Aerodynamic Stability Analysis of High-Speed Sport Equipment: Sandwich Rotating Auxetic Meta-Beams for Rackets Using Various Shear Deformation Theories

This paper presents a numerical analysis method to optimize the aeroelastic stability of highspeed rotating sports equipment, such as tennis rackets. We model these implements as sophisticated sandwich beams, rotating at competition-level angular velocities. The core utilizes re-entrant auxetic metamaterials (with a negative Poisson's ratio) for enhanced energy absorption and stability, while the facesheets are reinforced with CNTs for maximum strength-to-weight ratio. A unified formulation based on Euler–Bernoulli (EBT), Timoshenko (TBT), and Reddy (RBT) shear deformation theories is developed to assess the influence of shear flexibility on the flutter boundaries and vibrational characteristics of the hybrid rotating system. The aerodynamic forces are modeled using piston theory, and the governing equations of motion are derived through Hamilton’s principle. The resulting coupled differential equations are discretized and solved using the generalized differential quadrature method (GDQM), ensuring high numerical accuracy. The study demonstrates how CNT reinforcement, auxetic core geometry, rotation-induced stiffening, and aerodynamic pressure interact to modify natural frequencies, damping trends, and critical aerodynamic parameters. Comparisons among EBT, TBT, and RBT reveal significant differences in predicted stability limits, particularly for configurations with compliant auxetic cores. The results provide new physical insights into the combined effects of nanocomposite reinforcement, negative Poisson’s ratio architecture, and rotational dynamics, offering benchmark data for future investigations and practical guidelines for designing