Research On Vibration And Acoustic Insulation Properties Of Cylindrical Shells Of 1D Generalized Phononic Crystals

Phononic crystals (PCs) possess the ability of controlling the propagative characteristics of different elastic waves and thus to arousing wide attention of the academic circle. In recent years, the basic theory and calculating algorithm of the band gap in PCs have been researched extensively. In addition,the concept of PCs has been gradually extended, which is not confined to the stage of the natural lattice structure(construct models in the rectangular coordinate system).we have expanded the concept of PCs to generalized phononic crystals(GPCs) by introducing the generalized periodic into our former research.Based on the previous studies, the concept of generalized phononic crystals (GPCs) was further introduced into the cylindrical shell structures, and a type of cylindrical shells of generalized phononic crystals (CS-GPCs) was constructed, the structure field and acoustic-structural coupled field of the composite cylindrical shells were examined respectively in this paper. For the structure field, considering the Bloch theorem is no longer suitable for this kind of generalized periodic situation, a kind of analysis method of transfer matrix eigenvalue based on the mechanical state vector was proposed to calculate the energy band structure. Through the energy band structure, we found that there is an obvious wave band gap emerging when propagating in the CS-GPCs for modes with different order, whose forming mechanism includes two aspects, i.e., the wave front expansion effect and the Bragg scattering effect. In addition, we further discussed the related influences of the longitudinal wave mode and shear wave mode in structure on these band gaps, and some useful conclusions were drawn. For acoustic-structural coupled field, the expressions of the acoustic transmission coefficients for different modes were built, and the frequency responses were numerically calculated to verify the band gap characteristics of the CS-GPCs. Furthermore,the acoustic pressure distribution of the internal and external acoustic fields was also analyzed in detail, and the influence laws of the parameters (offset distance and frequency) of the line source on acoustical pressure distribution and its directivity were explored.Our results show that, for the analysis of GPCs, the method of transfer matrix eigenvalue analysis based on mechanical state vector is a very effective way owing to that it can not only calculate the band structure to reveal the band gap phenomenon, but also distinguish the contribution of the wave front effect and the Bragg scattering effect more easily. Due to the introduction of the Bragg scattering effect, the CS-GPCs has more significant acoustic or elastic wave band gap characteristics than the homogeneous cylindrical shells (HCS), thus exhibiting stronger ability of suppressing the propagation of wave effectively that may have potential applications in the field of sound isolating (e.g.,sound insulation cover); additionally,the acoustical pressure distribution inside and outside of the CS-GPCs has significant directivity properties which mainly depend on the offset distance and the frequency of the sound source.