# Estimation of damping from wave induced vibrations in ships

## Dämpningsuppskattning av våginducerade vibrationer i fartyg

[Examensarbete på avancerad nivå]

Wave induced vibrations in the ship hull girder have become a concern with the rapidly increasing size and structural flexibility of container vessels since it increases both ultimate loading and fatigue damage. Damping of the hull girder reduces the vibrations after a wave impact and the resonance level from steady state vibrations. The effect, magnitude and origin of the damping are however not well defined in current classification guidelines regarding wave induced vibrations. Speed, draft, ship size, natural frequency and response amplitude are parameters that possibly could influence the damping. It’s difficult to isolate the importance of each parameter on the damping from full scale measurements since the effects are coupled. A better approximation of the damping leads to more accurate assessment of ultimate loading and fatigue damage from wave induced vibrations. This thesis aims to evaluate and find an accurate and robust method to estimate the total damping from full scale stress measurements of ships and to investigate how the damping affects the ultimate and fatigue strength of a ship. There are different methods to estimate damping, mainly divided into time domain and frequency domain methods. Six different methods were benchmarked with respect to accuracy, sensitivity to damping ratio, natural frequency, sample length and sampling frequency. The possibility to implement the methods in hull stress monitoring systems on board the vessels is also investigated. The benchmark study included two methods implemented in the commercial software ARTeMIS modal pro. The evaluation process was done on artificially created stress signals from single-degree-of-freedom systems where the damping ratio and natural frequencies could be predefined. The influence of damping on the fatigue damage was evaluated using rainflow counting (RFC), the Basquin equation and the Palmgren-Miner accumulation rule on the synthesized stress signal. The damping showed to have a considerable effect on the fatigue damage calculated on the high frequency part of the stress signal; by doubling the damping ratio, the vibrational damage can be reduced by up to 88%. The damping is more effective on reducing the fatigue damage for ships with lower natural frequencies, i.e. longer ship. The model does not consider wave frequency stresses and is therefore not applicable on physical problems. Regarding ultimate loading, the damping reduces the vibrational part of the stresses that are superimposed on the total stresses. The results were used to formulate a suggestion for a revised rule text regarding wave induced vibrations for DNV GL. By including the effects of a higher damping than expected, the ultimate loading assessment can be reduced and vice versa. Full scale measurement data from 14 container vessels, 2 LNG carriers, 3 ore carriers and 2 tankers were investigated. Dependencies between damping ratio and other parameters, such as, size, speed, response and ship type were evaluated. The results were scattered and no clear correlations could be found, save for a moderate correlation between the response amplitude and the damping. Ship size didn’t show any clear correlation, but type of vessel showed a distinct difference between slender container vessels and blunt ore carriers/LNG-carriers/oil tankers. It was concluded that container vessels generally have a damping ratio between 1.5 and 2%, while the blunt vessels generally lie between 0.5 and 1% damping ratio.

**Nyckelord: **benchmark study, damping estimation, fatigue strength, springing,ultimate strength, wave induced vibrations, whipping