Total (practical) stability of ships

In this paper the “total (practical) stability” concept is introduced to nonlinear forced rolling motion of a ship. This is achieved by employing “boundedness” and “Lyapunov's function” approach. In this respect two new theorems are proved and conditions and domain of Practical Stability are evaluated. The Paper also contains a critical review of the present status of international intact ship stability regulations. A qualitative discussion of oscillatory rolling motion and the capsizing phenomena is presented.     

Forced vibration analysis of an offshore tower carrying an eccentric tip mass with rotary inertia due to support excitation

Dynamic responses of structures due to earthquake excitation are the important problems in engineering, thus, the information concerned is plenty. However, most of the literature is relating to the discrete methods, particularly to the finite element method (FEM), and the one relating to the method combining both the “continuous” and “discrete” models is rare. The objective of this paper is to provide some information in this respect. First, the analytical solution for the natural frequencies and normal mode shapes of a “continuous” tower, without contacting water (or “dry” tower), carrying an eccentric tip mass possessing rotary inertia is determined. Next, the partial differential equation of motion for the forced vibration of the tower, contacting water (or “wet” tower), subjected to support excitation is transformed into a matrix equation by using the last natural frequencies and normal modes shape of the freely vibrating dry tower. Finally, the numerical integration method is used to solve the matrix equation to yield the seismic response of the wet tower. In theory, the mode superposition method is correct only if the total number of modes considered approaches infinity, however, numerical results of this paper reveal that superposition of only the lowest six modes will yield excellent results to be very close to the corresponding ones obtained from the conventional FEM. For this reason, the CPU time required by the presented approach is less than 5% of that required by the conventional FEM.     

Static and dynamic aspects of a capsize phenomenon

Capsizing of ships constitutes a primary group of casualties that leads to loss of life and money. Unfortunately, its mechanism has yet to be fully resolved due to underlying complex dynamics and parameters. Upon studying the causes in more detail, designing safer ships against capsizing may become a reality. In the present study, a relatively different approach called “reserve of stability” or “stability margins” which utilizes both statical and nonlinear dynamical aspects of stability is employed to analyze ship hydrodynamics. For this purpose a nonlinear roll model in beam waves has been implemented. In order to apply the theory, a capsized vessel is chosen to be analyzed in terms of stability. The necessary data about the vessel at the time of capsizing were collected from the published work found in the naval architecture literature. Suggestions are made based on the results of the analysis to improve ship stability qualities in a seaway.     

Propulsion of single-screw ships

On the basis of the little clause in the “Outline Specification” for a new ship: “Trial speed at a load draught of … with the engine at maximum continuous rating has to be …” some aspects regarding propulsion of single-screw ships are discussed, especially the problem of how to combine the hull form, the propeller and the machinery for propulsion in such a way that an optimal solution is obtained.In order to limit the problem, only ships provided with a single conventional propeller for propulsion are considered.A parameter study of a single-screw vessel has been done in order to get some concrete information on the interaction between ship, engine and propeller, and to investigate how the ship propeller power curve should be placed in relation to the engine operation area and to investigate changes in this relationship when the conditions change.     

Eventual stability of flooded ships

This paper deals with stability investigations of forced nonlinear rolling motion of a ship with a flooded compartment. The mathematical stability analysis has been realized in the sense of Eventual Stability. Two stability regions have been constructed through two Lyapunov functions generated by using Variable Gradient Method and the method of Puri. Having obtained stability conditions for the governing equations of the motion, dissipativeness of the motion, and maximum rolling angles have been obtained by using a theorem given by Bibikov and Sanovskii (1971).     

The discrete methods for free vibration analyses of an immersed beam carrying an eccentric tip mass with rotary inertia

In this paper, a beam without contact with water is called the “dry” beam and the one in contact with water is called the “wet” beam. For a partially (or completely) immersed uniform beam carrying an eccentric tip mass possessing rotary inertia, the conventional analytical (closed-form) solution is achieved by considering the inertial forces and moments of the tip mass and rotary inertia as the boundary conditions at the tip end of the beam. However, it has been found that the approximate solution for the last problem may be achieved by two techniques: Method 1 and Method 2. In Method 1, the basic concept is the same as the conventional analytical method; but in Method 2, the tip end of the beam is considered as a free end, while the inertial forces and moments induced by the tip mass and rotary inertia are considered as the external loads applied at the tip end of the beam. The main differences between the formulation of Method 1 and that of Method 2 are: In Method 1, the “normal” shapes of the “dry” beam are functions of the frequency-dependent boundary conditions but the external loads at the tip end are equal to zero; On the contrary, in Method 2, the “normal” mode shapes of the “dry” beam are determined based on the zero boundary conditions at the tip end of the beam but the external loads at the tip end due to the inertial effects of the tip mass and rotary inertia must be taken into consideration for the free vibration analysis of the “wet” beam. Numerical results reveal that the approximate solution obtained from Method 2 are very close to that from Method 1 if the tip mass moment of inertia is negligible. Besides, the two approximate solutions are also very close to the associated analytical (closed-form) solution or the finite element solution. In general, it is hoped that there exist several methods for tackling the same problem so that one may have more choices to incorporate with the specified cases. It is believed that the two approximate methods presented in this paper will be significant from this point of view.     

Study on the dynamic characteristic of a U-type tuned liquid damper

By means of Lagrange's equation, the “coupled” equations of motion for a horizontal plate carrying a U-type tuned liquid damper (TLD) are derived. The “uncoupled” equations of motion for the liquid (in the TLD) and the structural system are then obtained by decoupling the “coupled” ones. Unlike the existing literature to indirectly determine the natural frequencies of a damped vibrating system by using the resonant method, the “complex” eigenvalues of the coupled damped system are obtained directly from the associated eigenvalue equations. Besides, the pressure intensities in the two air chambers and the sizes of the two vertical tanks together with the horizontal conduit are arbitrary in the formulation of this paper. The influence of some key parameters of the TLD on the dynamic responses of the structural system is studied.     

Estimation of survival probability for a ship in beam seas using the safe basin

The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge-Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”.     

“Batfish” a depth controllable towed body for collecting oceanographic data

“Batfish” is a streamlined vehicle developed to house fast-responding oceanographic sensors. It is towed behind a ship or small vessel and its depth is controlled from the vessel by a manually or automatically produced command signal. Variable-angle wings permit the vehicle to be lowered and a novel control surface, which eliminates the need for heavy ballast, assures lateral stability. There are two models: the standard and the wide-wing Batfish. The standard Batfish has collected temperature and conductivity data at depths of up to 200 m when towed at 10–25 km/hr, and the wide-wing Batfish at depths to 400 m when towed at 10–16km/hr.     

Multi-vessel seakeeping computations with linear potential theory

The wave-induced motion of two vessels in close proximity is studied using traditional two-dimensional (2D) and three-dimensional (3D) boundary element methods. Added mass, damping, and the behavior of the free surface between the vessels are examined in some detail. As expected based on previous work, the response of the water between the vessels is found to have a profound effect on the hydrodynamic forces. At “critical frequencies” corresponding to standing waves between the hulls, the hydrodynamic forces undergo significant drastic changes. The 2D and 3D results are compared, and the effects of a skew angle between the vessels are examined. Some of the consequences of the behavior at the critical frequencies for simulations in the time domain are examined, the most significant of which is a very lightly damped impulse response.     

Alternative placement technique for antifer blocks used on breakwaters

In this study, a placement technique named as “alternative placement technique” was developed for antifer blocks and the results of its application to a breakwater model were presented. This placement technique was compared with the existing techniques such as the “regular placement technique”, the “irregular placement technique” and the “sloped wall placement technique” by experiments. The comparison was carried out considering armor layer stability, prototype placement, clarity of the placement technique’s definition, armor layer cost, and wave runup. As a result of this investigation the “alternative placement technique” was found to be superior to the other existing placement techniques.     

A metamodel-based towed system simulation

The objective of this exercise was the development of a computer simulation of a US Navy towed system (towed body and line array) capable of near real-time predictive capabilities. The purpose of the computer simulation was to be able to determine the lateral motion of the towed body in response to ship maneuvers. The theoretical approach was to develop a spatial-domain computer simulation of each of the towed system components treated as a system, and then develop a “metamodel” of the response by using simple algebraic expressions. At-sea trials were conducted aboard US Navy vessels to verify the simulation and fine-tune its performance.     

Numerical simulation of ship stability for dynamic environment

The prediction of ship stability during the early stages of design is very important from the point of vessel’s safety. Out of the six motions of a ship, the critical motion leading to capsize of a vessel is the rolling motion. In the present study, particular attention is paid to the performance of a ship in beam sea. The linear ship response in waves is evaluated using strip theory. Critical condition in the rolling motion of a ship is when it is subjected to synchronous beam waves. In this paper, a nonlinear approach has been tried to predict the roll response of a vessel. Various representations of damping and restoring terms found in the literature are investigated. A parametric investigation is undertaken to identify the effect of a number of key parameters like wave amplitude, wave frequency, metacentric height, etc.     

Using wavelet transforms to analyze nonlinear ship rolling and heave-roll coupling

The use of wavelet transforms is explored to investigate the nonlinear dynamical characteristics of ship roll and coupled heave-roll motion. The harmonic character, double period character and chaotic character are observed via a time–frequency window of the wavelet transform. Typical wave parameters in different stability regions are considered. Features such as restoring rolling, divergence rolling, steady state and chaotic responses of ship roll are obtained as well. The investigation in this paper not only highlights the feasibility of using wavelet transforms in the analysis of nonlinear dynamic characteristics of ship rolling in waves, but also shows how it could enhance the analysis abilities.     

Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 2: Simulations

Numerical simulations using a physiologically-based model of marine ecosystem size spectrum are conducted to study the influence of primary production and temperature on energy flux through marine ecosystems. In stable environmental conditions, the model converges toward a stationary linear log–log size-spectrum. In very productive ecosystems, the model predicts that small size classes are depleted by predation, leading to a curved size-spectrum.It is shown that the absolute level of primary production does not affect the slope of the stationary size-spectrum but has a nonlinear effect on its intercept and hence on the total biomass of consumer organisms (the carrying capacity). Three domains are distinguished: at low primary production, total biomass is independent from production changes because loss processes dominate dissipative processes (biological work); at high production, ecosystem biomass is proportional to primary production because dissipation dominates losses; an intermediate transition domain characterizes mid-production ecosystems. Our results enlighten the paradox of the very high ecosystem biomass/primary production ratios which are observed in poor oceanic regions. Thus, maximal dissipation (least action and low ecosystem biomass/primary production ratios) is reached at high primary production levels when the ecosystem is efficient in transferring energy from small sizes to large sizes. Conversely, least dissipation (most action and high ecosystem biomass/primary production ratios) characterizes the simulated ecosystem at low primary production levels when it is not efficient in dissipating energy.Increasing temperature causes enhanced predation mortality and decreases the intercept of the stationary size spectrum, i.e., the total ecosystem biomass. Total biomass varies as the inverse of the Arrhenius coefficient in the loss domain. This approximation is no longer true in the dissipation domain where nonlinear dissipation processes dominate over linear loss processes. Our results suggest that in a global warming context, at constant primary production, a 2–4 °C warming would lead to a 20–43% decrease of ecosystem biomass in oligotrophic regions and to a 15–32% decrease of biomass in eutrophic regions.Oscillations of primary production or temperature induce waves which propagate along the size-spectrum and which amplify until a “resonant range” which depends on the period of the environmental oscillations. Small organisms oscillate in phase with producers and are bottom-up controlled by primary production oscillations. In the “resonant range”, prey and predators oscillate out of phase with alternating periods of top-down and bottom-up controls. Large organisms are not influenced by bottom-up effects of high frequency phytoplankton variability or by oscillations of temperature.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

An efficient algorithm for strapdown accelerometer-based motion measurement

The paper is concerned with the measurement of motion of free floating bodies using accelerometers strapped to a cross-arm mounted on the body. The measurement system has been studied with the help of a formulation involving a set of coupled nonlinear initial-value equations involving the angular acceleration components. A PC-based software using the Bulirsch-Stoer technique has been developed to solve the initial-value problem so as to deduce the body motions from the measured accelerations. Suitable filtering strategy has been employed at every stage of numerical integration. The reliability of the strapdown accelerometer system together with software developed has been validated using a “dry” test. Typical motion measurements have been done in all the six degrees of freedom of a tug model in a wave flume. The method is deemed to be an efficient and cost-effective technique suitable for free floating bodies and for large motions.     

An experimental method for determining the frequency-dependent added mass and added mass moment of inertia for a floating body in heave and pitch motions

Most of the existing relevant materials have been obtained from experiments, in which evaluating the added mass at the resonant frequency corresponding to the peak of a frequency-response curve obtained from the “forced” vibration analysis is the most popular technique. In this paper, a simple experimental method was presented where the “free” vibration responses instead of the “forced” ones were used to determine the values of m_ah and I_ap. The main part of the experimental system is composed of a floating body (model) and a spring–shaft shaker. The “free” vibration of this main part was induced by imposing on it an initial displacement (and/or an initial velocity), and from the time histories of displacements information such as the “damped” natural frequencies, damping ratios, sectional added mass coefficients (C_V and C_P) were obtained. Since the displacements of the spring–shaft shaker are “translational” and those of the floating body due to pitch motions are “angular”, a technique for the transformation between the associated parameters of the two components of the main part was presented.     

Tracking the last sea-level cycle: seafloor morphology and shallow stratigraphy of the latest Quaternary New Jersey middle continental shelf

Seafloor geomorphology and surficial stratigraphy of the New Jersey middle continental shelf provide a detailed record of sea-level change during the last advance and retreat of the Laurentide ice sheet (120 kyr B.P. to Present). A NW–SE-oriented corridor on the middle shelf between water depths of 40 m (the mid-shelf “paleo-shore”) and 100 m (the Franklin “paleo-shore”) encompasses 500 line-km of 2D Huntec boomer profiles (500–3500 Hz), an embedded 4.6 km² 3D volume, and a 490 km² swath bathymetry map. We use these data to develop a relative stratigraphy. Core samples from published studies also provide some chronological and sedimentological constraints on the upper <5 m of the stratigraphic succession.The following stratigraphic units and surfaces occur (from bottom to top): (1) “R”, a high-amplitude reflection that separates sediment >46.5 kyr old (by AMS ¹⁴C dating) from overlying sediment wedges; (2) the outer shelf wedge, a marine unit up to 50 m thick that onlaps “R”; (3) “Channels”, a reflection sub-parallel to the seafloor that incises “R”, and appears as a dendritic system of channels in map view; (4) “Channels” fill, the upper portion of which is sampled and known to represent deepening-upward marine sediments 12.3 kyr in age; (5) the “T” horizon, a seismically discontinuous surface that caps “Channels” fill; (6) oblique ridge deposits, coarse-grained shelly units comprised of km-scale, shallow shelf bedforms; and (7) ribbon-floored swales, bathymetric depressions parallel to modern shelf currents that truncate the oblique ridges and cut into surficial deposits.We interpret this succession of features in light of a global eustatic sea-level curve and the consequent migration of the coastline across the middle shelf during the last 120 kyr. The morphology of the New Jersey middle shelf shows a discrete sequence of stratigraphic elements, and reflects the pulsed episodicity of the last sea-level cycle. “R” is a complicated marine/non-marine erosional surface formed during the last regression, while the outer shelf wedge represents a shelf wedge emplaced during a minor glacial retreat before maximum Wisconsin lowstand (i.e., marine oxygen isotope stage 3.1). “Channels” is a widespread fluvial subarial erosion surface formed at the late Wisconsin glacial maximum 22 kyr B.P. The shoreline migrated back across the mid-shelf corridor non-uniformly during the period represented by “Channels” fill. Oblique ridges are relict features on the New Jersey middle shelf, while the ribbon-floored swales represent modern shelf erosion. There is no systematic relationship between modern seafloor morphology and the very shallowly buried stratigraphic succession.