scienceislife8533 ® 15-Дек-2019 05:11

Parametric Roll Instability of Ships


Year: 2008
Language: english
Author: Faculty of Mathematics and Natural Sciences University of Oslo
Format: PDF
Quality: eBook
Pages count: 113
Description: MASTER OF SCIENCE THESIS
Parametric roll may be defined as the spontaneous rolling motion of the ship
moving in head or following seas that comes about as a result of the dynamic
instability of motion. The development of the parametric roll occurs under the
conditions that the encounter angular frequency is approximately twice the roll
angular frequency, the wavelength is equal to the ship length and the roll damping
is insufficient to dissipate the parametric roll energy.
In this Thesis the dynamic roll behaviour for 5 different combinations of wave
heights and wavelengths for different initial conditions and different initial wave
positions, without and with a realistic amount of damping have been studied.
The Methods used are the three Equations of roll motion based on three variants
of the stiffness term in the basic Mathieu equation with damping.

Contents

1 Introduction 1
1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Ship Stability and Parametric Rolling 5
2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Roll Motions of Ship in Calm Water . . . . . . . . . . . . . . . . 10
2.3 Stability of Ship in Longitudinal Waves . . . . . . . . . . . . . . . 10
2.4 Parametric Roll Resonance Phenomenon . . . . . . . . . . . . . . 11
2.4.1 Conditions for the Development of the Phenomenon . . . . 12
2.4.2 Development of the Phenomenon During One Roll Period . 12
2.5 Effect of Roll Damping . . . . . . . . . . . . . . . . . . . . . . . . 14
3 A Simple Dynamic Model of Parametric Roll 17
3.1 An Analogy to the Rolling Motion . . . . . . . . . . . . . . . . . . 17
3.2 The Mathieu Equation with Damping . . . . . . . . . . . . . . . . 18
3.3 Solution of the Mathieu Equation . . . . . . . . . . . . . . . . . . 20
3.4 Solutions without Roll Damping . . . . . . . . . . . . . . . . . . . 20
3.4.1 Bounded Solutions . . . . . . . . . . . . . . . . . . . . . . 21
3.4.2 Unbounded Solutions . . . . . . . . . . . . . . . . . . . . . 21
3.5 Effect of Roll damping on the Solutions . . . . . . . . . . . . . . . 22
3.5.1 Effect on the Bounded Solutions . . . . . . . . . . . . . . . 22
3.5.2 Effect on the Unbounded Solutions . . . . . . . . . . . . . 23
3.6 Ince-Strutt Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.6.1 Original Ince-Strutt Diagram . . . . . . . . . . . . . . . . 24
3.6.2 Enlarged Ince-Strutt Diagram . . . . . . . . . . . . . . . . 25
4 Ship Data and GZ Data 27
4.1 Ship Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 GZ Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Some GZ Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5 Calculation Methods 31
5.1 Three Variants of the Stiffness Term . . . . . . . . . . . . . . . . 31
5.2 1st Equation of Roll Motion . . . . . . . . . . . . . . . . . . . . . 32
5.3 2nd Equation of Roll Motion . . . . . . . . . . . . . . . . . . . . . 33
5.4 3rd Equation of Roll Motion . . . . . . . . . . . . . . . . . . . . . 33
5.5 Solutions of the Equations of Roll Motion . . . . . . . . . . . . . 34
5.5.1 Solution of the 1st Equation . . . . . . . . . . . . . . . . . 34
5.5.2 Solution of the 2nd Equation . . . . . . . . . . . . . . . . 35
5.5.3 Solution of the 3rd Equation . . . . . . . . . . . . . . . . . 35
5.6 Estimation of the Coefficients in the Differential Equations . . . . 35
5.6.1 Estimation of the Coefficients in Equations (5.16) . . . . . 36
5.6.2 Estimation of the Coefficients in Equations (5.18) . . . . . 41
5.6.3 Estimation of the Coefficients in Equations (5.20) . . . . . 42
5.7 Initial Wave Position . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.8 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6 Results 45
6.1 Results for the 1st Method . . . . . . . . . . . . . . . . . . . . . . 45
6.1.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.1.3 Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.1.4 Case 4 and case 5 . . . . . . . . . . . . . . . . . . . . . . . 49
6.2 Results for the 2nd Method . . . . . . . . . . . . . . . . . . . . . 50
6.3 Results for the 3rd Method . . . . . . . . . . . . . . . . . . . . . . 51
7 Conclusions 53
A MATLAB Runs 55
A MATLAB Input Files 61
Bibliography 95

Screenshots

PARAMETRIC ROLL INSTABILITY.pdf

Скачать [2 KB]

Спасибо

Похожие релизы

Course Of Ship's Stability And Trim - Faculty of Navigation [2010, PDF]
Water Waves and Ship Hydrodynamics: An Introduction - A. J. Hermans [2011, PDF]
Marine Hydrodynamics - J. N. Newman [2017, PDF]
Reducing Container Loss Guidance - Britannia P&I Club [2022, PDF]
Ship Stability for Mates/Masters - Martin A. Rhodes [2013, PDF]
Tsunamis and Hurricanes: A Mathematical Approach - Ferdinand Cap [2006, PDF]
The Aero- and Hydromechanics of Keel Yachts - J. W. Slooff [2015, PDF]
The Management of Merchant Ship Stability, Trim & Strength - I.C. Clark BSc MSc [2002, PDF]
Diamond 53 - Handymax Bulk Carrier - Stability information manual - Carl Bro [2006, PDF]
Probabilistic Theory of Ship Dynamics - R. E. D. Bishop, W. G. Price [1974, PDF]
  • Ответить

Текущее время: Сегодня 17:37

Часовой пояс: GMT + 3