Page 253 - Dynamic Loading and Design of Structures

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Figure 5.18 Ringing behaviour of monotower. (a) Platform layout; (b) wave profile and overturning
moment (Farnes et al., 1994).

load when it is superimposed on the linear wave load. Hence, small non-linear wave loads
have no effect on the extreme value distribution of a quasi-static system and the response may
be considered Gaussian.
The inertia of a dynamically responding system delays and amplifies the response. The
delay and amplification are dependent on the ratio of the load period and the natural period.
With a βof about 0.3 for the steady-state wave load, the DAF is about 1.1. The duration of the
non-linear wave load impulse (which is about 5.5 sec in Figure 5.18(b)) is close to the natural
period and implies a DAF of about 1.4 according to elementary results for a SDOF system.
The response from the impulse is, hence, delayed and amplified more than the response from
the linear load. The relative delay of the response from the impulse compared with the linear
part shifts the minima responses from the two components closer together in time and the
non-linear response contributes considerably to the total extreme minima. This is shown in
Figure 5.18b. The response from the impulse will continue to oscillate with the natural period
and it is rather unlikely, except for some particular wave periods, that a maximum in
proceeding oscillation will increase the following maximum in the linear response. The
distribution will, hence, be skewed upwave.