterer and the material substitutions of the intermediate scatterer on the sub-wavelength band gaps are studied.The main research work and innovations of the thesis are as follows:1.A new mechanism of sub-wavelength band gap formation(lattice resonance mechanism)is proposed.The physical view of localization degree is introduced and the characteristics of lattice resonance mechanism and local resonance mechanism are compared.It is found that lattice resonance mechanism is different from the special wave properties of local resonance mechanism.The scatterers(rubber-wrapped solids)with low-frequency resonance characteristics are put into different liquids,gases and solids respectively to obtain the general methods of sub-wavelength band gaps.2.The lattice resonance mechanism is compared with the existing two mechanisms,and the mechanisms of the three band gaps are different.In the Bragg scattering mechanism,the backscattering waves are enhanced by the coherent interference of the scattering waves,thus forming non sub-wavelength band gaps;in the lattice resonance mechanism,the backscattering waves are enhanced by the nonlocal resonance of the whole lattice,thus forming sub-wavelength band gaps;in the local resonance mechanism,the backscattering waves are enhanced due to the near independent resonance of a single scatterer,thus forming sub-wavelength band gaps.3.The influences of various parameters on the position of the lattice resonance full band gaps were analyzed,and the application range of sub-wavelength band gaps is expanded.The effects of material losses on the transmission spectrum of lattice resonant phononic crystals are studied,and the loss of the elastic material and the outer layer can enlarge the first direction band gap width to a certain extent,and the loss of the substrate and the central scatterer has little effect on the band gap transmissions.4.The band gap natures of the 3×3 lattice resonance supercells are studied,and it is found that both local and non-local modalities can be generated in the original band gap range.With the increase in the amount of scatterers removed,the complete band gap width decreases to varying degrees,which indicates that the lattice resonance phononic crystals are highly dependent on the perfect periodic structure(This is also the difference between lattice resonant phononic crystals and local resonant phononic crystals).When the intermediate scatterer is translated,a new band line will be obtained at a position larger than the initial frequency of the band gaps.When one or more materials of the intermediate scatterer are replaced,the original band gap structures will be divided.In particular,for the cases that the outer layer is removed and only the elastic material is retained,multiple energy band modes within the band gaps range are realized on the basis of expanding the full band gaps width.In a word,under the lattice resonance mechanism,the supercell band gap structures have local modialities,which provides a theoretical reference for the designs of new type of sub-wavelength acoustic filters.