Springing responses of ships with forward speed based on a multi-module hydroelastic method

Abstract

A hydroelastic analysis method for flexible ships with forward speed is developed based on the beam-connected-discrete-modules (BCDM) approach. In this method, the flexible ship is first discretized into multiple rigid modules connected by a hull girder, thereby establishing the hydroelastic analysis model. The time-domain Rankine source method, which incorporates steady flow through the double body flow model, is employed to calculate the hydrodynamic forces acting on the multi-module system. The subsequent application of Fourier transformation facilitates the conversion of these forces into the frequency domain, where they are coupled with the structural stiffness of the hull girder to formulate the hydroelastic equations for advancing ships. Additionally, the time-domain hydroelastic equation is derived based on Cummins’ equation. The validity of the proposed method is conducted by comparing the zero-speed hydroelastic responses and the motions of advancing ships with the published data and numerical results from commercial software. Furthermore, the global responses of both flexible and rigid ships under varying forward speed conditions are thoroughly investigated. The results demonstrate that the flexible deformation plays a crucial role in the global responses of advancing ships, and hydrodynamic forces associated with forward speed have significant contribution to the hydroelastic responses.