Analysis of Vertical Bending Moment on an Ultra Large Containership Induced by Extreme Head Seas

2014 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Rigid Body ◽  
Bending Moment ◽  
Variable Stiffness ◽  
The Body ◽  
Experimental Results ◽  
Irregular Waves ◽  
Time Step ◽  
Strip Theory ◽  
Vertical Bending Moment ◽  
Body Response

This paper discusses the numerical analysis of an ultra large containership model in severe head seas. A body nonlinear time domain code based on the strip theory is used for the calculation of the rigid body response of the vessel. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship at each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. The numerical vertical bending moment is compared with the experimental results. The experiment was conducted on a flexible model in both regular and irregular waves. The model comprised six segments that were joined with an aluminum backbone of variable stiffness characteristics in order to replicate the hydroelastic behavior of the real ship. The model was tested for two ship speeds, 15 and 22 knots. For the first three harmonic values of the vertical bending moment, a good agreement between the numerical and the experimental results are found. However, higher harmonics significantly contributed to the total experimental vertical bending moment, in regular waves with 8m wave height and a ship speed of 15 knots. Similarly, the value of the fourth harmonic was 32% of the first harmonic values when the ship encountered a 5m regular wave with 22 knots speed. On comparison of the rigid body response in irregular seas, the hydroelastic loads resulted in 49% increase in the maximum value of the vertical bending moment.

Short Term Distribution of Loads Acting on a Cruise Vessel in Extreme Seas Using a Body Nonlinear Time Domain With Second Order Froude-Krylov Pressure

2015 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Surface Condition ◽  
Bending Moment ◽  
The Body ◽  
Short Term ◽  
Weakly Nonlinear ◽  
Strip Theory ◽  
Vertical Bending Moment ◽  
Nonlinear Time Domain

Short term probability distribution of the vertical bending moment acting on a cruise vessel in extreme seas is calculated using a body nonlinear time domain method based on strip theory. The hydrodynamic forces are calculated for the exact wetted surface area under the incident wave profile. The incident potential satisfies the weakly nonlinear free surface condition based on the Stokes expansion. The disturbance potential satisfies the linear free surface and body boundary conditions. Certain practical engineering techniques are employed for the calculation of the body nonlinear forces. The statistics and the probability of distribution of the numerical vertical bending moment are compared with the experimental results measured in the wave tank.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

1981 ◽  
Vol 25 (04) ◽  
pp. 243-251
Author(s):  
J. Juncher Jensen ◽  
P. Terndrup Pedersen
Keyword(s):  
Linear Part ◽  
Vertical Motion ◽  
Bending Moment ◽  
Irregular Waves ◽  
Bending Moments ◽  
Shear Forces ◽  
Strip Theory ◽  
Wave Heights ◽  
Exciting Forces ◽  
Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

Response Based Identification of Critical Wave Scenarios

2012 ◽  
Author(s):  
Günther F. Clauss ◽  
Marco Klein ◽  
Carlos Guedes Soares ◽  
Nuno Fonseca
Keyword(s):  
Linear Method ◽  
Bending Moment ◽  
Extreme Wave ◽  
Offshore Structure ◽  
Sea State ◽  
Worst Case ◽  
Strip Theory ◽  
Wave Conditions ◽  
Vertical Bending Moment ◽  
Method Approach

In the last years the identification and investigation of critical wave sequences regarding offshore structure responses became one of the main topics in the ocean engineering community. Thereby the area of interest covers the entire field of application spectra at sea — from efficient and economic offshore operations in moderate sea states to reliability as well as survival in extreme wave conditions. For most cases, the focus lies on limiting criteria for the design, such as maximum global loads, maximum relative motions between two or more vessels or maximum accelerations, at which the floating structure has to operate or to survive. These criteria are typically combined with a limiting characteristic sea state (Hs, Tp) or a rogue wave. For the investigation of offshore structures as well as the identification of critical wave sequences, different approaches are available — most of them are based on linear transfer functions as it is an efficient procedure for the fast holistic evaluation. But, for some cases the linear method approach implies uncertainties due to nonlinear response behavior, in particular in extreme wave conditions. This paper presents an approach to these challenges, a response based optimization tool for critical wave sequence detection. This tool, which has been successfully introduced for the evaluation of the applicability of a multi-body system based on the linear method approach, is adjusted to a nonlinear task — the vertical bending moment of a chemical tanker in extreme wave conditions. Therefore a nonlinear strip theory solver is introduced into the optimization routine to capture the nonlinear effects on the vertical bending moment due to steep waves acting on large bow flares. The goal of the procedure is to find a worst case wave sequence for a certain critical sea state. This includes intensive numerical investigation as well as model test validation.

Steep Wave Effects on Wave Induced Vertical Bending Moment Using a 3D Numerical Wave Tank

2017 ◽  
Author(s):  
Shivaji Ganesan Thirunaavukarasu ◽  
Debabrata Sen ◽  
Yogendra Parihar
Keyword(s):  
Comparative Study ◽  
Incident Wave ◽  
Bending Moment ◽  
Wave Steepness ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Strip Theory ◽  
Numerical Wave ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper presents a detail comparative study on wave induced vertical bending moment (VBM) between linear and approximate nonlinear calculations using a 3D numerical wave tank (NWT) method. The developed numerical approach is in time domain where the ambient incident waves can be defined by any suitable wave theory. Certain justifying approximations employed in the solution of the interaction hydrodynamics (diffraction and radiation) enabling the NWT to generate stable long duration time histories of all parameters of interest. This is an extension of our earlier works towards the development of a practical NWT based solution for wave-structure interactions [1]. After a brief outline of the implemented numerical details, a comprehensive validation and verification of vertical shear force (VSF) and bending moment RAOs computed using the linearized version of the NWT against the usual linear results of strip theory and 3D panel codes are presented. Next we undertake the comparative study between the fully linear and approximate nonlinear versions of the present code for different incident wave steepness. In the approximate nonlinear formulation, the ambient incident wave is defined by the full nonlinear numerical wave model based on Fourier approximation method which can generate very steep steady periodic nonlinear waves up to the near wave breaking limit. The nonlinearities associated with the incident Froude Krylov and hydrostatic restoring forces/moments are exact up to the instantaneous wetted surface at the displaced location, but the hydrodynamic diffraction and radiation effects are linearized around the mean wetted surface. The standard S175 container hull is considered for the comparative studies because of its geometric nonlinearities. Numerical simulations are performed for four different wave lengths with increasing wave steepness. It is observed that the computed wave induced VBM amidships from the approximate nonlinear results can be almost 30% higher compared to the results from a purely linear solution, which can be a critical issue from the safety point. Significant higher harmonics are also observed in the approximate nonlinear results which at some times may be responsible for exciting the undesirable whipping/springing responses.

Prediction of Ship Responses in Large Amplitude Waves Using a Body Nonlinear Time Domain Method With 2nd Order Froude-Krylov Pressure

2014 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Surface Area ◽  
Time Domain ◽  
Time Instant ◽  
The Body ◽  
Regular Waves ◽  
Time Step ◽  
Strip Theory ◽  
Practical Engineering ◽  
Wetted Surface Area ◽  
Nonlinear Time Domain

The paper analyzes the effect of 2nd order waves on the vertical ship responses in extreme seas. The numerical simulations are carried out using a body nonlinear time domain code based on strip theory. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship for each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. First order Froude Krylov pressures are replaced with a second order model for the present study. The 2nd order Froude-Krylov pressures are integrated upto the exact wetted surface area for each time instant. The ship responses in regular waves with varying steepness are analyzed. Finally, the vertical ship responses are compared with the responses in design waves measured in the wave tank.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

Determination of global design loads for large high-speed catamarans

2002 ◽  
Vol 216 (1) ◽  
pp. 79-94
Author(s):  
S E Heggelund ◽  
T Moan ◽  
S Oma
Keyword(s):  
High Speed ◽  
Bending Moment ◽  
Wave Loads ◽  
Strip Theory ◽  
Non Linear ◽  
Design Loads ◽  
Linear Effects ◽  
Operational Criteria ◽  
Vertical Bending Moment

Methods for calculation of design loads for high-speed vessels are investigated. The influence of operational restrictions on design loads is emphasized. Relevant operational criteria for high-speed displacement vessels are discussed. Procedures and criteria for numerical calculation of operational limits are incomplete and should be further investigated. Operational limits and design loads for a 60 m catamaran are calculated on the basis of linear strip theory. Non-linear effects on design loads are assessed from calculations in regular waves. Simplified formulae commonly used by classification societies for prediction of operational limits seem to over-predict the reduction of motions and wave loads at reduced speed. When operational limits typically given by the shipmaster or the operator are used, the design loads found by direct calculations are comparable with design loads given by classification societies. For vertical bending moment and torsion, the use of active foils is found to increase the linear loads. Owing to reduced motions, the foils reduce the non-linear loads and hence the total loads. The effect of non-linear horizontal loads is not investigated but can be important for transverse bending moment.

scholarly journals Comparison and Validation of Hydrodynamic Load Models for a Semi-Submersible Floating Wind Turbine

2018 ◽  
Author(s):  
John Marius Hegseth ◽  
Erin E. Bachynski ◽  
Madjid Karimirad
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Extreme Values ◽  
Global Analysis ◽  
Single Point ◽  
Bending Moment ◽  
Experimental Results ◽  
Distributed Model ◽  
Fe Model ◽  
Load Models

In global aero-hydro-servo-elastic analyses of floating wind turbines (FWTs), the hydrodynamic loads are usually found from potential flow theory and applied in a single point of a rigid hull. When the hull is relatively stiff, this approach ensures correct behaviour for the six rigid body degrees-of-freedom (DOFs), but provides no information about the internal loads in the hull. The current work considers a simplified method to include distributed, large volume hydrodynamics in the global analysis, where frequency-dependent loads from potential theory are applied on a finite element (FE) model of the hull in a strip-wise manner. The method is compared to conventional load models for a braceless 5MW semi-submersible FWT, and validated against experimental results from model tests with focus on internal loads and rigid body motions in the main wave-frequency range. The global motions are accurately predicted by the distributed model for all investigated load cases. Good agreement with experimental results is also seen for the column base bending moment in wave-only conditions, although extreme values are not captured correctly due to limitations in linear theory. In combined wave-wind conditions, the measured bending moments are significantly increased because of the wind-induced mean angle of the platform. This effect is not considered in the numerical model, which therefore underestimates the moment response. However, an approach which calculates the loads in the actual mean configuration of the hull is found to give reasonably accurate results, at least in moderate wave conditions.

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