Tensile-compressive modes and vibration characteristics of penetrating projectile

Projectile’s structural vibration during high-speed penetration of hard targets is an important factor causing mixed overload signals and charge’s localized-deformation magnification issues, which restricts the destructive capability of projectiles. To accurately characterize the elastic vibration characteristics of the penetrating projectile, a refined theoretical modal modeling method for the projectile was derived based on the theories of variable cross-section rods. Furthermore, two 30-kg mass projectiles with the same mass and outline but different internal cavity structures were manufactured, together with an even hollow cylindrical bar with the same mass and outer diameter. Using these three structures as examples, theory test and simulation mode analyses were conducted to explore the modal features of the projectile from the perspectives of characteristic frequencies and their corresponding low-order tensile-compressive modes. The structural similarities and differences between projectile and even bar were compared, and the influence of charges on projectile modes was explored. Eventually, the vibration characteristics of the projectile penetrating semi-infinite and multi-layer concrete targets were deduced with the introduction of projectile’s modal characteristics measured separately. Research has shown that the Mindlin-Herrmann rod models have derived similar modal characteristic compared with simulation and test results, while the even bar model shows larger discrepancies. In weak load environments, the charge increases the structural damping, and the higher the modal order of the projectile, the weaker the coupling relationship between the projectile and the charge. However, the applicability of this conclusion in harsh load environments still needs to be explored. The low-order tensile-compressive modes dominate the vibration characteristics of the penetrating projectile, and the deformation and overload distribution are mostly affected by the first-order tensile-compressive mode, while the high-order modes supplement the vibration of the projectile. Benefiting from the variable cross-section effect, projectiles with short and concentrated inner cavities have better anti-vibration characteristics during ideal penetration. Projectile’s vibration characteristics obtained through modal analysis provides more reliable guidance for the design of the projectile-fuse-charge system.