Consistent formulation of ship motions in time domain simulations by use of the results of the strip theory
Based on the three dimensional time domain impulse response function (IRF) and frequency domain hydrodynamic coefficients, such as the infinite frequency added mass and damping, and radiation restoring coefficients, the IRF method is used in this work to obtain consistent formulations of linear radiation forces and ship motions. The new developments are twofold. First, the hydrodynamic added mass at infinite frequency and radiation damping in the time domain are theoretically derived using the strip theory. Second, via Kramers Kronig (K K) relationship for forward speed, it is observed that the added mass and damping coefficients in the frequency domain and radiation restoring coefficients in the time domain should satisfy the K K relationship to obtain the linear hydrodynamics in the time domain consistent with those from the frequency domain in strip theory. Following the K K relationship and the frequency domain added mass and damping coefficients obtained by the strip theory, the new expressions of radiation restoring coefficients are derived. Finally, numerical validations are performed to confirm the consistent formulation proposed in this work.