Numerical Simulation of Multiple Floating Structures With Nonlinear Constraints

2002 ◽  
Vol 124 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Degrees Of Freedom ◽  
Order Theory ◽  
Frequency Domain Analysis ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Mooring Lines ◽  
Floating Structures ◽  
Irregular Wave ◽  
Exciting Forces

A versatile and efficient numerical analysis is developed to compute the responses of a moored floating system composed of multiple floating structures. Structures such as tankers, semisubmersibles, FPSOs, SPARs, TLPs, and SPMs connected by mooring lines, connectors or fenders may be analyzed individually or collectively including multiple interaction. The analysis is carried out in the time domain assuming rigid body motion for the structures, and the solution is generated by a forward integration scheme. The analysis includes the nonlinearities in the excitation, damping, and restoring terms encountered in a typical mooring system configuration. It also allows for instabilities in the tower oscillation as well as slack mooring lines. Certain simplifications in the analysis have been made, which are discussed. The exciting forces in the analysis are wind, current, and waves (including a steady and an oscillating drift force), which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. For regular waves either linear, stretched linear or fifth order theory may be used. The irregular wave may be included as a given spectral model (e.g., PM or JONSWAP). The vessels are free to respond to the exciting forces in six degrees of freedom—surge, sway, heave, roll, pitch, and yaw. The tower, when present, is free to respond in two degrees of freedom—oscillation and precession. The loads in the mooring lines are determined from prescribed tension-strain tables for the lines. Rigid mooring arms can be analyzed by allowing for compression in the load-strain table. Fenders may be input similarly through load compression tables. In order to establish the stability and accuracy of the solution, comparison of the results with linearized frequency domain analysis was made. The analysis is verified by several different model test results for different structure configurations in regular and random seas. Some of the interesting aspects of nonlinear system are shown with a few examples.

Motions of Articulated Towers and Moored Floating Structures

1989 ◽  
Vol 111 (3) ◽  
pp. 233-241 ◽  
Author(s):  
S. K. Chakrabarti ◽  
D. C. Cotter
Keyword(s):  
Degrees Of Freedom ◽  
Single Point ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Floating Structure ◽  
Mooring Lines ◽  
Random Seas ◽  
Exciting Forces ◽  
The Time Domain

A versatile and efficient method of analysis has been developed to analyze a mooring system composed of a floating structure, e.g., a ship, mooring lines, fenders, and an articulated tower. The floating structure is assumed to be large, but may have an arbitrary shape, and the tower is assumed to be axisymmetrical. Although the program treats the floating structure and tower as a system, each body may be examined alone in the absence of the other. The analysis is carried out in the time domain assuming rigid body motion, and the solution is generated by a forward integration scheme. This approach permits nonlinear line and fender forces to be incorporated readily into the analysis. The exciting forces in the analysis are wind, current, and waves, which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. The vessel is free to respond to the exciting forces in six degrees of freedom—surge, heave, sway, roll, pitch, and yaw. The tower is free to respond in two degrees of freedom—oscillation and precession. The analysis has been extensively verified with several different model tests for different structure configurations in regular and random seas. These include an articulated tower, a single-point mooring tanker system, a floating caisson and an inclined mooring tower.

A Parametric Study of Low-Frequency Damping of Mooring System

2014 ◽  
Author(s):  
Minglu Chen ◽  
Shan Huang ◽  
Nigel Baltrop ◽  
Ji Chunyan ◽  
Liangbi Li
Keyword(s):  
Low Frequency ◽  
Structure Design ◽  
The Body ◽  
Body Motion ◽  
Mooring Line ◽  
Offshore Structure ◽  
Frequency Oscillation ◽  
Low Frequency Oscillation ◽  
Line System ◽  
Irregular Wave

Mooring line damping plays an important role to the body motion of moored floating platforms. Meanwhile, it can also make contributions to optimize the mooring line system. Accurate assessment of mooring line damping is thus an essential issue for offshore structure design. However, it is difficult to determine the mooring line damping based on theoretical methods. This study considers the parameters which have impact on mooring-induced damping. In the paper, applying Morison formula to calculate the drag and initial force on the mooring line, its dynamic response is computed in the time domain. The energy dissipation of the mooring line due to the viscosity was used to calculate mooring-induced damping. A mooring line is performed with low-frequency oscillation only, the low-frequency oscillation superimposed with regular and irregular wave-frequency motions. In addition, the influences of current velocity, mooring line pretension and different water depths are taken into account.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

The Anchor-Last Deployment Problem for Inextensible Mooring Lines

1975 ◽  
Vol 97 (3) ◽  
pp. 1046-1052 ◽  
Author(s):  
Robert C. Rupe ◽  
Robert W. Thresher
Keyword(s):  
Numerical Model ◽  
Equations Of Motion ◽  
Simultaneous Equations ◽  
Mooring Line ◽  
Integration Scheme ◽  
Lumped Mass ◽  
Mooring Lines ◽  
Concentrated Masses ◽  
Predictor Corrector ◽  
Lagrange’S Method

A lumped mass numerical model was developed which predicts the dynamic response of an inextensible mooring line during anchor-last deployment. The mooring line was modeled as a series of concentrated masses connected by massless inextensible links. A set of angles was used for displacement coordinates, and Lagrange’s Method was used to derive the equations of motion. The resulting formulation exhibited inertia coupling, which, for the predictor-corrector integration scheme used, required the solution of a set of linear simultaneous equations to determine the acceleration of each lumped mass. For the selected cases studied the results show that the maximum tension in the cable during deployment will not exceed twice the weight of the cable and anchor in water.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

DESIGN AND DEVELOPMENT OF AN EFFICIENT COMPUTER SIMULATION MODEL FOR RESPONSE ANALYSIS OF A MOORED SEMI-SUBMERSIBLE

2021 ◽  
Vol 161 (A1) ◽  
Author(s):  
V Domala ◽  
R Sharma
Keyword(s):  
Computer Simulation ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Experimental Results ◽  
Response Analysis ◽  
Computer Simulation Model ◽  
Governing Equations ◽  
Design And Development ◽  
Mooring Lines ◽  
Steel Wires

This paper presents the design and development of an efficient modular ‘Computer Simulation Model (CSM)’ for response analysis of a moored semi-submersible. The computer simulation model is designed in two split models (i.e. computational and experimental models) and each of these models consists of various modules. The modules are developed from basic governing equations related to motion and modules are integrated and we aim for a seamless integration. The moored semi-submersible is represented mathematically as six degrees of freedom dynamic system and the coupling effects between the structure and mooring lines are considered. The basic geometric configuration of semi- submersible is modelled and analyzed for stability computations in MS-Excel*TM and then the basic governing equations related to motion are modelled mathematically in a module and solved numerically with Ansys-AQWA**TM. The computational model is validated and verified with some available experimental results. The CSM is utilized to study the surge and sway responses with respect to the horizontal range of mooring lines and our results show good validation with the existing experimental results. Our presented results show that the fibre wires have minimum steady state response in surge and sway degrees of freedom as compared with the steel wires. However, they have large drift as compared with steel wires. Finally, we show that the computer simulation model can help in detailed analysis of responses and results can be utilized for design and development of new age semi-submersibles for optimum performances for a given set of parameters.

Experimental Study on a 3-Dimensional Hydro-Elastic Deformation of “Underwater Platform” With Multi-Towers in Waves

2016 ◽  
Author(s):  
Ken Haneda ◽  
Motohiko Murai ◽  
Jun Yamanoi
Keyword(s):  
Elastic Deformation ◽  
Body Motion ◽  
Offshore Wind ◽  
Elastic Response ◽  
Experimental Result ◽  
Elastic Model ◽  
Mooring Lines ◽  
3 Dimensional ◽  
Floating Offshore Wind Turbines ◽  
Head Waves

Underwater platform was proposed in OMAE 2015 for the purpose of enhancing productivity of various types of renewable energy converter on the sea and its feasibility study was carried out through 2 types of tank experiment [1]. The underwater platform which is a very large frame shape structure connects several floaters under the sea to share power cables and mooring lines and to keep relative distances between the floaters. In the experiment, 1/200 scale elastic model with three spar buoys was used. The buoys imitated spar type floating offshore wind turbines (FOWTs). From the experiment, it was shown that the platform with large draft can reduce its response in waves. In this paper, we report new result and knowledge obtained by additional model experiments use the 1/200 model. In the experiment, we changed the arrangement and draft of the model and measured hydro-elastic deformation of the underwater platform in waves. From the last experiment, relationship between draft settings and response was shown. In the experiment, relationship between wave angles and response was surveyed. From the experiment, we have confirmed followings: 1. Rigid-body motion is remarkable in beam waves, 2. Elastic response is remarkable in head waves, and 3. Remarkable torsional motion is occurred in 45 degrees’ waves. The more important thing, however, is that the experimental result indicated that the platform of large draft decreases its motion in the all the wave angles.

scholarly journals Enhancement of a 3-DOF submerged wave energy device using bistability

2020 ◽  
Vol 3 (2) ◽  
pp. 73-82
Author(s):  
Benjamin Schubert ◽  
William S. P. Robertson ◽  
Benjamin S. Cazzolato
Keyword(s):  
Wave Energy ◽  
Degrees Of Freedom ◽  
Phase Relationship ◽  
Bistable System ◽  
Viscous Drag ◽  
Regular Waves ◽  
Point Absorber ◽  
Exciting Forces ◽  
Bistable Mechanism ◽  
The Impact

The dynamic response of a submerged CETO shaped quasi-point absorbing wave energy converter coupled to a bistable power take off is presented in this study. Whilst the impact of bistability has been shown in a limited number of situations to improve the amount of power generated, many models have been restricted to a single degree of freedom and often ignore drag effects. To overcome these model limitations, a submerged single tether point absorber with a bistable power take off was modelled using both 1 and 3 degrees of freedom. The device was subjected to regular waves and included a simple model of viscous drag. The bistable mechanism was provided by a magnetic dipole model quantified by a dimensionless parameter applicable to any bistable system. The performance of the device was is assessed by the theoretical power generated. Over each model, the previously observed benefit of bistability was not consistently obtained. Simulations of regular waves demonstrated an increase in generated power for suboptimal conditions for some frequencies, while a reduction in generated power was observed in optimal conditions. The performance increase showed strong correlation to the phase relationship between the motion and exciting forces as a result of bistability.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

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