A honeycomb core design that embeds a rhombic honeycomb into a re-entrant honeycomb was proposed. A novel auxetic honeycomb sandwich panel (NAHSP) with a polyurea-metal laminated panel was developed to enhance the vibroacoustic performance. A numerical model of the NAHSP with polyurea-metal laminated (PML) faceplates was established and validated using ABAQUS software. Numerical simulations were used to analyze the vibration and acoustic responses of the NAHSPs in four different configurations. The results indicate that the PML faceplates and the honeycomb geometry effectively reduce vibration and suppress noise. The symmetrical PML-A faceplate structure outperforms the asymmetrical structure in vibration damping and sound insulation. The peak of the frequency/time response curve of the NAHSP decreases the most by 6 mm polyurea thickness, with an average sound insulation improvement of 9.4%. The honeycomb geometry with a tilt angle of −45° exhibits the best vibroacoustic performance for the NAHSP.
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