Relevant bibliographies by topics / Wave bending moments

Academic literature on the topic 'Wave bending moments'

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Published: 3 November 2023

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Journal articles on the topic "Wave bending moments"

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Ambur, Damodar R., Davresh Hasanyan, Liviu Librescu, and Zhanming Qin. "Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2063 (September 14, 2005): 3543–60. http://dx.doi.org/10.1098/rspa.2005.1512.

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The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal x -axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.
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Woodward, John B., Michael G. Parsons, and Armin W. Troesch. "Ship Operational and Safety Aspects of Ballast Water Exchange at Sea." Marine Technology and SNAME News 31, no. 04 (October 1, 1994): 315–26. http://dx.doi.org/10.5957/mt1.1994.31.4.315.

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A dry bulk carrier, a tanker, and a containership—taken as typical of ships trading to U.S. ports—are analyzed for possible hazards caused by emptying and refilling ballast tanks at sea. Using hydrostatic data furnished by the shipowners, hull bending moments and stabilities are investigated to find the tank-emptying operations that produce the greatest changes in those parameters. As should be expected, bending moment changes do not exceed allowable stillwater values. Changes in GM are insignificant. The worst hydrostatic cases serve as a guide to conditions that should be analyzed in rough water. The University of Michigan SHIPMO program shows that in waves of 10-ft significant height wave-induced bending moments and shears are far below the design values published by the American Bureau of Shipping. On the other hand, in waves of 20-ft significant height, the maximum wave heights that occur occasionally can cause moments or shears that exceed design values. For the 20-ft case, both linear and nonlinear versions of SHIPMO are used.
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Petranović, Tamara, Antonio Mikulić, Marko Katalinić, Maro Ćorak, and Joško Parunov. "Method for Prediction of Extreme Wave Loads Based on Ship Operability Analysis Using Hindcast Wave Database." Journal of Marine Science and Engineering 9, no. 9 (September 14, 2021): 1002. http://dx.doi.org/10.3390/jmse9091002.

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The method for the prediction of extreme vertical wave bending moments on a passenger ship based on the hindcast database along the shipping route is presented. Operability analysis is performed to identify sea states when the ship is not able to normally operate and which are likely to be avoided. Closed-form expressions are used for the calculation of transfer functions of ship motions and loads. Multiple operability criteria are used and compared to the corresponding limiting values. The most probable extreme wave bending moments for the short-term sea states at discrete locations along the shipping route are calculated, and annual maximum extreme values are determined. Gumbel probability distribution is then fitted to the annual extreme values, and wave bending moments corresponding to a return period of 20 years are determined for discrete locations. The system reliability approach is used to calculate combined extreme vertical wave bending moment along the shipping route. The method is employed on the example of a passenger ship sailing across the Adriatic Sea (Split, Croatia, to Ancona, Italy). The contribution of the study is the method for the extreme values of wave loads using the hindcast wave database and accounting for ship operational restrictions.
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Corak, Maro, Joško Parunov, and C. Guedes Soares. "Probabilistic Load Combination Factors of Wave and Whipping Bending Moments." Journal of Ship Research 59, no. 01 (March 1, 2015): 11–30. http://dx.doi.org/10.5957/jsr.2015.59.1.11.

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Extreme values of wave and whipping bending moments are important in structural design of large containerships. Since the extreme values of these two, partially correlated processes do not occur at the same time instant and even at the same environmental conditions, it is necessary to combine them by using probabilistic load combination methods. The correlation analysis between wave and whipping bending moments is performed and a practical method for calculation of the most probable load combination factor between considered bending moments is presented. Short-term load combination factors are calculated by reconstruction of the signal from the frequency domain solution. Results are validated by comparison with model test data of the 9400-TEU containership for various sea states and speeds and heading angles. Practical regression equations for estimation of the most probable short-term load combination factor are formulated. Regression equations are then used in the computation of the long-term distribution of combined bending moment. The procedure is demonstrated on the example of the two large containerships.
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O¨stergaard, C. "Partial Safety Factors for Vertical Bending Loads on Containerships." Journal of Offshore Mechanics and Arctic Engineering 114, no. 2 (May 1, 1992): 129–36. http://dx.doi.org/10.1115/1.2919960.

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International design codes for seagoing steel ships of today are in the process of testing a new safety format with load factors separately multiplied with nominal (code) values of still water and wave loads. This leads to two design values of these loads, the sum of which must not exceed a design value of the strength of the ship structure, which is again a nominal (code) value of strength, this time divided by a strength factor. Such load and strength factors are generally termed partial safety factors. In the paper, vertical still water and wave bending moments of containerships are considered as loads. The partial safety factors are determined on the basis of reliability analysis, i.e., the sum of the design values of the loads will not exceed a design serviceability limit state of the ship’s structure with given probability. To enable reliability analysis, distribution density of the ship’s strength to resist bending moments is based on a stochastic interpretation of nominal (code) values used in the conventional safety format. The probability density of the still water bending moment is obtained from recently published statistical data. The probability density of the wave bending moment is calculated using advanced hydrodynamic and spectral analysis, including long-term statistics of the (North Atlantic) seaway. Reliability and related design values are estimated using the FORM algorithm with due consideration of the different repetition numbers for which the stochastic models of the two bending moments are valid. The results are presented as nonlinear regression formulas and as diagrams that specify partial safety factors related to length and beam of containerships. The nominal values of bending moments to be used with these partial safety factors are given as functions of length, beam, and block coefficient of those ships.
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Sulisetyono, Aries, and Teguh Putranto. "Wave Load Analysis of the Corvette Ship in the Sea Water of Indonesia." Applied Mechanics and Materials 862 (January 2017): 291–95. http://dx.doi.org/10.4028/www.scientific.net/amm.862.291.

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Wave load prediction of ship should be considered in the design stage of ship’s construction. The excessive of wave load might cause a structural failure of ship during operational in seaway. The bending moment might be experienced on the ship structure that it contributes to stress concentration on the particular part of construction. This paper describes the prediction of bending moment and shear forces of the warship corvette type considered to the sea condition of Indonesia. The 3D diffraction theory was adopted to analyze ship’s motion responses, bending moments, and shear forces numerically. In this numerical simulation, the variations of speed and heading angle of ship were performed with respect to environmental condition of sea state 4, 5, 6 and 7. The simulation results had shown that the maximum shear force and bending moment was occurred on the area of mid-ship.
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Pedersen, P. T., and J. J. Jensen. "Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 223, no. 3 (June 12, 2009): 377–90. http://dx.doi.org/10.1243/14750902jeme143.

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A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment in slender mono-hull displacement vessels is presented. The procedure takes into account main ship hull characteristics such as length, breadth, draught, block coefficient, bow flare coefficient, forward speed, and hull flexibility. The wave-induced loads are evaluated for specific operational profiles. Non-linearity in the wave bending moment is modelled using results derived from a second-order strip theory and water entry solutions for wedge-type sections. Hence, bow flare slamming is accounted for through a momentum type of approach. The stochastic properties of this non-linear response are calculated through a monotonic Hermite transformation. In addition, the impulse loading attributable to, for example, bottom slamming or a rapid change in bow flare is included using a modal expansion in the two lowest vertical vibration modes. These whipping vibrations are added to the wave frequency non-linear response, taking into account the rise time of the impulse response as well as the phase lag between the occurrence of the maximum non-linear load and the maximum impulse load. Previous results for the sagging bending moment are validated by comparison with fully non-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Owing to the few input parameters, this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Another application area is for novel single-hull ship types not presently covered by the rules of the classification societies. As one application example the container ship MSC Napoli is considered. Further validations are needed, however, in order to select proper values of the parameters entering the analytical form of the slamming impulse.
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Perišić, Nevena, and Poul Henning Kirkegaard. "Low-Cost Tower Root Fatigue Load Estimation for Structural Health Monitoring of Grouted Connections in Offshore Wind Turbines." Key Engineering Materials 569-570 (July 2013): 676–83. http://dx.doi.org/10.4028/www.scientific.net/kem.569-570.676.

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The sinking of wind turbines (WTs) with monopile foundations is one of the major issues in the offshore wind industry nowadays. Dynamic wind and wave loads act on the WTs causing vibrations of the structure. However, grouted connections in the monopiled WTs are not designed well enough to transfer bending moments from the wind loading. When the load capacity of the grouted connection is reached, stress cracks appear in the grout causing transition piece to slide down. Direct measuring of the fatigue load, called the tower bending moment, causing fatigue failures and sinking of the WTs is expensive and practically unfeasible. This paper suggests a low-cost, model-based algorithm for indirect measuring of the tower bending moments from the WT dynamic response measurements. The bending moment is estimated recursively using well-known Kalman filter theory. The method is validated using WT simulated data, assuming different measurement noise levels.
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Mansour, A. E., and J.-P. Wasson. "Charts for Estimating Nonlinear Hogging and Sagging Bending Moments." Journal of Ship Research 39, no. 03 (September 1, 1995): 240–49. http://dx.doi.org/10.5957/jsr.1995.39.3.240.

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Abstract This paper presents charts for preliminary estimates of the nonlinearities associated with wave bending moments acting on a ship moving in a stationary sea. Deviation of the actual hull shape above the waterline from "vertical wall" is characterized by a flare coefficient. The charts show the influence of the flare coefficient, among other parameters, on a nonlinearity parameter which may be used to estimate the difference between wave hogging and sagging moments. Three application examples are given at the end of the paper to illustrate how the charts can be used in conjunction with linear strip theory results in order to estimate slightly nonlinear hogging and sagging moments.
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Gui, E. H., and V. A. Squire. "Random vibration of floating ice tongues." Antarctic Science 1, no. 2 (June 1989): 157–63. http://dx.doi.org/10.1017/s0954102089000234.

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A normal mode approach is used to model the behaviour of a linearly-damped, elastic, ice beam floating on a fluid foundation and subjected to a random distributed loading. As an example, two loading regimes are considered to act on the Erebus Glacier Tongue, McMurdo Sound: broad bandwidth (‘white noise’) loading, and an ocean wave-type pressure distribution beneath the tongue. For white noise input, the root mean square (rms) deflexion is found to good accuracy within the first few modes, but the rms bending moment increases with the number of modes included in the summation due to the unlimited frequency content of the forcing. Solutions for the rms deflexion and bending moments quickly converge to their mathematical limit after six modes when the forcing is due to ocean waves. A local maximum in rms bending moment near the end of the beam confirms that waves may be important as a mechanism for iceberg calving.
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Dissertations / Theses on the topic "Wave bending moments"

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Kim, Shinwoong. "Experimental study on wave bending moments of a zero-speed rigid containership model in regular, irregular, and equivalent design waves." Electronic Thesis or Diss., Ecole centrale de Nantes, 2023. http://www.theses.fr/2023ECDN0001.

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La thèse vise à étudier les mouvements et les chargements internes d’un modèle de porte-conteneur rigide formé de 9 segments dans des vagues extrêmes. L’étude est principalement expérimentale et est réalisée avec une maquette sans vitesse d’avance dans une houle de face et une houle oblique (-120 degrés). L’étude aboutit à des résultats soulignant l’importance de la prendre en compte les aspects non linéaires des vagues et des réponses structurelles correspondantes.Dans des conditions de mer de face, trois types de vagues sont testés. Des vagues régulières sont utilisées pour s’assurer que le modèle se comporte de manière similaire à la campagne précédente effectuée avec la même maquette. Une approche de type Monte Carlo avec un certain nombre de réalisations de 2 heures 30 de vagues irrégulières est ensuite utilisée pour construire des données de référence. Enfin, des vagues equivalentes de design (EDW) sont générées pour vérifier, en particulier, la faisabilité d’une approche EDW irrégulière appelée First Order Reliability Method (FORM). Un algorithme numérique FORM couplé avec le solveur HOSNWT est développé et validé par rapport aux résultats Monte Carlo. Les caractéristiques géométriques des signaux EDW et VBM ainsi que leurs statistiques sont étudiées. L’étude vise peut-être deux quantités. Le premier est la hauteur de crête de la vague dans un scénario de vague seule, et le second est le VBM du modèle segmenté. L’utilisation du solveur de génération d’onde non linéaire HOS-NWT, permet une validation croisée avec la mesure expérimentale car les vagues générées sont comparables. Dans la condition de vagues obliques, l’étude est limitée aux vagues régulières avec différentes cambrure de vagues afin de fournir des données de référence pour les futures études. L’effet de non-linéarité des vagues sur les moments de flexion horizontaux et verticaux des vagues avec une cambrure variable est démontré
The present thesis aims to study the motions and the internal loads of a 9-segmented rigid containership model in extreme waves. The study is mainly experimental and is carried out on a zero-speed model in a 180-degree head sea and a -120 degree oblique sea. The study leads to results highlighting the importance of the consideration of nonlinear wave descriptions and corresponding nonlinear structural responses.In head sea conditions, three wave approaches are considered. Regular waves are used to ensure that the model behaves similar to the earlier campaign. A Monte Carlo approach with a number of full scale 2h30 irregular wave realizations is used to have reference data. Finally, irregular equivalent design waves (EDW) are studied to check, in particular, the feasibility of one irregular EDW approach called First Order Reliability Method.A numerical algorithm coupling with the HOS-NWT for the FORM EDW is developed and the validation compared to the Monte Carlo results is performed in terms of geometrical characteristics of the EDW and IW signals along with their statistics. The study targets mainly two quantities. The first is the wave crest in a wave-only scenario, and the second is the VBM of the segmented model. The use of the HOSNWT, a nonlinear wave generation solver, enables cross-validation with experimental measurement.In the oblique wave condition, the study is limited to regular waves with various wave steepness with the intent to provide reference data for future benchmark studies. The wave nonlinearity effect on the horizontal and vertical wave bending moments with varying steepness is shown
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Xu, Jinsong. "Estimation of wave-induced ship hull bending moment from ship motion measurements." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0029/NQ62460.pdf.

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Rogers, Charles. "Development of a Computational Method for the Prediction of Wave Induced Longitudinal Bending in Ships." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/honors_theses/17.

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This thesis documents the development of a computational method for wave induced longitudinal bending in ships. First, there will be a discussion about the importance of longitudinal bending in ship design. The paper will then outline the basic physics at work in the system. It will review the wave forcing computation as well as the response of the vessel. It will then document the progression of the program, which was constructed in Fortran 90, as it solves the linear differential equation for the vessel bending caused by an incoming wave. The entire program then appears at the end of the paper. While the current program is not complete the theory behind it is valid and the code can be augmented to include non-linear components in the future.
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Nordblad, Erik. "Opening New Radio Windows and Bending Twisted Beams." Doctoral thesis, Uppsala universitet, Institutet för rymdfysik, Uppsalaavdelningen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-158797.

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In ground based high frequency (HF) radio pumping experiments, absorption of ordinary (O) mode pump waves energises the ionospheric plasma, producing optical emissions and other effects. Pump-induced or natural kilometre-scale field-aligned density depletions are believed to play a role in self-focussing phenomena such as the magnetic zenith (MZ) effect, i.e., the increased plasma response observed in the direction of Earth's magnetic field. Using ray tracing, we study the propagation of ordinary (O) mode HF radio waves in an ionosphere modified by density depletions, with special attention to transmission through the radio window (RW), where O mode waves convert into the extraordinary (X, or Z) mode. The depletions are shown to shift the position of the RW, or to introduce RWs at new locations. In a simplified model neglecting absorption, we estimate the wave electric field strength perpendicular to the magnetic field at altitudes normally inaccessible. This field could excite upper hybrid waves on small scale density perturbations. We also show how transmission and focussing combine to give stronger fields in some directions, notably at angles close to the MZ, with possible implications for the MZ effect. In a separate study, we consider electromagnetic (e-m) beams with helical wavefronts (i.e., twisted beams), which are associated with orbital angular momentum (OAM). By applying geometrical optics to each plane wave component of a twisted nonparaxial e-m Bessel beam, we calculate analytically the shift of the beam's centre of gravity during propagation perpendicularly and obliquely to a weak refractive index gradient in an isotropic medium. In addition to the so-called Hall shifts expected from paraxial theory, the nonparaxial treatment reveals new shifts in both the transverse and lateral directions. In some situations, the new shifts should be significant also for nearly paraxial beams.
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Book chapters on the topic "Wave bending moments"

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Rajendran, Suresh, and C. Guedes Soares. "Effect of Slamming and Green Water on Short-Term Distribution of Vertical Bending Moment of a Containership in Abnormal Waves." In Lecture Notes in Civil Engineering, 333–45. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3119-0_19.

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Takami, Tomoki, Shohei Ozeki, and Kazuhiro Iijima. "On the Assessment of Extreme Wave-Induced Bending Moment of a Ship by FORM and Reduced Order Method Based on Coupled CFD and FEA." In Lecture Notes in Civil Engineering, 691–702. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-4624-2_42.

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Tekgoz, M., and Y. Garbatov. "Quasi-static wave induced bending moment prediction of an off-shore support vessel in head sea using the 2-D strip and 3-D panel methods." In Trends in Maritime Technology and Engineering Volume 1, 233–41. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003320272-26.

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"Wave loads Long-term prediction of combined wave and whipping bending moments of containership." In Analysis and Design of Marine Structures, 15–22. CRC Press, 2013. http://dx.doi.org/10.1201/b15120-4.

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_orak, M., J. Parunov, and C. Soares. "Long-term prediction of combined wave and whipping bending moments of containership." In Analysis and Design of Marine Structures, 3–10. CRC Press, 2013. http://dx.doi.org/10.1201/b15120-3.

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"Structural reliability & risk Short-term probabilistic combination of wave and whipping bending moments." In Maritime Technology and Engineering, 665–72. CRC Press, 2014. http://dx.doi.org/10.1201/b17494-70.

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Keser, Anabel, Michiel Verdult, Harleigh Seyffert, and Apostolos Grammatikopoulos. "The Design, Production, Verification, and Calibration of an Elastic Model of a Catamaran for Hydroelastic Experiments." In Progress in Marine Science and Technology. IOS Press, 2023. http://dx.doi.org/10.3233/pmst230019.

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Catamarans are popular in the offshore sector as they combine good transverse stability and ample deck space with low wave resistance. However, their slender hull shape results in low restoring qualities in heave and pitch motions. The large motions in rough weather can often result in water impacting the underside of the deck connecting the two hulls, a phenomenon called wet deck slamming. The impulse excitation from wet deck slamming can then produce a transient hydroelastic response of the structure called whipping. Whipping excites mode shapes that would not normally be present in the response, as their natural frequencies are significantly higher than the wave encounter frequency. This results in detrimental contributions to fatigue life through high-amplitude cyclical bending moments. Both the calculation of slamming loads and the prediction of resulting structural responses have been a challenge for several decades. The highly nonlinear and three-dimensional character of the phenomenon, combined with the strongly coupled fluid-structure interaction means that it is unpredictable, and even the definition of slamming events has been a matter of disagreement among researchers. Experiments are still a vital part of these investigations, for validating ever-improving numerical techniques. An essential issue with experiments is the extent to which mode shapes and natural frequencies can be emulated in model scale. Traditional hydroelastic models are segmented and use either a flexible backbone or flexible joints to introduce stiffness. This often results in an excellent description of the 2-node bending mode, but an increasing error for higher modes leads to stress inaccuracies. In this investigation, a continuous model of a catamaran is designed and produced for hydroelastic experiments. The advantages and limitations of the concept are identified, the verification against structural models is presented, and the calibration of the measurements is discussed.
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Wang, Zhaohui, Jørgen Juncher Jensen, and Jinzhu Xia. "On the effect of green water on deck on the wave bending moment." In Developments in Marine Technology, 239–45. Elsevier, 1998. http://dx.doi.org/10.1016/s0928-2009(98)80159-5.

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Conference papers on the topic "Wave bending moments"

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Clauss, Gu¨nther F., Christian E. Schmittner, Janou Hennig, Carlos Guedes Soares, Nuno Fonseca, and Ricardo Pascoal. "Bending Moments of an FPSO in Rogue Waves." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51504.

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The increasing numbers of reported rogue waves with extreme crest and wave heights and unusual group pattern with the consequence of severe damages raise the question if such exceptional events have to be considered routinely for the design of ships and offshore structures. For the investigation of the effects of rogue wave impacts time domain simulation methods are required in addition to traditional frequency domain methods which may not be sufficient to consider these extreme events. In this paper the vertical bending moments at the midship section of an FPSO are investigated using state of the art numerical simulation tools in combination with experiments. For the seakeeping tests the extremely high New Year Wave (registered in the North Sea) is generated in the wave tank, and motions and structural forces are analyzed at model scale. For validation the results are evaluated deterministically and compared to numerical simulations. The time domain calculation allows to artificially change local wave characteristics. The steepness of the selected rogue wave is varied and the influence on wave induced loads is studied. A comparison with standard procedures of seakeeping analysis and classification rules closes the paper.
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Fonseca, Nuno, Ricardo Pascoal, and Carlos Guedes Soares. "Probability Distributions of Vertical Bending Moments on a FPSO in Abnormal Wave Seastates." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29753.

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A method to calculate the responses of a FPSO in deterministic wave traces with abnormal waves, has been applied to calculate the motions and global structural loads induced by a large set of abnormal waves that were measured in different places. The present paper is focused on the probability distributions of the motions and global structural loads induced by the seastates which included the abovementioned abnormal waves. The objective is to compare the distributions of the wave elevation with the abnormal wave crest and trough, and to compare the distributions of the platform responses with the responses induced by the abnormal waves. In this way it is possible to conclude if the abnormal waves induce abnormal responses of the platform, or if on the other hand there are wave groups with waves smaller than the abnormal wave that induce larger responses.
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Huang, Wenbo. "Random Combination Factors for Still Water and Wave Bending Moments." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96665.

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Abstract Based on the extreme value of the primary loads of ship hull girder instead of characteristic values, the more reasonable load combination factors are defined. In order to evaluate the random variation of newly defined load combination factors, based on Ferry-Berges & Castanheta (FBC) and Poisson square wave models, the still water bending moments (SWBM), vertical wave bending moments (VWBM) and their combined processes are simulated to get the random realizations of load combination factors. The statistical analysis results show that the load combination factors take the value of 1 with the highest probability and can be well fitted by the Weibull distribution. Such information should be incorporated appropriately in the reliability analysis of ship hull girder.
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Clauss, Gu¨nther F., Andre´ Kauffeldt, and Katja Jacobsen. "Longitudinal Forces and Bending Moments of a FPSO." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29091.

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For the design of FPSOs the vertical bending moment is a key parameter to ensure safe operation. If analyzed at water line level, however, the unknown influence of longitudinal forces may distort the results. Hence, a segmented FPSO model with midship force transducers at two levels is investigated in various deterministic wave sequences to identify the vertical bending moment and its associated neutral axis as well as the superimposing longitudinal forces. It is shown that the neutral axis is far below the water line level, with the consequence, that extreme cyclic loads at deck level would be expected. However, as the associated longitudinal forces — even if significant — generate a counteracting moment, this effect is largely compensated. Both, frequency- and time-domain results are presented. With frequency-domain analysis the profound data for the standard assessment of structures, concerning seakeeping behaviour, operational limitations and fatigue are obtained. In addition, time-domain analysis in real rogue waves gives indispensable data on extremes, i.e. motions and structural forces.
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Leira, Bernt J. "Combination of Multiple Extreme Bending Moment Components." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83528.

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A procedure for estimating the combined load effect for processes with different zero-crossing periods is described. The procedure is illustrated by application to the combination of wave-induced bending moments. The basic formulations related to the distribution of maxima and extremes for a scalar Gaussian process are first reviewed. Subsequently, an outline of the procedure for multi-component processes is given. The developed formulation is then applied for analysis of the combined bending moment load effect. Two cases of such combinations are addressed (i) A case with widely different velocity variances (ii) A case involving a non-linear combination of the bending moments. A geometric approach to the interpretation and derivation of associated load effect combination factors is also demonstrated.
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Ganesan Thirunaavukarasu, Shivaji, Debabrata Sen, and Yogendra Parihar. "Steep Wave Effects on Wave Induced Vertical Bending Moment Using a 3D Numerical Wave Tank." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61161.

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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.
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7

Peng, Sheng, Pandeli Temarel, S. S. Bennett, Weiguo Wu, Zhengguo Liu, and Yiwen Wang. "Symmetric Response of a Hydroelastic Scaled Container Ship Model in Regular and Irregular Waves." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23860.

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Wave-induced vibrations, such as whipping and springing, of container carriers have been attracting much attention because of their effects on hull-girder bending moments and fatigue damage. An investigation has been carried out comparing experimental measurements and numerical predictions of symmetric wave-induced loads (i.e. vertical bending moment) of the latest River-sea link container ship design, LPP = 130 m. The dual mission characteristics, namely rivers and open seas, make this type of ship an extremely interesting type of container carrier, particularly in terms of springing and whipping. A backbone beam segmented model is used in the experiments with the focus on springing- and whipping-induced vertical bending moments, for the model travelling at Fn = 0.21 in regular and long-crested irregular head waves, of 2.5m full-scale height or significant wave height. In addition higher order (harmonics) vertical bending moments (VBM) are also extracted from the experiments. The measurements are taken at amidships and the fore and aft quarters. Numerical predictions, for both the full-scale vessel and segmented model, are obtained using the two-dimensional linear hydroelasticity theories, where the hull structure is idealized as a non-uniform beam and the fluid actions evaluated using strip theory. The measured model test results, in relatively moderate conditions based on a particular area of operation for this low-draught vessel, indicate that nonlinear springing accounts for a significant portion of the total wave-induced bending moments in regular and, to an extent, irregular waves and slamming effects are small due to the operational area selected. The numerical predictions in regular waves show that linear hydroelasticity analysis can only predict similar trends in the variation of the VBM and the resonance peak. On the other hand, in long crested irregular waves the linear hydroelasticity analysis provides peak statistics that are commensurate with the measurements. The numerical predictions were obtained for two variants, having L = LPP and L = 0.9 LPP, the latter corresponding to the length of the backbone.
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Houtani, Hidetaka, Sadaoki Matsui, and Wataru Fujimoto. "Numerical Investigation of the Statistics of Vertical Bending Moments of Ships in Nonlinearly Evolving Irregular Waves." In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/omae2023-104733.

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Abstract This study investigated ship response statistics in waves evolving due to nonlinear quasi-resonant interactions. For that purpose, a nonlinear strip method, NMRIW-II (nonlinear motion in regular and irregular waves), has been extended such that nonlinear wave fields precomputed by the higher-order spectral method (HOSM) can be input. In the numerical simulation, the significant wave height and nonlinear order of the input irregular waves were varied to investigate the impact of wave nonlinearity on ship responses. Furthermore, a container ship and a wall-sided ship were used in numerical simulations to separate the nonlinearity influences attributed to the hull geometry and wave. The lengths, breadths, drafts, and water plane geometries were the same between these ships. The numerical results revealed that the body (hull-geometry) nonlinearity enhances the tail of the sagging moment peak probability distributions. Furthermore, an increase in large wave occurrence due to nonlinear quasi-resonant interaction was revealed to further enhances the tail of the sagging moment peak probability distributions.
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Parunov, J., and M. Corak. "Influence of Environmental and Operational Uncertainties on Vertical Wave Bending Moments of Containerships." In William Froude Conference: Advances in Theoretical and Applied Hydrodynamics - Past And Future. RINA, 2010. http://dx.doi.org/10.3940/rina.wfa.2010.11.

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10

Jia, Huirong, and Torgeir Moan. "Reliability Analysis of Oil Tankers With Collision Damage." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57102.

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This paper deals with reliability analysis of a damaged tanker conditioned upon collision damage and the damage scenarios following collision. A tanker in full load condition (FLC) and two damage sizes are considered. The ultimate strength of the damaged tanker is assessed by applying Smith’s method, and an interaction equation for vertical and horizontal bending moments (VBM and HBM) is established. The still-water bending moment is calculated by the hydrostatic code ShipShape and the 3D hydrodynamic code WASIM is employed to calculate the wave induced vertical and horizontal bending moments. Correlation between vertical and horizontal bending moments is also considered. An out-crossing rate method is adopted to estimate the failure probability for the vector load effect process, and Monte Carlo simulations are used to account for model uncertainties.
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