Properties Of Elastic Waves Propagating In Randomly Disordered And Quasi Periodic Phononic Crystals

Since Kushwaha proposed the concept of "phononic crystal"(PNC),an artificial periodic elastic/acoustic structure that exhibits so-called "phononic band gaps",a great deal of attention has been focused on this kind of artificial lattice structures.The essential property of the PNC is its band gaps(or stopbands) which have numerous potential engineering applications such as acoustic filters,control of vibration isolation, noise suppression and design of new transducers.However in practical cases,disorder in certain degree or completely disorder always exists due to randomly distributed material defaults or manufacture errors during production process.Disorder in the PNCs will lead to the wave localization phenomenon which can be used to control the wave propagation.Because of the lack of periodicity the mathematic process becomes more difficult and some parameters used to describe the band structures fail.In this thesis,we study the following problems for elastic waves propagationg in disordered phononic crystals:(1) The concept of the localization factor calculated by the transfer matrix method is introduced to describe the band structures and localization behaviors of elastic waves propagating obliquely in 1D perfect and randomly disordered PNCs.The results show that the localization factor is an effective parameter in characterizing the band structures and localization phenomenon of 1D perfect and randomly disordered PNCs.(2) The plane-wave-expansion based transfer matrix method(PWE-based TMM) is generalized to calculate the localization factor which is introduced to describe the band structures and localization behaviors of 2D perfect PNCs and 2D PNCs randomly disordered in one direction and perfect in the other direction.The band structures in the first Brillouin Zone are discribed by the localization factors.The results show that the localization factor is an effective parameter in characterizing the band structures of 2D perfect PNCs and 2D PNCs randomly disordered in one direction and perfect in the other direction.The studies of the above two problems show that the localization factor which can be calculated simplely is an effective parameter in characterizing the wave localization phenomenon of the 1D disordered systems.As the disorder of the system increases,the value of the localization factor increases in the pass bands and decreases in the band gaps.The localization behavior is more pronounced at higher frequencies.(3) Combined with the plane wave expansion method,the supercell technique is used to calculate the dispersion curves of 2D randomly disordered PNCs in which the radius or locations of the scatterers are disordered.The band structures expressed by the dispersion curves have a good aggrernent with those by the frequency response calculated by the finite element method.And the results show that there appear many flat bands as the defected states in the band structures of the randomly disordered PNCs.This implies that the localization phenomenon exists at the corresponding frequencies of the flat bands.(4) A quasi periodic system is another intermediate case between the perfectly ordered and completely disordered systems.Treating this system as a disordered one deviating quasi-periodically from a periodic one we study the properties of the wave propagating in the 1D(Fibonacci sequency) quasi periodic phononic crystals (QPNCs) and the 2D phononic crystal with Fibonacci sequency in one direction and translational symmetry in the other direction using the transfer matrix and PWE-based TMM,respectively.The band structures of the above two systems are expressed by the localization factors and response.The results show that the localization phenomenon appears when the wave propagates in the QPNCs,and that the localization factor is an effective parameter in characterizing the band structures of the QPNCs.The band gaps of the QPNCs are more and narrower than those of its periodic average structure and randomly disordered systems.Pure passbands appear if we introduce translational symmetry to the QPNCs.More structures in the frequency bands are obtained if the mirror symmetry is further introduced.For the QPNCs band gaps may appear in the low frequencies.At last, the supereell technique combined with the PWE method is used to conduct a primary research on the band structures of the 2D QPNC with 8-fold symmetry.In addition,the parameters of the localization factor,the dispersion curve and the frequency response in charactering the properties of wave propagation and localization phenomenon are discussed and compared in this thesis.