## Design of ocean platforms against ringing response

##### Résumé

The purpose of this thesis is to numerically investigate the ringing phenomenon in drag-dominated small offshore structures in an ocean environment. The ringing is a transient response to an impact wave, and it occurs in the surge response when it is observed in small structures. The peak response during ringing tends to be large, and the response decays slowly. Other researchers have observed that ringing occurs where the fundamental frequency is several times above the dominant wave frequency. However, the effects of physical properties other than the fundamental frequency have not been explored. For instance, should the ringing response change when the geometric configuration changes while the fundamental surge frequency remain the same? In order to answer this question, we consider platforms with and without leg bracings. They are simplified as a beam clamped at one end and has a point mass at the other end. The leg bracings are modeled as a discrete spring. The beam is modeled as an Euler-Bernoulli beam. The fluid force is modeled using Morison's equation, the waves are modeled random with many frequency components according to JONSWAP spectrum, Airy wave theory is used to obtain the fluid field. The sample time history of the random wave is expressed as a series of sinusoidal functions with sample frequencies obtained from the spectrum. The impact wave is generated by setting the random phases of each frequency component zeros. The same impact wave profile is used for all ringing simulations. The response is obtained numerically using finite difference equations for the spatial coordinate and Runge-Kutta method for the resulting ordinary differential equations in time. The parameters that are varied are the point mass, spring stiffness, location of the spring, while the properties of the beam itself are unchanged. The point mass, spring stiffness and the location of the spring are predetermined so that the resulting system would have a desirable fundamental frequency. Duration of ringing is measured by its exponential decay constant, zeta-omega. This decay constant is further normalized by the decay constant of an equivalent linear system for fair comparisons. The equivalent linear system is when the drag component of the fluid force is linearized and the fluid force is applied only up to the still water level instead of the instantaneous water level. It is found that the decay rate shows strong correlation with the point mass but not with the spring stiffness and the location of the spring. As the point mass increases, the response decays slower, slower compared to the equivalent linear system. It is also found that the point mass has even stronger effect on the decay rate than the frequency relationship between the structure and the fluid. That is, the duration of ringing seems slightly by the frequency relationship once the ringing exists.