Vibration and acoustic insulation properties of generalized phononic crystals

Based on the previous studies, the concept of generalized phononic crystals (GPCs) is further introduced into the cylindrical shell structures, and a type of cylindrical shells of generalized phononic crystals (CS-GPCs) is constructed. Subsequently, the structure field and acoustic-structural coupled field of that composite cylindrical shells are examined respectively in this paper. Considering the Bloch theorem is not capable of explaining the generalized periodic situation existing in this structure field, a new analysis method involving transferring matrix eigenvalue based on the mechanical state vector is proposed to calculate the energy band structure. Through observing the energy band structure, an obvious wave band gap is obtained when the elastic wave propagates 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 explore the related influences of the longitudinal wave mode and shear wave mode in structure on these band gaps, and some conclusions are illustrated. For acoustic-structural coupled field, the expressions of the acoustic transmission coefficients for different modes are built, and the frequency responses are numerically calculated to verify the band gap characteristics of the CS-GPCs. Furthermore, the acoustic pressure distribution of the internal and external acoustic fields is 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 are explored.