The cause of relative heave motion of floating bodies in waves is investigated. In the analysis, different wave pressure approximations near the wave surface are used. The pressure fields considered include the linear wave approximations, effective wave slope approach and hydrostatic pressure with reference to the moving free surface. Also considered is a pressure distribution which satisfies the linearized boundary condition at the free surface (i.e. at z = n, where n IS the Instantaneous wave surface elevation) The latter Yields reasonable heave responses and IS convenient to use in non-linear dynamic analysis.
In the study of heave motion of a floating body, the hydrostatic and hydrodynamic forces, sometimes, have to be evaluated by considering not only the static position of the body but also its heave motion relative to the moving free surface. If the relative heave motion is small, forces can usually be calculated based on the un-displaced position of the body, i.e., ignoring the relative motion. However, in the assessment of heave induced dynamic roll instability of a floating body, the relative heave motion is the main excitation of the coupled system; It cannot be assumed to be small (Liaw et aI., 1993). It is therefore very important in studying dynamic stability of floating bodies to have a proper understanding of the possible mechanism of relative heave motions. In order to simplify the mathematical modelling for stability analyses, the wave kinematics is often assumed to be governed by the linear wave theory. The commonly used model in stability analysis simulates the heave motions using a harmonically excited linear oscillator (Kerwin, 1955; Paulling and Rosenberg, 1959; Blocki, 1980) Based! on the linear oscillator modes heave resonance will occur when the wave frequency coincides With the natural heave frequency of the floating body.
