This paper describes the development of an analysis model, which is suitable for the evaluation of the hull girder response of ships due to waves including torsion effect. To this aim, springing effects on hull girder was re-evaluated including non-linear wave excitations and torsional vibrations of the hull. The Timoshenko beam model was used to calculate the stress distribution on the hull girder and solved using superposition method. The strip method was employed to calculate the hydrodynamic forces and moments on the hull. Viscous effects, which may be important for calculation of wave-induced twisting moment on the hull, were accounted for in a simplified manner. Example calculation results show a reasonable agreement with previous results for both symmetric and anti-symmetric responses
The modern ships are getting bigger and lighter with shallow draft and large breadth, which makes the ship flexible with both her bending and torsional rigidities being small. For such ships, precise estimation of wave-induced bending moments, shear forces and torsional moments are important. Otherwise, flexible hull girder may easily suffer from the fatigue damage due to wave excitation such as springing, whipping and etc. Ship springing is the resonant response of the ship to a hydrodynamic excitation due to incident waves. It could occur in low to moderate sea states, when the encountering wave frequency matches the natural frequency of hull girder. Springing is due to both linear and non-linear excitation mechanisms. The linear exciting forces are associated with waves of small wavelengths relative to the ship length. The non-linear ship response, which is quadratic to wave amplitude, comes from the sum frequency between the incident waves. For ships with low natural frequency, a linear theory is usually applied to calculate the springing excitation and the motion coefficients using strip or slender-body approximations.