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Bending Moments and Shear Forces in Ships Sailing in Irregular Waves
Abstract
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.
... Where this method of calculating internal forces is primarily required for ships with a low block coefficient value, i.e., for container ships. Jensen and Pedersen (Jensen and Pedersen, 1981) noted that there are large nonlinearities of vertical shear forces and bending moments in the case of container ships. Soares et al. (Soares, Fonseca & Pascoal, 2004) noted that for ships with a small block coefficient (i.e., container ship), the wave induced structural loads are highly non-linear. ...
... However, for vessels with a high block coefficient value, such as bulk carriers and tankers, the use of a linear model is sufficiently accurate and effective. Jensen and Pedersen (Jensen & Pedersen, 1981) noted that the effects of wave non-linearities induced a bending moment and shear force in the case of a VLCC carrier sailing were small in a moderate sea. ...
... The Ikeda et al. (Ikeda, Himeno & Tanaka, 1978) empirical method was used for the estimation of additional roll damping parts. Wave loads were calculated by the use of the diffraction method detail presented in (Jensen & Pedersen, 1981). ...
Dear Readers,
We are pleased to present this year’s first issue (No. 65) of the Scientific Journals of the Maritime University of Szczecin. This year will bring many new challenges, also for the journal, where we continually focus on improved quality. We would like to thank the authors, reviewers and readers for their contribution to our journal. I hope that we will continue to develop this path together.
This issue presents the research results and authors’ views in seven articles organized into three thematic sections: Civil Engineering and Transport, Mechanical Engineering, and Economics, Management and Quality Science.
The Civil Engineering and Transport section features two articles. The first article presents an analysis of internal forces and roll motion during a nodule loading simulation for a ship at sea. The study carried out a full assessment of a ship’s behaviour during loading, which took into account wave height and period around the Clarion–Clipperton Zone by the use of an operational efficiency index. The second article addresses the International Convention for the Safety of Life at Sea (SOLAS). The Convention aims to improve the safety of life at sea by laying down rules and regulations for the construction of ships and providing models for the documents created.
The Mechanical Engineering section consists of three articles. In the first article, the authors analysed the special configuration of a multi-role moving-column machining centre by the finite element method. In the second article, a CFD-based numerical approach was developed and applied to a trimaran hull in the presence of regular and irregular waves. According to the authors, the proposed CFD method reduces the simulation time and calculation resources needed to determine a ship’s motion. The third article presents the results of the testing of long-distance heat transfer surfaces in marine diesel engines, including elliptical and flat-oval tubes. The study used mathematical models that involved equations from conservation of energy, equations of motion, continuity and state, where the RSM of turbulence was also used to complete the equation system.
The Economics, Management and Quality Science section includes two articles. The first article analyses the factors affecting the performance of VTS operators. Its general conclusion is that the effective work of VTS operators, combined with a specific maritime environment and vessel traffic management support system, are the key determinants for ensuring the reliability and safety of the entire system. The second article’s authors wanted to see if a multi-criteria analysis was appropriate for the evaluation and implementation of energy-efficient mobility in seaports. The multi-criteria model for the selection of the most appropriate energy-efficient mobility solution was tested for two Croatian private marinas.
The articles featured in this issue reflect the authors’ theoretical and practical inspirations, contributing to important and state-of-the-art scientific research. We believe that these findings will become the basis for further reflection, discussion, and broader research.
dr hab. Izabela Dembińska, Associate Professor
Editor-In-Chief
Szczecin, 31.03.2021
... the early fluid analysis method for ships, and beam theory. The second-order nonlinear strip theory was applied to the existing method to solve nonlinear problems with large ranges of motion and deformation (Jensen and Pedersen, 1981). Attempts were also made to solve three-dimensional hydroelastic analysis problems by applying the potential theory and the finite element method (Wu, 1984;Price and Wu, 1985;Bishop et al., 1986). ...
Studies on very large offshore structures are increasing owing to the development of deep sea, large-scale energy generation using ocean resources, and so on. The enlargement of offshore structures makes the hydroelastic effect and low natural frequency related responses important. Numerical analyses and model tests for hydroelastic and higher-order springing responses of fixed cylindrical structures are conducted in this study. The panel methods with and without the hydroelastic effect with shell elements, and the Morison analysis method with beam elements are applied. To observe the hydroelastic effect for structural strength, two structures are considered: bottom-fixed cylindrical structures with high and low bending stiffnesses, respectively. The surge motions at the top of the structure and bending stresses on the structure are observed under regular and irregular wave conditions. The regular wave conditions are generated considering the ratios of the cylindrical outer diameter to the wave lengths, and keeping the wave steepness constant. The model tests are performed in the three-dimensional ocean engineering basin in the KRISO (Korea Research Institute of Ships and Ocean Engineering). From the numerical and experimental results, in which the hydroelastic responses are only observed in the case of the structure with a low bending stiffness, it is confirmed that the hydroelastic responses are highly dependent on the structural stiffness. Additionally, the higher-order phenomenon on the specified wave condition is analyzed by observing the higher-order springing responses when the incident wave frequency or its multiples with the high wave height coincides with the natural frequency of the structure.
... These methods require model test verification. Jensen and Petersen (1981) noted that the effects of wave nonlinearity induced bending moments and shearing forces for a sailing VLCC carrier were small under moderate conditions at sea. For vessels with high block coefficient value, such as bulk carriers and tankers, linear models are sufficiently accurate and effective. ...
... To improve the structural design of ships subjected to wave induced loading Dr. Jensen and Prof. Pedersen developed a quadratic strip theory for ships with flexible hull girders, which can be applied in the frequency domain 11,13 . This procedure is well suited for short and long term probabilistic prediction of wave induced hogging and sagging bending moments and shear forces in ships with large bow flare, such as container vessels 32,52,80 . ...
... Dans ce cadre, Pedersen (1982) a montré l'importance de la prise en compte des sections ouvertes dans l'établissement des caractéristiques modales de structure du navire en vue de la modélisation de la torsion. Jensen et Pedersen (1981) proposent une formulation 2D non linéaire afin de prédire plus précisément la réponse de springing sur lesétats de mer modérés. Cette formulation s'appuie sur la précédente en y incluant les termes quadratiques liésà la houle non linéaire par une procédure de perturbation. ...
Avec l’accroissement de la taille des navires marchands de type porte-conteneurs, les interactions entre la réponse de tenue à la mer classique et la réponse structurelle sont de plus en plus présentes. Les fréquences propres de réponse structurelle de la poutre navire se rapprochent des fréquences de houle océaniques. La modélisation des interactions houle structure devient un enjeu clé dans les étapes de design par les architectes et de validation par les sociétés de classification. Dans ce contexte, on se propose de développer un nouvel outil d’interaction fluide-structure associant une modélisation RANSE de l’écoulement en différences finies sous ICARE-SWENSE, code développé conjointement par le LHEEA et la société HydrOcéan, et un modèle de poutre analytique, le toutdans le cadre d’une approche modale. Grâce à l’emploi d’une formulation simple pour le traitement de la structure, l’outil de couplage hydroélastique sur houle hérite des propriétés de tolérance aux grands pas de temps d’ICARE-SWENSE, tout en prenant en compte les effets hydrodynamiques non linéaires. Les résultats présentés sur des cas de barge en diffraction et en radiation suivant les modes de déformation élastique permettent de valider les premières étapes de la mise en place du couplage. Une attention particulière est portée sur les seuils d’apparition des non linéarités de l’écoulement et leur impact sur la réponse structurelle.Une première implémentation est proposée pour la résolution du modèle libre des modes élastiques. Des études paramétriques de résistance ajoutée sur houle régulière et bichromatique viennent compléter les travaux dans la perspective de futurs calculs sur houle irrégulière.
... During the process of towing a wind turbine unit, the wave conditions are not regular waves. In order to study the towing of the CBF under waves, it is also necessary to consider the irregularity of ocean waves [24]. According to irregular wave theory, an irregular wave surface can be seen as a superposition of many regular wave units, which have different amplitudes, propagation directions, frequencies, and phases, and all conform to the theory of micro-amplitude. ...
Offshore wind power is an important of source renewable energy. As a new technology, the one-step integrated transportation and installation technology of offshore wind power has broader application prospects. In order to ensure stability during the towing process, it is necessary to study the behavior of the wind turbine transportation structure. The numerical model of the specialized transportation vessel was set up by MOSES software. An analysis in the frequency domain and time domain was conducted considering the effects of draft, speed, and wave height on the towing stability of the wind turbine transportation vessel. The results show that the one-step integrated transportation method can ensure stability of the wind turbine during the towing process. Reducing draft, increasing speed, and increasing wave height will reduce the towing stability of the wind turbine. In the practical towing process, the combination of various adverse situations will be avoided.
p>Waves, winds and currents can cause specific environmental effects that a marine structure has to withstand. Amongst these, wave action is the fundamental source of load on the marine structure. In order to ensure safety, operability, economy and design-life duration of a marine structure, theoretical estimates of wave loads and structural response play an increasingly important role in the overall design process. The interaction between a structure and a fluid medium is of great concern in numerous engineering problems, e.g., slamming of ships in rough seas, vibration of water retaining structures under earthquake loading etc. All these dynamic problems include the interaction, which takes place between the structure and surrounding fluid. It is of practical importance to estimate the effect of the induced fluid loading on the dynamic state of the vibrating structure. If the vibration takes place in a relatively low-density fluid, such as air, in comparison with the structural material, in most situations, the loading will have a comparatively small influence on the vibration. However, when the vibrating structure is in contact with a fluid which has a comparable density, such as water, the fluid loading which depends on the structural surface motions will significantly alter the dynamic state of the structure from that of the in vacuo vibration. In other words, the equations of structural and fluid motions are inexorably linked. Therefore, development, improvement and application of numerical techniques for analyzing such an interaction become one of the most important activities of naval architecture researchers. The following document is about the interaction mentioned above and particularly studied on the slamming issue and its main characteristic, transient excitation and response. A dry analysis is presented on simple beams, idealized SWATH ship as a preamble to a future wet deck slamming analysis and plates (unstiffened and stiffened). As the basis of subsequent harmonic and transient analyses, modal characteristics of each system is studied and in conjunction with the results obtained from these, responses on frequency and time domain are calculated in this document. In the following part of the thesis beams and plates are analysed under transient excitation, since this is the basis for modelling the excitation and response induced by slamming. Results are produced and compared both using theoretically established convolution method and ANSYS (transient analysis with full and mode superposition methods). Realistic stiffened plates and their equivalent flat plates are also studied and analysed in the subsequent sections. Difficulties encountered during the structural modelling (finite element modelling) are briefly outlined, with particular emphasis to the importance of the selection of appropriate finite elements.</p
Springing and whipping play an important role in determining the fatigue damages of ultra-large container ships in waves, and it is widely acknowledged that the separation of the contributions of springing and whipping on fatigue damages is difficult. In this paper, the effects of springing and whipping on a targeted 21,000 TEU container ship are numerically investigated. The springing responses are calculated based on the linear 3D frequency domain hydroelasticity theory, while a 3D nonlinear time domain hydroelasticity formulation which couples the 3D hydrodynamic theory, 1D Timoshenko beam theory, 2D generalized Wagner method and 1D green water theory, is adopted to obtain the slamming-induced whipping response. Spectral analysis method is analyzed and compared with an indirect time domain method. Through investigating the characteristics of the accumulated fatigue damages with respect to the significant wave heights and characteristic wave periods of short-term sea states, the contributions from springing and whipping to the accumulated fatigue damages are generally separated for most short-term sea states. In addition, several short-term sea states are chosen to present detailed information on the extents to which springing and whipping increase the fatigue damages relative to the low-frequency structural responses counterpart.
This paper outlines the theoretical development and some validation of a quadratic strip theory method coupled to a global finite element model to predict the global structural response of the Korea Research Institute of Ships and Ocean Engineering (KRISO) hull geometry due to regular, head seas waves in the time-domain. The method attempts to capture some body-nonlinear effects of the dynamic problem due to time-varying underwater hull geometry by drawing a relationship between the coefficients, A33, B33, and C33 and the local draft, Ts. In addition, the hull girder is considered flexible and structural damping may be included. A segmented model test in head seas was also performed, and the linear and nonlinear numerical results are compared to the experimental data. It is found that the theory shows reasonably good agreement with the model test data, and that nonlinear effects account for a significant increase in predicted bending moment.
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