Analysis of Offshore Structural Dynamics with Nonproportional Damping

Abstract

A method of analysis of the nonproportionally damped motions of fixed offshore structures in waves is presented. The damping considered is that due only to radiation, and is assumed to be linear. Since both the radiation damping and the added mass are frequency dependent, the damping is, by nature, nonproportional. Hence, the standard normal‐mode analysis cannot be used. To isolate the modes, the matrix equation of motion of the assumed lumped‐mass system is first transformed into a first‐order equation. The complex eigenvectors and eigenvalues for the underdamped system are then obtained through matrix iteration, The displacement of each mass is obtained in deterministic seas. One of the most important results of this analysis is the demonstration of the ability of the technique to predict the movement of the nodal points over time. That is, the nodal points move up and down the centerline of the structure over each period. This means that the analyst can predict the positions of maximum stresses and strains over each cycle, a capability that the standard normal‐mode technique lacks.