Derivation of 3D Dynamics for Rigid Floating Structures under Directional Wave Excitation

Modular floating structures (MFS) offer a sustainable pathway towards the expansion of coastal cities in adaptation to flooding and sea level rise driven by climate change. It is therefore necessary to develop analytical methods easily accessible to architects or structural engineers for the rapid prototyping of MFS designs. This work develops novel closed-form expressions describing the rigid body dynamics of symmetrically loaded rectangular pontoons across all six degrees of freedom (DOF) excited by surface waves approaching from any arbitrary direction. The derivations were based on Airy wave theory assuming frequency-independent added mass and damping. When benchmarked against numerical solutions from ANSYS/AQWA for two MFS prototypes, the analytical approach proved capable of predicting the response amplitude operators (RAO) across all DOFs, wave directions, and structural configurations. However, while the response of mass-dominated DOFs (surge, sway, and yaw) were well captured, the damping ratio for stiffness-dominated DOFs (heave, roll, and pitch) must be judiciously selected to yield accurate RAO results. A parametric investigation further elucidated the contribution of structural geometry and wave directionality on the critical accelerations experienced by an idealized floating structure founded upon a square pontoon under realistic sea states. It was discovered that the largest accelerations were triggered by waves approaching orthogonally to the pontoon. Ultimately, this work facilitates a more streamlined approach for the dynamic analysis of compliant floating bodies to supplement detailed modeling efforts via numerical methods.