Torsional Vibration of a Damped Shaft System Using the Analytical-and-Numerical-Combined Method

Torsional vibration analysis of the propulsive shaft system of a marine engine—one of the most important tasks in preliminary ship design—is carried out today by either the Holzer method, the transfer matrix method (TMM), or the finite-element method (FEM). Of the three methods, Holzer is the most popular and is adopted by shipyards worldwide. The purpose of this paper is to present an analytical-and-numerical-combined method (ANCM) to improve the drawbacks of existing methods. In comparison with the Holzer method (or TMM), the presented ANCM has the following merits: the mass of the rotating shaft is inherently considered, the damping effect is easily tackled, and the forced vibration responses due to various external excitations are obtained with no difficulty. Since the order of the overall property matrices for the equations of motion derived from the ANCM is usually lower than that derived from the conventional finite-element method (FEM), the CPU time required by the former is usually less than that required by the latter, particularly in the forced vibration analysis. Besides, the sizes (and the total number) of the elements for the FEM have a close relationship with the locations of the disks and the dampers and so does the accuracy of the FEM, but various distributions (or locations) of the disks and the dampers will not create any problems for the ANCM.