Free and forced vibration of cylindrical sandwich shells with embedded cavities: a layerwise hard-constraint Ritz-DtN approach

Official URL: https://dx.doi.org/10.1016/j.oceaneng.2026.127980

A layerwise hard-constraint Ritz formulation, integrated with a modal fluid added-mass operator derived from the inverse exterior Dirichlet-to-Neumann relation, is developed for free and forced vibration analysis of cylindrical sandwich shells with cylindrical or ellipsoidal cavities. The shell kinematics are represented by nine generalized displacement fields expanded using axial Chebyshev polynomials and circumferential Fourier harmonics. Essential boundary conditions are imposed exactly through null-space projection, avoiding artificial springs and penalty parameters. The cavity-containing core is modeled using geometry-dependent Mori-Tanaka equivalent properties. The surrounding water is treated as an inviscid, incompressible, and irrotational potential fluid, yielding a real, frequency-independent added-mass operator without discretizing the exterior domain. Thus, hydrodynamic added inertia is captured, while fluid compressibility and acoustic radiation damping are neglected. The formulation is validated against published solutions and independent three-dimensional finite-element models. Across 56 verified natural frequencies, the mean absolute percentage difference from 3D-FEM results is 0.558%, with a maximum deviation of 1.867%. Relative to converged M3 3D-FEM models, wall-clock speed-ups range from 41.59 to 352.74. Parametric results show strong sensitivity to cavity volume fraction, but comparatively modest sensitivity to ellipsoidal-cavity aspect ratio. Load position alters modal participation and resonance amplitudes without changing eigenfrequencies within the adopted linear vibration framework.