Research On Vibration And Acoustic Characteristics Of Generalized Phononic Crystal Spherical Shell

Phononic crystal(PC)is a new composite material or structure whose elastic constants or density is periodically distributed.It has attracted wide attention for its unique characteristics such as elastic wave band gap,defect states,negative refraction,and sound focusing.These features make PC have a broad application prospects in the field of noise and vibration isolation,noise functional devices,etc.Translational periodicity of most existing PCs imitates from natural crystal lattices,however,such specific periodicity form greatly restricts the spatial configuration of PCs,impeding further development of the theory and application of PCs.Therefore,in this paper,translational periodicity is expended,and the concept of generalized phononic crystal(GPC)is proposed and defined.Combined with spherical coordinates,a kind of one-dimensional GPC spherical shell with radial periodicity is constructed,and the characteristics of its radial vibration,acoustic insulation and scattering are studied.The main contents of the paper are as follows.Firstly,the radial vibration characteristic of GPC spherical shell is studied.Based on the elastic wave theory in solids,using the transfer matrix method combined with localization factor,spherical longitudinal wave bandgaps are theoretically analyzed and numerically discussed and the calculation results are vertisfied by the simulation of finite structure afterwards.On the basis,influence of the various material parameters and structural parameters on vibration attenuation is further analyzed.In addition,the study on the stress distribution of GPC spherical shell within longitudinal wave bandgap is carried out,revealeing stress concentration and its occurrence mechanisms.Secondly,sound insulation characteristics of GPC spherical shell is studied.Based on the acoustic radiation model with the point sound source located at the center of a GPC spherical shell,acoustic transmission coefficient,reflection coefficient,and reduction coefficient are theoretically analyzed and numerically studied,with the analytical method of spherical shell dynamics theory and fluid dynamic theory.Simulation is also performed by finite element method to verify the correctness of calculation results.Moreover,the effects of the fluid parameters inside and outside of GPC spherical shell on acoustic transmission coefficient are discussed in detail.Furthermore,the case of that point sound source locates in the non-centere of GPC spherical shell is also taken into consideration.Similarly,the acoustic radiation model is firstly built to study the sound insulation properties of GPC spherical shell for an arbitrary point sound source.The sound field inside and outside of the GPC spherical shell can be expressed as superposition of infinite sub-mode acoustic wave by Flourier transformation.With the use of state vector transfer matrix method and boundary coordination conditions,reflection and transmission coefficients of different sub-mode acoustic components are analyzed theoretically and studied numerically.Besides,for comparison,insertion loss method is introduced to calculate the overall noise reduction of GPC spherical shell and homogeneous spherical shell.Simulation is also made to verify the results.Finally,the condition that plane sound wave incidents on a GPC spherical shell is considered,with the shell filled with fluid medium both inside and outside.Theoretical analysis is given and the form function of back infinity is calculated on the basis.The influence of main parameters on the form function is also discussed.It is shown that GPC spherical shell has a significant radial vibration bandgap in which sound wave excited by the point sound source located at the center can be effectively suppressed and structural and material parameters of GPC spherical shell have important implications on the bandgap.The arrangement of the two materials constituting the GPC spherical shell has significant influence on the stress in the structure and amount of sound reduction.In the case of a non-central point sound source,GPC spherical shell still has significant sound insulation advantages compared with homogeneous spherical shell.When the plane sound wave is incident on the GPC spherical shell,the periodicity will bring some impact on backscattering spectroscopy.