A confined cylindrical bubble model for cavities induced by hydrodynamic ram

Hydrodynamic Ram (HRAM) caused by high-velocity projectile impact on liquid-filled containers generates elongated, confined cavities whose dynamics are strongly influenced by structural boundaries. Existing models often rely on semi-infinite approximations with empirically fitted parameters, limiting their physical interpretability and predictive use. This study develops a confined cylindrical bubble model that explicitly captures cavity–structure interaction. A radial velocity field is constructed to satisfy boundary conditions at both the cavity and container walls, and the governing equation is derived via the Euler–Lagrange framework, incorporating liquid compressibility and wall elasticity through linearized pressure–volume relations. The model is validated against experiments at multiple axial positions, with good agreement achieved via calibration of an effective stiffness parameter. For the tested impact velocities and container configuration, the calibrated stiffness is spatially consistent, indicating it may characterize local confinement, with further experiments under varied conditions confirming this behavior. To reduce reliance on fitting, a plate–shell-based estimation of stiffness is proposed and shown to align well with experimental values. The model recovers prior semi-empirical formulations as limiting cases, and offers a physically grounded, analytically tractable framework for predicting confined cavity dynamics under HRAM conditions.