Influence of initial imperfections of plating on the vibration of ship hulls.

Abstract

The influence of imperfections of deck plating on the vibration of ship hulls is studied. The process is divided in two steps; in the first one, the forced vibration of a predeformed plate with a specified in plane harmonic force is analyzed. In the second, this local vibration of the deck plates is coupled to the oscillation of the ship hull. In the plate vibration problem, after a discretization is performed, a nonlinear ordinary differential equation is obtained; it includes quadratic and cubic nonlinearities, and externally forcing and parametric excitations. The nonlinear equation is solved using the Harmonic Balance method. The analysis of the problem with decreasing values of predeformation allows visualization of the evolving solution-branches: from the mainly externally forced case for large predeformations, to the mainly parametrically excited case for small values of predeformation. The coupling between parametric and forcing excitation produces a new change in the stability of one of the branches. This change in stability is related to the appearance of the unstable region in the purely parametrically excited case. To couple the local vibration of the plate with that of the hull, the hull girder is modeled as an Euler beam with constant section. Even though this model does not consider the effects of shear force and rotary inertia, it allows the objective of this work to be reached with a less complex formulation. The hull oscillation is then represented using one of the linear mode shapes of free vibration. It was found that when the natural frequencies of the hull mode and deck panels approach each other, the dynamic coupling becomes important and the oscillation of the hull excites high levels of deck plate vibration. This effect manifests itself as a change in the natural frequency of the hull girder mode. Also since the deck panels can vibrate in and out of phase with the hull, the above mentioned influence can be of decreasing or increasing type, decreasing in the case of in phase oscillation, and increasing in the out-of-phase case.