Horizontal Motions of an SPM Tanker Under Alternative Mooring Configurations

1995 ◽  
Vol 117 (4) ◽  
pp. 223-231 ◽  
Author(s):  
T. Jiang ◽  
T. E. Schellin ◽  
S. D. Sharma
Keyword(s):  
Degrees Of Freedom ◽  
Single Point ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Line Tension ◽  
Wave Forces ◽  
Restoring Force ◽  
Linearized Stability ◽  
Wind Actions ◽  
Control Forces

Horizontal motions of a tanker single point moored in current, wind, and waves were numerically investigated under four alternative configurations, namely, buoy mooring (SBM), articulated tower mooring (ATM), bow turret mooring (BTM), and internal turret mooring (ITM). The analysis was based on a previously validated, comprehensive mathematical model of the equations of motion in three degrees of freedom (surge, sway, and yaw) that considers five sets of forces: 1) nonlinear quasi-steady hydrodynamic response and control forces; 2) linear memory effects due to radiated waves; 3) nonlinear mooring restoring force characteristics; 4) empirical wind actions; and 5) first-order wave forces and wave drift forces. Locally linearized stability analyses showed that restoring characteristics have no influence on static bifurcations (typical for BTM and ITM) and only minor influence on dynamic bifurcations (typical for SBM and ATM). However, nonlinear time domain simulations revealed that they do affect the form of asymptotic motion trajectories as well as line tension amplitudes. It was found that turret position is a significant parameter and motion behavior is sensitive to the direction of wind and waves relative to current. Comparison of simulated time histories between autonomous and nonautonomous modes indicated that the traditional spectral analysis treating high-frequency and low-frequency responses separately may not be valid for locally unstable cases.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

2021 ◽  
Author(s):  
Renan F. Corrêa ◽  
Flávio D. Marques
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Nonlinear Behavior ◽  
Limit Cycle Oscillation ◽  
Restoring Force ◽  
Aeroelastic System ◽  
Technical Literature ◽  
Practical Applications

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.

Motion Prediction of a Single-Point Moored Tanker Subjected to Current, Wind and Waves

1990 ◽  
Vol 112 (1) ◽  
pp. 83-90 ◽  
Author(s):  
T. Jiang ◽  
T. E. Schellin
Keyword(s):  
Digital Simulation ◽  
Single Point ◽  
Wave Spectrum ◽  
Memory Effects ◽  
Wave Forces ◽  
Restoring Force ◽  
Low Frequencies ◽  
Frequency Wave ◽  
First Order ◽  
Drift Forces

Horizontal motions of a tanker attached to a single-point mooring (SPM) terminal were predicted using digital simulation in the time domain. Excitations from steady current, gusting wind, and irregular seaway were included. Hydrodynamic forces generated by the ship’s motion and the action of its propeller and rudder were calculated in accordance with a previously validated, nonlinear quasi-steady four-quadrant maneuvering model, extended to include linear memory effects due to waves generated by the moving ship. Memory effects were approximated by a vectorial recursive state space model corresponding to a set of higher order differential equations. A nonlinear relationship of the force in the mooring hawser was assumed to represent restoring force characteristics of the SPM system. Wave excitation forces comprised first-order forces at wave frequencies and second-order drift forces at low frequencies. First-order wave forces were obtained by superposition of force components corresponding to regular wave components comprising the wave spectrum. Based on the low-frequency wave envelope, drift forces were calculated using mean drift force coefficients in regular waves. Selected sample simulations are presented to illustrate the use of this digital simulation method.

Study on the Multi-Body Dynamic Characteristics of FPSO Soft Yoke Mooring System Based on Symplectic Algorithm

2019 ◽  
Author(s):  
Wenhua Wu ◽  
Baicheng Lyu ◽  
Ji Yao ◽  
Qianjin Yue ◽  
Zhang Yantao ◽  
...  
Keyword(s):  
Stress State ◽  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Single Point ◽  
Differential Algebraic Equations ◽  
Mooring System ◽  
Algebraic Equations ◽  
Restoring Force ◽  
Hamilton System ◽  
Multi Body

Abstract The soft yoke single-point mooring (SYMS) system is the main mooring approach for the floating production storage and offloading (FPSO) unit. As a typical multi-rigid-body system, a SYMS consists of the single-point turret, yoke, mooring legs, and mooring support. It releases the rotational degrees of freedom of an FPSO through the combined effects of multiple joint structures, so as to deliver the weather-vane effect of the FPSO. In this paper, a multi-body dynamics model of the soft yoke mooring system was established. To deal with the difficult integration in the process of solving differential-algebraic equations, a symplectic numerical integration method was proposed on the basis of the Zu Chongzhi method. The proposed solution format had simple symplectic property automatically satisfying the Hamilton system, as well as a high accuracy in solving nonlinear systems. The measured data of the FPSO’s six degrees of freedom (6DoF) under two different sea conditions were selected, and the mooring restoring force of the SYMS was calculated. The calculated results showed that the symplectic solution method could the actual stress state of the structures with more obvious dynamic characteristics. Furthermore, the displacement and stress state of the single-body structures, such as the mooring legs and yoke, and the analysis result could comprehensively evaluate the overall working state of the SYMS.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

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