Nonlinear Roll Damping Research Articles

Numerical and experimental study on nonlinear roll damping characteristics of trimaran vessel

Roll damping prediction is a complex problem in the field of ship hydrodynamics. For trimaran vessels, there are some issues about the roll damping to be discussed and studied in depth due to multi-hull form. A high-precision prediction method by CFD of roll damping for trimaran vessel is established, and the roll decay motion of multi-forward speeds and multi-degrees of freedom are validated by experiment. The characteristics of linear and nonlinear roll damping are studied by the variation of initial angles and layouts, and the influence of ship forward speed is also analyzed. Due to the strong flow interference and nonlinearity of the emergence of the side hull, an interval section method is proposed to integrate the whole decay curve, so as to calculate the roll damping more accurately. The roll damping components with different layouts and bilge keels are divided by numerical method and verified by empirical formula, and the existence of the flow interference damping has a great influence on nonlinear roll damping. The research on roll damping of trimaran vessel is devoted to improve its roll motion performance, providing reference and help for the research on damping-increasing and anti-rolling methods.

Study of telescopic gangway motions in time domain during offshore operation

The dynamic response of the telescopic gangway strongly links to the relative motion which is significant when the gangway vessel works along with another floating unit in proximity. The failure might cause operational downtime or even personnel casualty. In this paper, gangway motions, including extension, retraction, rotations, and relative motions, are studied numerically in the time domain and compared to experimental measurements. The hydrodynamic interaction of the multi-body system is analyzed by 3D diffraction and radiation computation in the frequency domain. The nonlinear roll damping is calibrated and validated in both free decay and regular waves. Two uni-directional scenarios of primary irregular waves and one bi-directional scenario of both primary and secondary irregular waves are taken into account in the study. Remarkable vertical motion up to 10 m between gangway departure and landing points are observed even if the significant wave height is only 3.25 m. Extreme value analysis shows the gangway inclination can be as high as 17° which exceeds the maximum acceptance so that enhanced slip resistance feature must be added on the gangway. The different patterns of gangway motion trajectory in the vertical plane are also illustrated to corroborate the conclusion.

Experimental Determination of Non-Linear Roll Damping of an FPSO Pure Roll Coupled with Liquid Sloshing in Two-Row Tanks

Wave excited roll motion poses danger for moored offshore vessels such as Floating Production Storage and Offloading (FPSO) because they cannot divert to avoid bad weather. Furthermore, slack cargo tanks are almost always present in FPSOs by design. These pose an increased risk of roll instability due to the presence of free surfaces. The most common method of determining roll damping is roll decay tests, yet very few test have been performed with liquid cargo, and most liquid cargo experiments use tanks that span the entire width of the vessel; which is seldom the case for full scale FPSO vessels during normal operations. This paper presents a series of roll decay test carried out on a FPSO model with two two-row-prismatic tanks with different filling levels. To directly investigate the coupling between the liquid sloshing and the vessel motion, without modifying the damping, tests were performed at a constant draft. The equivalent linear roll damping coefficients consisting of linear, quadratic and cubic damping terms are analyzed for each loading condition using four established methods, the Quasi-linear method, Froude Energy method, Averaging method and the Perturbation method. The results show that the cubic damping term is paramount for FPSOs and at low filling levels, were the FPSO is more damped. Recommendations regarding the applicability of the methods, their accuracy and computational effort is given and the effect of the liquid motion on the vessel motion is discussed.

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship’s rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, followed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.

Linear and non-linear roll damping of a FPSO via system identification of a third order equation with sway-roll coupled damping effects

This work focuses on roll decay experiments performed on hulls normally used as FPSOs. Considering the practical case of beam seas, Newton's second law and the Newton-Euler theorem lead to coupled sway, heave and roll equations for an arbitrary pole. Assuming symmetry, the heave equation is uncoupled, leaving the sway and roll equations coupled. The research shows that, even if inertia is decoupled, damping coupling is unavoidable and cannot be neglected. Nevertheless, a third order equation dealing only with roll can be constructed. The latter is used to develop a robust approach that uses system identification techniques to obtain damping properties from the decay tests. In this approach, non-linear damping is assessed using a cycle-by-cycle linear approach that uses system identification to match all the information obtained from the decay test. Both held-over and pre-oscillation tests are discussed, and new concept is presented: the coupled damping number (CDN), which relates the product of the main diagonal damping terms with coupling damping coefficients. The CDN is proven to be null for potential flows, and turns out to be very small even when viscous effects are present such as in decay tests, at least for typical FPSO hulls.

Melnikov Chaos in a Modified Rayleigh–Duffing Oscillator with ϕ6 Potential

The chaotic behavior of the modified Rayleigh–Duffing oscillator with [Formula: see text] potential and external excitation is investigated both analytically and numerically. The so-called oscillator models, for example, ship rolling motions. The single well and triple well potential cases are considered. Melnikov method is applied and the conditions for the existence of homoclinic and heteroclinic chaos are obtained. The effects of nonlinear damping on roll motion of ships are analyzed in detail. As it is known, nonlinear roll damping is a very important parameter in estimating ship responses. It is noted that the pure and unpure quadratic damping parameters affect the Melnikov criterion in the heteroclinic and homoclinic cases respectively while the pure cubic parameter affects the amplitude in both cases. The predictions have been tested with numerical simulations based on the basin of attraction. It is pointed out that certain quadratic damping effects are contrary to cubic damping effect.

Nonlinear roll damping of a barge with and without liquid cargo in spherical tanks

Damping plays a significant role on the maximum amplitude of a vessel's roll motion, in particular near the resonant frequency. It is a common practice to predict roll damping using a linear radiation–diffraction code and add that to a linearized viscous damping component, which can be obtained through empirical, semi-empirical equations or free decay tests in calm water. However, it is evident that the viscous roll damping is nonlinear with roll velocity and amplitude. Nonlinear liquid cargo motions inside cargo tanks also contribute to roll damping, which when ignored impedes the accurate prediction of maximum roll motions. In this study, a series of free decay model tests is conducted on a barge-like vessel with two spherical tanks, which allows a better understanding of the nonlinear roll damping components considering the effects of the liquid cargo motion. To examine the effects of the cargo motion on the damping levels, a nonlinear model is adopted to calculate the damping coefficients. The liquid cargo motion is observed to affect both the linear and the quadratic components of the roll damping. The flow memory effect on the roll damping is also studied. The nonlinear damping coefficients of the vessel with liquid cargo motions in spherical tanks are obtained, which are expected to contribute in configurations involving spherical tanks.

Identification of the nonlinear roll damping and restoring moment of a FPSO using Hilbert transform

Roll motion is a major concern of ship and offshore operators because it has a direct impact on the boarding comfort of crews, downtime of the process plant and structural integrity of the hull and appurtenance system. Nevertheless, the nonlinear effects involved in the roll motion of ship and offshore structures are not only incompletely understood, but also inaccurately predicted during the design stage. Therefore, efforts have been made to identify the dynamic characteristics of the roll motion of a FPSO using a novel dynamic system identification scheme based upon the Hilbert transform. First, the system identification scheme using the Hilbert transform was applied to the idealized single DOF nonlinear oscillator problem with quadratic damping and quintic stiffness terms. The solution of the single DOF problem was solved numerically using the 4th order Runge–Kutta method and the target damping and stiffness coefficients were determined by applying the Hilbert transform to the numerically obtained free decay signal. A comparison was also made with traditional logarithmic decrement technique for the damping coefficient. Second, the system identification method was applied to the model test results of a FPSO with a bilge keel, where the nonlinear effect of roll damping and restoring is expected to be dominant. This methodology can be applied to full scale measurement data to achieve a clearer understanding on the nonlinear effect of roll motion.

Study on the Treatment of Nonlinear Roll Damping in Hydrodynamic Calculation and Structural Analysis

In order to insure the consistent wave loads in hydrodynamic calculation and structural analysis, the treatment of nonlinear roll damping in roll motion, wave torsional moment and structural analysis are studied. The nonlinear roll damping moment is applied to the structural model by means of the equivalent nodal forces. Taking a supply ship and a FPSO as example, the calculation results show that the problem of torsional moment distribution divergent on the bow and the unbalanced structural model is improved greatly, which would be helpful to provide the reliable basis to design the structures.

A roll-motion control system for a mobile-wheeled platform: a preliminary test platform for roll-motion control of ships

Ship stabilization against roll motion caused by uncertainties, such as external waves or wind impact, nonlinear roll damping and parametric variation etc., is an important problem. Among announced approaches, the active fin stabilizer is a very effective and widely adopted procedure; however an accurate model of a whole nonlinear dynamic system is difficult to obtain. On the other hand, the mobile-wheeled platform also has highly nonlinear dynamic characteristics and it is difficult to evaluate the appropriate control effort to steer and balance on a bumpy road. To deal with these two systems, there existing some restricted resemblance between them, an intelligent roll-motion controller is developed in this paper. Firstly, to confront the uncertainties, a hetero-associative neural observer is added into a novel translated fuzzy sliding-mode controller (FSMC) to predict uncertainties. The neural observer can speed up the response and increase the self-tuning capability of the FSMC. In the proposed roll-motion controller, a compact gyroscope and accelerometer are used to detect the rolling conditions; the gathered data are sent to a microcontroller to calculate the command. Finally, to verify the effectiveness of the proposed controller, some preliminary simulations for ship stabilization are provided under the assumption that the sea surface is modeled as a one-dimensional linear free surface. Then, some experimental results are provided for a mobile-wheeled platform steered on a bumpy road. The performance is also compared with a conventional PD controller and a pure FSMC under the same conditions.

The Nonlinear Roll Damping of a FPSO Hull

The ship-rolling problem is a subject that has been studied for a long time. Since Froude's time (in the 19th century) to nowadays, this subject was revisited several times in order to adjust the theory to changes in ship hulls, dimensions, materials, appendages, etc. On the other hand, ship analysis technological resources, including both experimental techniques and computational capacity (that did not exist in Froude's time), have also amazingly improved. But despite all those technological developments, the assessment of the nonlinear roll damping of some types of hulls still is a challenging problem. The floating production storage and offloading (FPSO) hull fitted with larger bilge keels, for instance, has behaved in such a way that it is impossible to obtain results from nowadays industry standards via decaying tests. This paper discusses an alternative way to assess the nonlinear damping behavior of FPSO hulls with large bilge keels. Since it is fairly easy to perform decaying tests, the paper also proposes an alternative way to analyze the FPSO properties through this kind of testing by grouping multiple results instead of using only a single test. This artifice brought improvements, such as an increased agreement between the alternative model and the experimental data. The paper also compares the more traditional approaches with the alternative method and finally shows the latter's applicability.

Recovering the functional form of the nonlinear roll damping of ships from a free-roll decay experiment: An inverse formulism

The purpose of this paper is to identify the functional form of the nonlinear roll damping for a particular ship based on an experiment. The problem of damping identification is formulated as an integral equation of the first kind. However, the solution of the problem lacks stability properties, due to the ill-posedness of the first-kind integral equation. To resolve this problem, a stabilization technique (known as a regularization method) is applied to the present problem of the identification of nonlinear damping. The identified results for nonlinear roll dampings are compared with those from a conventional roll identification method. The findings of the present study are validated by the direct comparison of experimental data on free-roll decay motion with the numerically simulated results.

A Numerical Investigation on Nonparametric Identification of Nonlinear Roll Damping Moment of a Ship from Transient Response~!2009-08-29~!2009-09-05~!2010-02-08~!

This paper is concerned with the determination of nonlinear roll damping moments of ships including similar floating structures. Using the measured motion response data of ship's roll motion, an inverse problem is formulated for the determination. The problem of damping determination is mathematically involved in a Volterra integral equation of the kind between the roll responses and unknown nonlinear roll damping. This first kind integral equation results in numerical instability, that is, solutions lack stability property. A regularization method is applied in order to suppress the instability. Any priori information is not required on the model of the nonlinear damping. The applicability of the present study is demonstrated through the numerical investigations using the given nonlinear roll equations from the tests.

Nonlinear Roll Damping of Ship Motions in Waves

Nonlinear roll damping has a profound influence on ship motions and stability in ocean waves. In this study, an experimental investigation is conducted on the nonlinear roll damping of a ship in regular and irregular waves. The random decrement method, previously used in linear roll damping prediction, is extended to nonlinear roll damping estimation in the data process. The accuracy of the nonlinear roll damping obtained by using the random decrement method is found to be dependent on the values of the threshold and segment number.

漁船の船型,状態に関する船体運動学的考察-II : 96トン型鋼製鮭鱒流綱漁船の横方向運動の場合

The author has investigated the characteristics of the motions of fishing boats to analyse theoretically the motions of the ship in the waves from the aspect of their seakeeping qualities. In the previous paper, the effect of the hull form and the ship's condition during navigation upon the longitudinal motions of the boat were analysed and discussed. In this paper, the author reports about the effect of these upon the transversal motions. The Ordinary Strip Method (O.S.M.) has been used to analyse the ship motions theoretically, and this method is used on the basis of linear theory. However, boats have stabilization equipments such as bilge keels to decrease the rolling angle, generally. Accordingly the conformal roll damping coefficient which takes nonlinear roll damping resistance into consideration is adopted to treat the linear differential equation of motion. Furthermore, the availability of the O.S.M. was verified with experiments using a simulated radio controlled 2-meter fishing boat model in wind waves.

Theoretical Calculations on the Motions, Hull Surface Pressures and Transverse Strength of a Ship in Waves

The authors tried the theoretical analysis on the motions, hull surface pressures and transverse strength of a gigantic oil tanker in regular waves.In the first place, the ship motions in regular waves from different directions were analysed by assuming the coupled equations of heaving and pitching motions and those of swaying, yawing and rolling motions based upon the modified strip theory. The non-linear roll damping was introduced into the latter coupled equations of motion.In the second place, the hydrodynamic pressures induced on the hull surface were evaluated theoretically by using the solutions of ship motions.Finally, the transverse strength calculations were performed for several cases of the ship in waves by using the obtained hull surface pressures and the estimated cargo oil pressures.The large hydrodynamic pressures were found in beam and quartering waves, which produced the large bending moments at the deck corner, bilge and bottom of longitudinal bulkhead in the transverse ring.