Rolling motion behavior of rockfall on gentle slope:an experimental approach

The effects of slope surface material, slope gradient, block shape, and block mass conditions on rockfall rolling velocity were estimated with orthogonal test approach. Visual analysis shows that the importance of the factors is slope surface material > slope gradient > block shape > block mass. All the factors except block mass have the F value greater than the critical value, suggesting that these three factors are the key factors affecting the rockfall rolling velocity. Factor interaction analysis shows that the effect of the slope gradient relies largely on the slope surface conditions, and the block shape has little influence if the slope gradient is larger than a critical value. An empirical model considering the three key factors is proposed to estimate the rolling velocity, of which the error is limited to 5% of the testing value. This model is validated by 73 field tests, and the prediction shows excellent correlation with the site test. Thus, this analysis can be used as a tool in the rockfall behavior analysis.

Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches

A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.

Probabilistic description of extreme oscillations and reliability analysis in rolling motion under stochastic excitation

Large-amplitude rolling motions, also regarded as extreme oscillations, are a great threat to marine navigation, which may lead to capsizing in ship motion. Therefore, it is important to quantify extreme oscillations, assess reliability of ship systems, and establish a suitable indicator to characterize extreme oscillations in ship systems. In this work, extreme events are investigated in a ship model considering a complex ocean environment, described by a single-degree-of-freedom nonlinear system with stochastic harmonic excitation and colored Gaussian noise. The stationary probability density function(PDF) of the system is derived through a probabilistic decomposition-synthesis method. Based on this, we infer the classical damage rate of the system. Furthermore, a new indicator, independent of the PDF, is proposed to quantify the damage related only to the fourth-order moment of the system and the threshold for extreme events. It is more universal and easier to determine as compared with the classical damage rate. A large damping ratio, a large noise intensity, or a short correlation time can reduce the damage rate and the value of the indicator.These findings provide new insights and theoretical guidance to avoid extreme oscillations and assess the reliability of practical ship movements.

The stability analysis of rolling motion of hypersonic vehicles and its validations

The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflected rolling motions are improved. The out- comes can serve as the basis for further study regarding the influence of pitching and lateral motion on the stability of rolling motion. To validate the theoretical results, numerical simulations were do^e for the rolling motion of two hypersonic vehicles with typical configurations. Also, wind tunnel experiments for four aircraft models with typical configurations have been done. The results show that： 1） there exist two dynamic patterns of the rolling motion under statically stable condition. The first one is point attractor, for which the motion of aircraft returns to the original state. The second is periodic attractor, for which the aircraft rolls periodically. 2） Under statically unstable condition, there exist three dynamic patterns of rolling motion, namely, the point attractor, periodic attractor around deflected state of rolling motion, and double periodic attractors or chaotic attrac- tors.

The stability of rolling motion of hypersonic vehicles with slender configuration under pitching maneuvering

The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.

Investigation on nonlinear rolling dynamics of amphibious vehicle under wind and wave load

Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.

Numerical Simulation of the Motion of A Floating Body with Partially Filled Tanks by A Pressure-Convection Particle Method

The moving particle semi-implicit（MPS）method has demonstrated its usefulness in practical engineering applications.Although it has wide applicability,it is still hard to predict the pressure precisely using the MPS method.A pressure-convection particle method based on the MPS method is proposed to overcome this problem.The improved performance of this new method is validated with computational and measured results.The approach is also applied to compute the problem of sloshing associated with floating body motion in waves.The pressure-convection MPS method demonstrated its capability to improve the prediction of pressure.

A Modified Logvinovich Model For Hydrodynamic Loads on an Asymmetric Wedge Entering Water with a Roll Motion

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

Nonparametric Identification of Nonlinear Added Mass Moment of Inertia and Damping Moment Characteristics of Large-Amplitude Ship Roll Motion

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of largeamplitude ship roll motion based on transient motion data through the nonparametric system identification method.An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data.However,this numerical approach leads to solution instability due to noisy data.Regularization is a technique that can overcome the lack of stability;hence,Landweber’s regularization method was employed in this study.The L-curve criterion was used to select regularization parameters(number of iterations)that correspond to the accuracy of the inverse solution.The solution of this method is a discrete moment,which is the summation of nonlinear restoring,nonlinear damping,and nonlinear mass moment of inertia.A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship,and the detections are matched with the inverse solution at the same discrete times.The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy.Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.

Mathematical Modelling of Response Amplitude Operator for Roll Motion of a Floating Body：Analysis in Frequency Domain with Numerical Validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.

Fluid Resonance Between Twin Floating Barges with Roll Motion Under Wave Action

The wave-induced fluid resonance between twin side-by-side rectangular barges coupled with the roll motion of the twin barges is investigated by both numerical simulation and physical model test.A 2D numerical wave flume,based on an open source computational fluid dynamics(CFD)package OpenFOAM,is applied for the numerical simulation.After numerical validations and convergent verifications,the characteristics of the fluid resonance in the gap between the twin rolling side-by-side barges are examined.The resonant frequency of the oscillating fluid in the gap between the twin rolling barges decreases compared with that between the twin fixed barges.Generally,the twin barges roll in the opposite directions,and their equilibrium positions lean oppositely with respect to the initial vertical direction.A physical model test is carried out for a further investigation,in which the twin barges are set oppositely leaning and fixed.From the present experimental results,a linear decrease of the resonant frequency with the increasing leaning angle is found.Combined with the numerical results,the deflection of the equilibrium positions of the twin barges is a relevant factor for the resonant frequency.Besides,the effects of the gap width and incident wave height on the fluid resonance coupled with roll motion are examined.

A Practical Hull Form Design of Ferry Using Hybrid Scheme Method and Performing Experiment

Prediction of ship performance in preliminary ship design is an important consideration. It could guarantee ship in safe and comfort. However, many design works did not involve simultaneously ship performances predictions in preliminary design. Moreover, ship designers sometimes modified a ship form to obtain proper design without ship performance consideration. Therefore, this study concerns on predictions of total resistance and added wave resistance of a ferry using a hybrid particle-grid method and then its motions response after modifying bow and stern parts by conducting experiment. Research results show total resistance and added wave resistance have a significant different, therefore, it would be an important consideration in determining ship powering in preliminary ship design. The non-dimensional added wave resistance increases in increasing wave length from λ/Lpp = 0.5 to 1.0 and it decreases after L/λ = 1.0. In addition, it tends to decrease caused by increasing ship speed. The comparison of averaged heave and pitch amplitudes between basic forms after modifying bow and stem parts is quiet similar. However, the rolling amplitude of the modified form is significantly higher comparing with the basic form. We conclude that a ship could be design in preliminary design take into account performances predictions by using numerical method and experimental work.

Modal Control of Cantilever Beam Using a Gyrostabilizer

In this paper,an experimental model of a horizontal cantilever beam with a rotating/oscillating attached to the shaker for harmonic excitation at the one end and a gyrostabilizer at the other end is built to verify the equations of the Lagrangian model.The primary focus of the study was to investigate the parameters of excitation amplitude,natural frequency,rotating mass(disk mass),and disk speed of gyro that would minimize the amplitude of the beam to identify these effects.Numerical and experimental results indicate that the angular momentum of the gyrostabilizer is the most effective parameter in the reduction of beam displacement.

Non-linearity Analysis of Ship Roll Gyro-stabilizer Control System

A gyro-stabilizer is the interesting system that it can apply to marine vessels for diminishes roll motion.Today it has potentially light weight with no hy­drodynamics drag and effective at zero forward speed.The twin-gyroscope was chosen.Almost,the modelling for designing the system use linear model that it might not comprehensive mission requirement such as high sea condition.The non-linearity analysis was proved by comparison the re­sults between linear and non-linear model of gyro-stabilizer throughout fre­quency domain also same wave input,constrains and limitations.Moreover,they were cross checked by simulating in time domain.The comparison of interested of linear and non-linear close loop model in frequency domain has demonstrated the similar characteristics but gave different values at same frequency obviously.The results were confirmed again by simulation in irregular beam sea on time domain and they demonstrate the difference of behavior of both systems while the gyro-stabilizers are switching on and off.From the resulting analysis,the non-linear gyro-stabilizer model gives more real results that correspond to more accuracy in a designing gyro-sta­bilizer control system for various amplitudes and frequencies operating condition especially high sea condition.

CHARACTERISTICS OF PRESSURE DROP AND CORRELATION OF FRICTION FACTORS FOR SINGLE-PHASE FLOW IN ROLLING HORIZONTAL PIPE

Gas-liquid two-phase flow occurs increasingly in some dynamic devices operating in the oceanic condition. The relative data are limited with respect to flow characteristics, so the present study is to investigate systematically single-phase pressure drop, and to develop the theory for frictional factor under the roiling condition. Using deionized water as the test fluid, a series of experiments of single-phase flow were conducted in pipe with the inner diameter of 34.5 ram. The test section was horizontally settled on the rolling apparatus, and its regularity was similar to simple harmonic motion. It is found that the pressure drop during rolling motion fluctuate with the change of the rolling period and rolling angle, which is significantly different from fluid motion in a steady state. By the contrast between experiment results and stable-state theory values, existing correlations can not predict present frictional factor very well. Therefore, in the present article, the single-phase frictional factor is correlated with the Reynolds number for rolling motion, and its computated results agree well with experimental data.

Experimental investigation of influence of strake wings on self-induced roll motion at high angles of attack

The modern high performance air vehicles are required to have extreme maneuverability,which includes the ability of controlled maneuvers at high angle of attack. However, the nonlinear and unsteady aerodynamic phenomena, such as flow separation, vortices interaction, and vortices breaking down, will occur during the flight at high angle of attack, which could induce the uncommanded motions for the air vehicles. For the high maneuverable and agile air missile, the nonlinear roll motions would occur at the high angle of attack. The present work is focused on the selfinduced nonlinear roll motion for a missile configuration and discusses the influence of the strake wings on the roll motion according to the results from free-to-roll test and PIV measurement using the models assembled with different strake wings at a = 60°. The free-to-roll results show that the model with whole strake wings(baseline), the model assembled with three strake wings(Case A)and the model assembled with two opposite strake wings(Case C) experience the spinning, while the model assembled with two adjacent strake wings(Case B), the model assembled with one strake wing(Case D) and the model with no strake wing(Case E) trim or slightly vibrate at a certain "×"rolling angle, which mean that the rolling stability can be improved by dismantling certain strake wings. The flow field results from PIV measurement show that the leeward asymmetric vortices are induced by the windward strake wings. The vortices would interact the strake wings and induce crossflow on the downstream fins to degrade the rolling stability of the model. This could be the main reason for the self-induced roll motion of the model at a = 60°.

Experimental and numerical investigation of the roll motion behavior of a floating liquefied natural gas system

The present paper does an experimental and numerical investigation of the hydrodynamic interaction and the response of a single point turret-moored Floating Liquefied Natural Gas(FLNG) system,which is a new type of floating LNG(Liquid Natural Gas) platform that consists of a ship-type FPSO hull equipped with LNG storage tanks and liquefaction plants.In particular,this study focuses on the investigation of the roll response of FLNG hull in free-decay motions,white noise waves and also in irregular waves.Model tests of the FLNG system in 60%H filling condition excited by both white noise waves and irregular waves combined with steady wind and current have been carried out.Response Amplitude Operators(RAOs) and time histories of the responses are obtained for sway,roll and yaw motions.Obvious Low Frequency(LF) components of the roll motions are observed,which may be out of expectation.To facilitate the physical understanding of this phenomenon,we filter the roll motions at the period of 30 s into two parts:the Wave Frequency(WF) motions and the Low Frequency(LF) motions respectively.The results indicate that the LF motions are closely related to the sway and yaw motions.Possible reasons for the presence of the LF motions of roll have been discussed in detail,through the comparison with the sway and yaw motions.As for the numerical part,the simulation of the modeled case is conducted with the help of the software SESAM.A good agreement between experiments and calculations is reported within the scope of trends.However,the numerical simulations should be further improved for the prediction of the FLNG system in the heading sea.

Probability density function solution to nonlinear ship roll motion excited by external Poisson white noise

The stationary probability density function (PDF) solution to nonlinear ship roll motion excited by Poisson white noise is analyzed. Subjected to such random excitation, the joint PDF solution to the roll angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the exponential-polynomial closure (EPC) method is adopted. With the EPC method, the PDF solution is assumed to be an exponential-polynomial function of state variables. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. The problem of determining the unknown parameters in the approximate PDF finally results in solving simultaneous nonlinear algebraic equations. Both slight and high nonlinearities are considered in the illustrative examples. The analysis shows that when a second-order polynomial is taken, the result of the EPC method is the same as the one given by the equivalent linearization (EQL) method. The EQL results differ significantly from the simulated results in the case of high nonlinearity. When a fourth-order or sixth-order polynomial is taken, the results of the EPC method agree well with the simulated ones, especially in the tail regions of the PDF. This agreement is observed in the cases of both slight and high nonlinearities.

Advances on numerical and experimental investigation of ship roll damping

This paper presents recent developments towards efficient and reliable methods for roll damping estimation based on numerical simulations as well as model tests using the harmonic excited roll motion(HERM)technique.A newly designed automatic roll damping estimation procedure shows the advantage of a just-in-time post processing of experimental measurement results.Real-time analysis of the measured roll damping values permits a considerable shortening of the test times.Thus,a large number of investigations can be carried out with relatively manageable effort in order to determine the roll damping behavior of different keel configurations or at operating conditions,e.g.,different sized keels or Froude numbers.In addition,HERM measurement method is applied to investigate the memory effect.For this purpose,different excitation schemes are introduced and the results are analyzed.Moreover,a study of the scale effect on the roll damping properties is conducted,in which experimental and numerical investigations are performed for two scales of a ship model.Furthermore,a method is developed that significantly reduces the effort of Reynolds average Navier-Stokes(RANS)-based simulations of roll motion.The reduction of simulation time is achieved by introducing an artificial damping.The obtained results show that the developed method is very well applicable for numerical as well as in experimental investigations.During the model tests using HERM technique,the model is free and the rudder is used to keep the straight-ahead course.The analysis of the numerical and experimental results shows that the influence of the rudder induced force and moment during HERM tests is not negligible and the contribution of the rudder must be taken into account by estimating the roll damping.Finally,a new concept is developed to investigate the parametric roll behavior of ships,which allows neglecting the consideration of the complex modelling of free surface waves in the simulations.During the RANS computations,a potential-based method is applied to compute the variation of restoring terms due the roll motion.