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Auxetic mechanical metamaterials that exhibit a negative Poisson's ratio (NPR) can be artificially designed to exhibit a unique range of physical and mechanical properties. Novel sandwich structures composed of uniform and gradient auxetic double arrowhead honeycomb (DAH) cores were investigated in terms of their vibration and sound transmission performance stimulated by nonhomogeneous metamaterials with nonperiodic cell geometries. The spectral element method (SEM) was employed to accurately evaluate the natural frequencies and dynamic responses with a limited number of elements at high frequencies. The results indicated that the vibrating mode shapes and deformations of the DAH sandwich models were strongly affected by the patterned gradient metamaterials. In addition, the sound insulation performance of the considered DAH sandwich models was investigated regarding the sound transmission loss (STL) from 1 Hz to 1500 Hz under a normal incident planar wave, and this performance was compared with that for hexagonal honeycomb sandwich panels. A programmable structural-acoustic optimization was implemented to maximize the STL while maintaining a constant weight and high strength. The results showed that the uniform DAH sandwich models with larger NPRs generally exhibited better vibration and acoustic attenuation behaviors and that the optimized gradient increasing NPR models yielded higher STL values than the optimized gradient decreasing NPR models for two specified frequency cases, with improvements of 6.52 dB and 2.52 dB and a higher bending stiffness but a lower overall STL. Thus, sandwich panels consisting of auxetic DAHs can achieve desirable vibroacoustic performance with a higher bending stiffness than conventional hexagonal honeycomb sandwich structures, and the design of gradient DAHs can be extended to obtain optimized vibration and noise-control capabilities. [ABSTRACT FROM AUTHOR]