Assessment of wave induced higher order resonant vibrations of ships at forward speed

Abstract

An efficient nonlinear time domain method computed higher order springing induced vertical bending vibrations of ships in waves. A weakly nonlinear time domain approach obtained the hydrodynamic response of the elastic hull girder, and a linear finite element model based on Timoshenko’s beam theory calculated its structural response. Coupling of the fully nonlinear stationary forward speed problem with the weakly nonlinear elastic body seakeeping problem constituted the major progress. We demonstrated that accounting for the nonlinear stationary forward speed problem significantly affected the prediction of springing-induced vibrations. Rigid body motions were computed via a nonlinear equations of motion. Elastic vibrations were computed using the modal superposition technique based on linear elastic motion equations. Radiation forces of the moving and vibrating hull structure (rigid body and elastic) were computed via convolution integrals, and Froude–Krylov and hydrostatic forces were combined and integrated over the instantaneous wetted surface. A waterline integral accounted for nonlinear effects of radiation and diffraction forces due to the changing wetted surface. A two-way coupling algorithm ensured accurate convergence. Comparisons of the numerically calculated midship vertical bending moment of a large container ship with experimental results showed good agreement. Investigations of the subject container ship advancing at forward speeds of 15 and 22kn in regular head waves focused on second, third, and fourth order springing.