Solving for hydroelastic ship response using Timoshenko beam modes at forward speed

In this study, we employ a hydroelastic analysis to investigate the motion response of large ship hulls, treating them as either Euler–Bernoulli or Timoshenko beams to consider the influence of shear effects. To enhance clarity, we provide a detailed derivation of the equation of motion within the framework of Timoshenko beams. This work solves forward-speed radiation and diffraction problems for flexible bodies, utilizing linearized potential flow theory including generalized modes. Two common base-flow models, the Neumann-Kelvin and double-body base flows, are included in the solver. The solution is numerically implemented in the high-order finite difference and open-source seakeeping solver Oceanwave3D-seakeeping. The numerical implementation involves the discretization of the geometry using overlapping, boundary-fitted grids, which has been validated by three examples involving a barge and two Wigley hulls. The influence of the Doppler shift due to forward speed on the hydroelastic motion response is also discussed. Through the integration of hydroelastic analysis using potential flow theory and advanced numerical techniques, this work contributes to a deeper understanding of the complex interaction between large ship hulls and waves, offering valuable insights for the maritime industry.