Compression and vibration isolation properties of metamaterials with variable Poisson’s ratios and cosine-shaped beams

• Bio-inspired cosine-beam metamaterials with tunable Poisson’s ratios are designed. • Theoretical models linking elastic constants to curved beams are established. • Structures offer energy absorption and vibration isolation for multifunctionality. Metamaterials have attracted considerable attention for their exceptional performance and multifunctionality. Traditional honeycomb structures with periodically arranged straight beams often exhibit limited mechanical properties and a narrow range of applications. To address these limitations, this study proposes a novel metamaterial design featuring cosine-shaped beams inspired by the biomechanics of the human spine and the curved architecture of cuttlebone, allowing for tunable Poisson’s ratios. The compression mechanical properties and vibration isolation performance of these structures are systematically investigated through analytical modeling, quasi-static compression experiments, finite element simulations, and vibration isolation tests. Results reveal that adjusting cell angles of structures can enhance deformation stability and enable stiffness tuning. Compared to straight beam structures, the proposed cosine-shaped beam structures exhibit wider vibration isolation frequency range. Structures with zero Poisson’s ratio demonstrate superior vibration isolation at small cell angles, while those with negative Poisson’s ratio at specific cell angle achieve an optimal balance of high strength, energy absorption, and vibration isolation. This study provides systematic guidance for designing metamaterials with adjustable multifunctional mechanical properties, offering innovative solutions for advanced engineering applications across diverse fields.