Development of a linear numerical model for closed membrane-type fish cage in waves

Closed floating membrane cages are emerging as a promising solution for sustainable marine aquaculture, yet their dynamic behavior under wave loading remains insufficiently understood. This paper presents a linear hydroelastic formulation for a three-dimensional closed membrane cage, accounting for the coupled dynamics of a pre-tensioned hemispherical membrane bag, an elastic floating collar, and the surrounding internal and external fluid domains. The membrane equations are derived for a spherical surface including pre-tension effects and are coupled to an elastic collar model using a Rayleigh-Ritz-based modal approach, while hydrodynamic loads and internal sloshing are evaluated within the framework of linear potential flow theory. The resulting frequency-domain model is applied to a representative full-scale cage to examine global rigid-body motions, elastic responses, internal free-surface dynamics, membrane deformation, and bag-collar contact forces. A generic closed membrane cage with an elastic floating collar is analyzed using the developed linear model. The applicability of the linear membrane assumption is assessed by defining an allowable regular wave amplitude based on a small dynamic tension criterion, revealing that the linear assumption for the membrane dynamics can be restrictive under realistic wave conditions, particularly in the short-wavelength regime and near coupled resonance periods. The coupled heave motion is identified as the dominant hydroelastic response, arising from a coherent amplification of axisymmetric bag deformation, internal sloshing, and rigid-body heave motion, which leads to pronounced resonance peaks and very large bag–collar contact forces. In contrast, surge-pitch coupling suppresses the rigid-cage surge resonance, while elastic collar modes are driven mainly by hydrodynamic radiation forces rather than direct coupling with membrane tension. The study provides a rational and computationally efficient benchmark for understanding hydroelastic mechanisms in closed membrane cages and for guiding the development of more advanced nonlinear models and experimental validation.