Vibro-acoustic response analysis of functionally graded conical-cylindrical-spherical combined shells under hydrostatic pressure

Conical–cylindrical–spherical (CCS) combined shells are representative of underwater vehicle hulls and exhibit complex vibro-acoustic behavior. Hydrostatic pressure alters their dynamics through prestress-induced geometric stiffness, while functionally graded materials (FGMs) enable through-thickness tailoring of stiffness, inertia, and acoustic radiation. However, the coupled effects of hydrostatic prestress and material gradation on forced vibro-acoustic responses remain insufficiently understood. This study develops a semi-analytical framework for FGM CCS shells under hydrostatic pressure. The structural model is established using Love thin-shell theory and the artificial spring technique, with continuous through-thickness material variation retained in the constitutive formulation. Hydrostatic pressure is represented by a prestress-induced geometric stiffness matrix, and the surrounding acoustic field is modeled using an axisymmetric boundary element method. The coupled equations are solved by the Rayleigh–Ritz method and verified against finite-element results for natural frequencies, critical pressure, forced vibration, and acoustic radiation, with additional assessment against published benchmarks. Results show that increasing hydrostatic pressure shifts structural and acoustic resonance peaks toward lower frequencies, while off-resonance sound pressure levels vary comparatively little for the cases examined. The gradient index produces distribution-dependent monotonic changes in natural frequencies, whereas relative acoustic levels depend on excitation frequency. Structural damping reduces sharp resonant peaks, and integrated sound-power comparisons indicate that material gradation primarily redistributes the radiated response within the investigated band under the prescribed point excitation. These findings offer guidance for pressure-resistant, low-noise underwater structural design applications.