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DEVELOPMENT OF ANALYTICAL NONLINEAR MODELS FOR PARAMETRIC ROLL AND HYDROSTATIC RESTORING VARIATIONS IN REGULAR AND IRREGULAR WAVES
Bulian, Gabriele
2006-03-31T11:28:15Z
Abstract
Parametrically excited roll motion has become a relevant technical issue, especially in recent years, due the increasing number of accidents related to this phenomenon. For this reason, its study has attracted the interest of researchers, regulatory bodies and classification societies. The objective of this thesis is the developing of nonlinear analytical models able to provide simplified tools for the analysis of parametrically excited roll motion in longitudinal regular and irregular long crested waves. The sought models will take into account the nonlinearities of restoring and of damping, in order to try filling the gap with the analytical modelling in beam sea. In addition, semi-empirical methodologies will be provided to try extending the usual static approach to ship stability based on the analysis of GZ curve, in a probabilistic framework where the propensity of the ship to exhibit restoring variations in waves is rationally accounted for.
The thesis addresses three main topics: the modelling of parametric roll in regular sea (Chapter 2 to Chapter 5), the modelling of parametric roll motion in irregular long crested sea (Chapter 6 and Chapter 7) and the extension of deterministic stability criteria based on the analysis of geometrical GZ curve properties to a probabilistic framework (Chapter 8). Chapter 1 gives an introduction, whereas Chapter 9 reports a series of final remarks. For the regular sea case an analytical model is developed and analysed both in time domain and in frequency domain. In this latter case an approximate analytical solution for the nonlinear response curve in the first parametric resonance region is provided by using the approximate method of averaging. Prediction are compared with experimental results for four ships, and the analytical model is investigated with particular attention to the presence of multiple stable steady states and the inception of chaotic motions. The influence of harmonic components higher than the first one in the fluctuation of the restoring is also investigated. In the case of irregular sea, the Grim's effective wave concept is used to develop an analytical model for the long crested longitudinal sea condition, that allows for an approximate analytical determination of the stochastic stability threshold in the first parametric resonance region. Experimental results are compared with Monte Carlo simulations on a single ship, showing the necessity of a tuning factor reducing the hydrostatically predicted magnitude of parametric excitation. The non-Gaussianity of parametrically excited roll motion is also discussed. Finally, on the basis of the analytical modelling of the restoring term in irregular waves, an extension of the classical deterministic approach to ship static stability in calm water is proposed, to take into account, although is a semi-empirical form, restoring variations in waves. Classical calm water GZ curve is then extended from a deterministic quantity to a stochastic process. By limiting the discussion to the instantaneous ensemble properties of this process, it is shown how it is possible to extend any static stability criterion based on the geometrical properties of the GZ curve, in a rational probabilistic framework taking into account the actual operational area of the ship and the propensity of the ship to show restoring variations in waves. General measures of restoring variations are also discussed, such as the coefficient of variation of metacentric height, restoring lever and area under GZ. Both the short-term and long-term point of view are considered, and the method is applied to three different ships in different geographical areas.
Insegnamento
Publisher
Università degli studi di Trieste
Languages
it