Sandwich structures that are embedded with cellular materials show excellent performance in terms of mechanics, electromagnetics, and acoustics. In this paper, sandwich panels with hybrid cellular cores of hexagonal, re-entrant hexagonal, and rectangular configurations along the panel surface are designed. The spectral element method (SEM) is applied to accurately predict the dynamic performance of the sandwich panels with a reduced number of elements and the system scale within a wide frequency range. The mechanical performance and the acoustic performance at normal incidence of the proposed structures are investigated and compared with conventional honeycomb panels with fixed cell geometries. It was found that the bending stiffness, fundamental frequencies, and sound transmission loss (STL) of the presented sandwich panels can be effectively changed by adjusting their hybrid cellular core configurations. Shape optimization designs of a hybrid cellular core for maximum STL are presented for specified tonal and frequency band cases at normal incidence. Hybrid sandwich panels increase the sound insulation property by 24.7%, 20.6%, and 109.6% for those cases, respectively, compared with conventional panels in this study. These results indicate the potential of sandwich structures with hybrid cellular cores in acoustic attenuation applications. Hybrid cellular cores can lead to inhomogeneous mechanical performance and constitute a broader platform for the optimum mechanical and acoustic design of sandwich structures.

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