ABSTRACT Floating Production Storage and Offloading (FPSO) vessels for offshore operations use a Dynamic Positioning system (DP), which includes a controller to correct the position variation of the FPSO subject to internal and external disturbances. Most of these positioning systems use a classic Proportional Integral Derivative controllers (PID) and their deferent variants, where the control law is determined adjusting three control gains: proportional, integral and derivative, usually heuristic techniques are employed to determine the control gains. In this study we propose a theoretical tuning procedure in order to determine the control gains in a simple way, analyzing the boundary conditions in the matrices of the FPSO dynamic model, as well as the relation they have with the control gains for the FPSO motion in an adjust domain. In order to guarantee the semi-global stability of the closed-loop system, a stability proof in the Lyapunov sense is carried out. The theoretical results were validated in numerical simulations using Matlab. These results show that the methodology presented in this work is highly satisfactory for the control gain selection in the trajectory tracking control problem for FPSO motion. INTRODUCTION A Floating Production, Storage and Offloading (FPSO) system is considered in this paper. In the last two decades FPSOs have been the dominant offshore platforms used in oil and gas fields. Fig. 1 shows the Ta'Kuntah FPSO, which was the first FPSO operated in the Cantarell Field in the Gulf of Mexico. A FPSO can be operated in deep water and sometimes must perform maneuvering movements and marine activities with other vessels as shown in Fig. 2 (Tamuri, 2009), these activities involve huge risks due to the environmental random forces presence, affecting the normal operation and sometimes causing severe accidents (Moan, 2002) and lack stability (Chen, 2008). In offshore basically there are two ways to maintain the FPSO position, the first is by Mooring Positioning (MP) and the second by Dynamic Positioning (DP) (Sorensen, 1996; Sorensen, 1997). In DP the principal advantage is the immediate positioning on a required set point, in other hand the MP systems are limited to operate about 500m (Veksler, 2016).

Abstract Many offshore platforms have been developed in the offshore fields in Indonesia since 1969. National authorities in Indonesia stated that the existing platforms required the performance of underwater inspection on a regular basis. However, underwater inspections are very costly. Hence, this paper proposed Risk-based Underwater Inspection (RBUI) analysis as a highly effective method of conducting underwater inspections. The analytical approach was adopted from the American Petroleum Institute Recommended Practice for Structural Integrity Management of Fixed Offshore Structures in which a mix of quantitative analysis and qualitative analysis methods were used. The analysis generated the Probability of Failure (PoF) and the Consequence of Failure (CoF) that were subsequently required to determine the risk level of a platform. Additionally, the exposure level was also categorized for each platform based on its consequence category and life safety aspects. The usage of a combination of risk levels and exposure categories resulted in different inspection intervals for each platform. In this study, only characteristic factors were used for the PoF calculation. The condition factors were accounted for in the anomaly treatment. Hence, the RBUI analysis for 14 fixed platforms in West Madura Offshore resulted in an inspection plan that accentuated safety, but also had a longer interval when compared with the previous time-based methods. Introduction The first offshore platform in Indonesia was built in 1969. Since then, there was a tremendous increase in the number of offshore platforms. Previously, based on Minister of Mining Regulations no. 05 /P/II/PERTAMBANGAN/1997 (1977), Indonesian authority necessitate regular inspections of all oil and gas offshore platforms in which minor, major, and complete inspections require annual, biennial, and four-year inspection periods, respectively. The decline in oil prices since 2014 has forced most oil companies to cut costs. Indonesian companies are not an exception to this matter. The implementation of the risk-based underwater inspection (RBUI) is an alternative to traditional cost cutting methods in underwater inspections. Therefore, a new regulation recommends instead of the conventional time-based method, the inspection should be performed by a risk-based method that considers the risk level of the offshore platforms.

ABSTRACT: A large number of offshore wind farms with fixed foundation have been built in Europe with the relatively state-in-art techniques. Much of the offshore wind source potential in United States, China and other counties is available in the water depth more than 50 meters, where floating offshore wind turbine shows their economic potential. Comparing with the onshore system, the offshore wind turbines sustain more complicated environment conditions with stochastic wind and wave. The floating offshore wind turbine (OWT) is still in their early stage. As a whole system, OWT is designed and analyzed using simulation tools capable of predicting the coupled wind-inflow, aerodynamic (aero), control system (servo), and structural-dynamic (elastic), incident waves, sea current, hydrodynamics (hydro), and foundation dynamics of the support structure in a coupled simulation environment. The so called aero-hydro-servo-elastic modeling is needed. In this work, the three-blade 5MW upwind wind turbine, which is the basic model under IEA Annex 23 Subtask 2 Offshore Code Comparison Collaboration (OC3) project, is supported by an OC3- Hywind spar buoy platform. The platform is connected by three mooring lines to the seabed. Coupled aero-hydro-servo-elastic model with full flexible components including the platform, blades, tower and drivetrain is used in the simulation by the open source code. Several primary design load cases with different wave and wind condition are investigated. The natural frequency, damping ratio, the statistic and frequency domain responses of the system are included. INTRODUCTION With the development of the industry, energy is becoming one of top 10 problems for the humanity in next 50 years. To release the dependence on coal, oil and other traditional energy resources with green house gas emission, people are paying more attention to new and renewable energy. Wind energy has developed very fast during last 30 years.

ABSTRACT: In this paper, shipyard's ship shifting and berthing job scheduling is analyzed and researched, so it provides the ideas of solution for the problem model. On this basis, using the related mathematical knowledge and modeling techniques, is built up the shifting job scheduling arrangements of varying stages of complex dynamic programming model. Finally use the bellman algebra theory and the mathematical knowledge to solve the model. INTRODUCTION In the ship-building and ship-repairing yard (especially in a repairing yard), there are two basic hardware resources: dock and pier. How to scientifically use the dock and pier will directly affect the total production value and economic performance benefit of shipyard, because amount of the dock and pier determine how many ships the shipyard can carry on, in other words, when the number of the dock and pier are determined, how to efficiently use and dispatch the dock and pier will affect the production control of repairing ship at dockyard. However, a large and fussy number of shifting and berthing jobs will consume a large amount of resource of the shipyard, and it will make some even all of the consequent production be interrupted during ship shifting and berthing, and the production efficiency will be greatly reduced too. If we can optimize the sequence of the shifting and berthing, it will be a great benefit due to improving the productivity of the shipyard. The topic of this paper is focus on the research of the shifting and berthing job scheduling. Throughout a large amount of information which has been published, there are some research about the berth allocation problem, but most of those are focus on the port scheduling (especially on the container port) (Imai, A, 2001). It is no direct research and discussion for the yard's shifting and berthing.

ABSTRACT: A fully coupled aero-elastic simulation technology is developed with enough sophistication to have the features required to perform loads analyses for a variety of wind turbine configurations. Blade and tower are modeled multiple rigid bodies which are connected beam elements to represent a flexibility for their bending and torsional behaviors. AeroDyn which is developed by NREL are chosen for aerodynamic analysis. This is a popular and open code and needs hub-height wind data, full field turbulent wind data and airfoil data to calculate an aerodynamic force. DAFUL, which is a commercial multi-body and structure dynamics analysis tool, is used for multi-body dynamics analysis considering a flexibility of the blade and tower. The interface to perform coupled analysis between these two softwares is developed with a user-subroutine of vector force in DAFUL. Analysis results of a sample model to verify This proposed simulation technology is applied to the analysis of a sample model for verification of the developed program. INTRODUCTION When there are no obstacles, the wind has fast and consistent speed. That wind is very useful for wind turbine. A sea provides the good wind and proper environment. A wind power generation can be classified into two groups, onshore wind turbines and offshore wind turbines, and offshore wind turbines can be sorted by the fixed type and the floating type wind turbines. Fixed type wind turbine systems are set up at relatively low depth of water near shore but floating type wind turbines are to be set up at more deep sea. The tower of the fixed type wind turbine is fixed on the ocean floor like onshore type, but the tower of a floating offshore wind turbine is to be fixed on the float and the movement of the float is to be controlled by a mooring system.

ABSTRACT: This paper presents the effect of axial extensibility on threedimensional behavior of the tensioned pipes/risers. The large strain model formulation is developed by variational approach based on the elastica theory and the work-energy principle. The finite element method is used to find the nonlinear static configuration and large static strain. The natural frequencies and mode shapes are calculated by using the assumed-modes finite element method. The pipes/risers perform tensioned beam behavior when the bending stiffness dominates, and the stability of the pipes/risers reduces as the axial extensibility increases. On the contrary, the pipes/risers perform the tensioned cable behavior when the axial stiffness dominates, and the stability of the pipes/risers increases as the axial extensibility increases. INTRODUCTION The tensioned pipes/risers have been applied in various fields of engineering industry. From the literature, several research works such as Skop and Clark (1972), Fang and Lyon (1996), Lee and Mote (1997), Öz and Boyaci (2000), Öz (2001), and Öz and Evrensel (2002) have employed the small displacement theory to study the tensioned pipes behaviors. The previous investigations could predict precisely the linear behavior of the tensioned pipes, which are encountered in applications of the pipelines for conveying gas, oil, water, dangerous liquids in chemical plant, and cooling water in nuclear power plant. In offshore applications, the tensioned pipes/risers are used as a linkage between the well bore and the floating vessel. Because of extreme ocean environments, the tensioned pipes/risers applied in deep water are usually experiencing the large displacement and large deformation. Consequently, the linear behavior with small deformation which was reported in previous works may be no longer valid. This paper is motivated to investigate the behavior of three-dimensional tensioned pipes/risers with large displacement and large deformation.

ABSTRACT: In the paper, we present the application of IDA-PBC (Interconnection and Damping Assignment Passivity-Based Control) method to a marine riser control. In reentry operations, it is required to move the riser's lower end to a seabed manifold smoothly as soon as possible. In the motion control system design, the performance is expected to be better with a nonlinear control method because the dynamics of a riser is strongly influenced by the nonlinear effect such as hydrodynamic forces. In the paper, a nonlinear controller for a simplified riser model is designed using passivity-based control method, and the advantage of the control method is shown through numerical simulations. INTRODUCTION Marine risers are widely used for the offshore oil drilling and production. It is also expected to play important roles in the other ocean activities such as scientific investigations. In the case of extremely bad weather, such as typhoon, the vessel holding a marine riser must detach its lower end from a seabed manifold, leave for a safer sea, and return to the original position when whether serves. Then, reentry operation is necessary to connect the lower end of a riser to a seabed manifold. Although a riser is made of rigid material and its diameter is tens of centimeters, it has characteristics as a flexible structure due to the long length up to thousands meters. Moreover hydrodynamic forces work on a marine riser, so its dynamics becomes very complex and the prediction of motion is difficult. Human operation of reentry might spend half a day because of the difficulty of predicting the behavior. Therefore it is strongly desired to develop a control system to support such a reentry operation. Pioneering works in Japan on the reentry control based in LQG control theory were done by Suzuki, H. et al (1993,1995,1997).

ABSTRACT: This paper presents a numerical and field experimental modal analysis on a real offshore platform in Bohai Bay, China. This platform is a steel jacket offshore platform with vertical piles. The field testing under wave-induced force and wind force etc. was conducted, in order to obtain the dynamic parameters of the structure, including the frequencies of the jacket platform, as well as the corresponding damping ratios and mode shapes. The Natural Excitation technology (NExT) combined with Eigensystem Realization Algorithm (ERA) and the peak picking (PP) method in frequency domain are carried out for modal parameter identification under operational conditions. The threedimensional finite element model (FEM) is constructed by ANSYS and an analytical modal analysis is performed to generate modal parameters. The analytical results were compared with experimental results. A good correlation was achieved between the finite element and ambient vibration test results. It is further demonstrated that the numerical and experimental modal analysis provide a comprehensive study on the dynamic properties of the jacket platform. According to the analysis results, the modal parameters identification under ambient excitation can calibrate finite element model of the jacket platform structures, or can be used for the structural health monitoring system. INTRODUCTION The technology of experimental modal analysis has been used extensively in mechanical engineering, civil engineering for the last decades. In the classical modal parameters identification approach, the modal parameters are found by fitting a model to the so-called Frequency Response Function (FRF), a function relating input loading and output response. In fact, large civil engineering structures such as offshore platform, bridges, high-rise buildings suffer various kinds of loading, in many cases, the loading of large structures are not easily measured under operational condition. On the other hand, these structures are difficult to excite artificially.

ABSTRACT: A method of multi-dimensional variable structure system synthesis for the control of autonomous underwater vehicle spatial motion is developed. The velocity controller based on the sliding mode properties is synthesised in order to compensate the arbitrary variations of control object parameters and dynamical coupling between the vehicle degrees of mobility. A special nonlinear correcting device is offered for the underwater vehicle position control. This device allows to compensate the kinematic correlations between its degrees of mobility. The efficiency of synthesised control system is confirmed by numerical simulation results. INTRODUCTION Recently the development of underwater robotics is one of priority directions in the field of World ocean research. Requirements to autonomous underwater vehicles (AUV) control systems are increased in accordance with the complications of the tasks solved by these objects. So, the control system should provide precise AUV motion on a given spatial trajectory in order to execute composite manoeuvres in a working area. In other cases (at operation of manipulator, for example) the precise positioning of the underwater vehicle in a given point of space with compensation of all external perturbances is required. Numerous factors render essential influence on control system operation quality in the indicated modes, such as a prior uncertainty and significant changes of AUV inertia and hydrodynamic characteristics, a strong dynamical coupling and kinematic correlations between degrees of mobility and uncontrollable external perturbances of a viscous environment. All this factors connected with nonlinearity, nonstationarity and multiconnectivity of the underwater vehicle dynamic model. The traditional linear regulators do not provide given control quality in the given situation. Moreover system in whole frequently loses serviceability. It induces the investigators to access to principles and methods of the adaptive and robust control theory (Slotine and Li, 1991; Ramadorai and Tarn, 1993).

ABSTRACT: This paper presents a model of tensile fracture of concrete as heterogeneous material on the basis of the phenomenological approach. A criterion of destruction is the work for formation of a new fracture surface. The developed test method of experimental definition of tensile concrete characteristics is described. Results from the research of a fracture surface are presented. The obtained statistical data used at realization of the proposed model. The experimental research of the fracture process in a bent reinforced-concrete beam show, that it is possible to use the proposed criterion for forecasting work building constructions. INTRODUCTION Exploitation safety of sea hydraulic engineering reinforced concrete constructions is ensured by means of the regular monitoring of their surfaces. As regards the construction toughness, a crack in the concrete within a protection layer does not prevent normal exploitation of reinforced concrete constructions. At the same time, crack results in transition of process of concrete external corrosion in internal on the one hand, and, on the other hand, they are stress concentrators at the solution of a fatigue problem. Another very important problem is how to provide requirements to strength characteristics of constructional building materials for maintenance of reliability and safety of hydraulic engineering constructions during the whole exploitation period. The fracture mechanics enables the analysis of cracks origin and growth process in metal, ceramics and other materials. But application of theoretical and experimental fracture mechanics methods to an estimation of strength and durability of reinforced concrete constructions is hampered because of concrete structure singularities. A simple model for tensile fracture of concrete is proposed to include the heterogeneity of material on a macro scale. In this work we develop a new experimental method for finding concrete fracture characteristics. Then the characteristics are used in calculation of reinforced concrete construction.

ABSTRACT: In autonomous system, it is important to establish a control scheme that works with stability even near singularity con£gurations. In this report, an on-line trajectory control scheme that uses the manipulability measure as a distance criteria to avoid manipulator singularities is described for robotic manipulators with dynamic change of the task priority. First, given tasks are reconstructed using a geometric projection on the given index function. Then, the reconstructed tasks are analyzed in the framework of task priority based method. From this analysis, the proposed algorithm is shown to have the property that the task priority is assigned dynamically. Using this algorithm, we easily set the criteria of changing task priority and estimate the performance of the given index function. Considering the measure of manipulability as a index function, the approach is suitable for avoiding kinematic singularities for autonomous operation of, for example, underwater robot. Based on a real-time evaluation of the measure of manipulability, this method does not require a preliminary knowledge of the singular con£gurations. The result shows a good performance near the singular con£gurations, as shown by simulation results. And, the proposed algorithm is also validated by experimental results. INTRODUCTION In the repeating tasks or simple tasks, the desired task trajectory can be planned avoiding the singular points. And, it can be also overcome by mechanical design. In the manageable area, even though the manipulator are fallen into the singular points, the damage and emergency situation can be restored manually after stopping the task. However, in the uncontrollable area-space, underwater, and etc.–, we can not desire the manual labor and the tele-operation is also limited. So, the stability over singularity is the most important in those cases. Comparing with the manipulability of each 1-DOF task, it sets the task priorities.

ABSTRACT: As ocean resources are developed continuously in deeper ocean, floating offshore structures are frequently deployed. A typical example is the turret-moored FPSO (Floating Production Storage & Offloading). In such a case, the produced crude oil is normally transported by a fleet of shuttle tankers. For the sake of safety, the shuttle tanker during offloading must maintain its position within a certain limit under the action of external forces with the help of conventional mooring system and/or Dynamic Positioning (DP) system. As the water depth increases, the conventional mooring system becomes ineffective and thus the DP system is recommended. In this paper, two important problems are discussed in relation with the design of the DP system. One is to reduce the excessive thruster modulation caused by wave-induced motions and the other is the thrust allocation. The thruster modulation can be reduced by implementing a Kalman filter for the estimation of the low frequency state vector by removing the wave frequency motion from the measured variables. Herein a static algorithm for thrust allocation is suggested in order to improve the thruster performance. The DP controller is designed based on the optimal control theory and also the robust ∞ H control theory. In order to exemplify the process, the nonlinear behavior of shuttle tankers is simulated, where the hydrodynamic forces are calculated by the Green's function method, while the restoring force of mooring lines is approximated by the catenary equation in a quasi-static fashion. Based on numerical simulations, the capability of the designed DP controller and the thruster modulation are examined. But it is found that the control command contains a certain amount of wave frequency components. Thus a more effective filter needs to be developed to improve the performance of the DP system.

ABATRACT: In this paper we propose a projection based observer that can be used to estimate state vectors such as position and velocity for its motion control using non-uniform interval multi-sensor outputs. The output measurement we will use in estimating the state is a series of known multi-sensor asynchronous outputs. The idea for the proposed projection based observer is that each measurement output give us a piece of information which we can use to project the state vector onto the null space of C (output matrix) in order to reduce the error of state estimation. We will explain how to construct the projection operator in a Hilbert space and show the noise rejection of this algorithm by using Lyapunov method. The applicability of the proposed based observer to SAUV (semi-Autonomous Underwater Vehicles) navigation system is demonstrated through computational analysis with theoretical data. Its comparison with traditional Kalman filtering is assessed for computer simulations of the KRISO SAUV and experiments of the FAU Ocean Voyager II Autonomous Underwater Vehicle. INTRODUCTION There are numerous applications where the usage of an Autonomous Underwater Vehicle is desired. Born from the military requirements for stand-off weapons, remote sensing, mine field mapping and clearance, and coupled with the rapid commercialization of microcomputer technology, it is now possible to foresee some civilian use for AUVs in ocean science, offshore operations, environmental monitoring and underwater inspection. One continuing issue is the precise navigation of such vehicles underwater. While differential GPS (DGPS) is widely used for survey ships and underwater vehicle while surfaced, the navigation problem underwater requires the fusion of data from sensors such as Doppler sonar in a ground locked mode, compass data (a three axis magnetometer), acoustic systems like a SSBL and low cost inertial units.

ABSTRACT: The safety assessment of existing platform is a complicated decision process, which depends upon many factors of uncertainty. The fuzzy Analytic Hierarchy Process Method (FAHP) Is presented in this paper for modeling and solving the problem. Detail information are given and the development is based on the fuzzy mathematics and the artificial intelligence techniques as well. Practical example is shown for the purpose of illustrating the strategy. Further development of combination the "soft" science to the "hard" engineering can potentially be seen. INTRODUCTION The collapse of offshore jacket is caused by successive damage of its components, characterized by a series of damage stage. The jacket structure will collapse until the structural integrity finally vanishes, while the structure behaves as a kinematic mechanism and approaches to its ultimate state, on which founds the theoretical basis of safety assessment of the structure. Above mentioned situation is much realistic, on the one hand, it is becoming increasingly necessary to re-assess the adequacy of existing platforms in safety, which were built in 60s or 70s; on the other hand, since the cost of open sea engineering work is extremely expensive, one would rather avoid to take a capital repair for reinforcing a damaged platform instead of taking more precise estimation of the residual strength of the structure based on more reasonable safety assessment. The objective of safety assessment of to establish a criterion of whether the existing structure can safely perform its function. Along this line, the problem is how to realize this acceptable, though it is indeterministic or fuzzy, criterion for safety assessment The safety assessment is related to the quantitative evaluation of defaults or damages in individual member as well as to its influence to the carrying capacity of the structure.

ABSTRACT: This paper describes a structural system formed by hyperboloidal body of one sheet to be used as an offshore structures for natural resource development and ocean space utilization, how this system has useful and effective characteristics, and high potential. At first stage, the concept of how to use and applied fields at where this form can be used are mentioned. At the next stage, the validity for this concept is provided judging from fluid dynamics point of view. INTRODUCTION Offshore structures by hyperboloidal bodies of one sheet (H. P. body) can be expected to apply effectively to ocean space utilizations and natural resource developments. This structural analysis based on the interaction problems between fluid and structure must attract attention of not only structural designers but also researchers in the applied mechanics field. This paper is mentioned in the order of the following: Concepts and fields, how to use and at where H.P. bodies can be used. Study has been conducted on the hydrodynamic forces acting on H.P. bodies to test the appropriateness of these engineering aspects. Wave load characteristics induced by variation of the form and variation of water depths, assuming that the H.P. body is rigid. The hydrodynamic load characteristics by earthquakes in the same conditions as above. Added mass analysis which depends on vibrational mode shapes, and natural frequency analysis on coupled vibration problems assuming that the H.P. body is elastic. CONCEPTS HOW TO USE AND FIELDS WHERE THIS FORM CAN BE USED AT The following reasons can be pointed out in support of the concept. (1) Since H.P. forms widen toward the bottom and upper parts, they can ensure large interior space in the underwater portion and broad working decks in the air, and they can be used as structures with large scale span(Fig. 1).

ABSTRACT: Dynamic effects from the barge motion during davit lifting of offshore pipelines have been estimated through this study. In this paper a geometrically nonlinear finite cable element is presented to use in the modeling of davit lines. The cable element is derived directly from the compatibility equations and flexibility matrix of elastic catenary cable theory for the arbitrary plane loading and geometry. Also the generalized beam element derived on the basis of large deflection theory is used to model the pipeline and the elastic bi-linear spring element is utilized to model the seabed A computer program has been developed to perform the static or dynamic analysis of the offshore pipeline installation problems In the program Newmark- β method is used to obtain a time domain solution for the dynamic response of the pipeline and cable. Newton-Raphson" s iteration method is used to solve the nonlinear system of algebraic static or dynamic equations at each time step The barge motion can be directly considered as a support motion. Results from the static and dynamic analysis of a conventional davit lifting system of submarine pipeline by the computer program are summarized and presented. INTRODUCTION In the installation of a conventional riser system a davit system may be mobilized to lift submarine pipeline to which riser section is weld-connected on a barge above seawater level. In such a case an exact evaluation of dynamic effects on stresses of pipeline and cable tensions of davit lines by an wave induced barge motion can be so essential and the evaluated results so significant In the actual projects of the offshore pipeline installation only the margin of 25 or 30 percent of SMYS against the dynamic amplifications during davit lifting is generally given to the static stress level of pipe without any detailed dynamic analysis.

1. INTRODUCTION The growing confidence in the use of flexible risers for offshore production duties has encouraged designers towards the use of more ambitious geometres. The increasing range of applications have Imposed stricter requirements on the analysis software which need to be continuously updated to accommodate these new demands. Currently, many flexible user analysis packages are available which use different techniques for static and dynamic analysis using linear and non-linear methods. These are often validated through comparisons of simpler geometries with analytical solutions as well as with other programs. However, few programs have been compared with model test results or with full scale data. Comparisons with full scale data have so far been impossible due to the scarcity of such data. It has now become necessary to establish benchmark tests to compare different flexible user analysis software and to obtain an Idea of the reliability of different analysis techniques and sensitivity of their underlying formulations. This paper takes a step in this direction by reporting on the verification of a finite element based flexible user hydrodynamic analysis software named REFLEX. The package employs several non-linear static analysis methods as well as dynamic analyses using both the frequency domain and the time domain approaches. Simulations have been carried out using data from published works of numerous other investigators to provide a comparative assessment of different formulations. The verification study also uses comparisons of results of numerical analyses with both in house and independent model tests. 2. HISTORICAL OVERVIEW Static analysis of flexible risers has evolved through extension of the traditional catenary equations to allow for the effects of internal fluid weight, buoyancy and internal and external pressure forces. These equations allow computation of the static profile of a flexible riser under weight and pressure loads.

ABSTRACT: The free bending vibrations of fixed off shore cylindrical structures partially or totally submerged in water are discussed. This investigation is necessary for the dynamic response analysis of offshore structures under wave or earthquake loadings. A general solution of the small harmonic vibration problem of a vertical cylindrical pile submerged in an ideal fluid of an infinite layer is given. The solution for hydrodynamic pressures on cylindrical piles including the effect of surface waves was obtained. The equation of fluid-structure interaction was solved by the variational Bubnov-Galerkin method. The added mass distribution profiles along the height of the fixed cylindrical structure depending on different values of the ratios of diameter to height and water depth are presented. INTRODUCTION The offshore exploration and the increase in the depth of fixed offshore structures with one or several cylindrical supports have led to the activization of fluid - structure study. In numerous theoretical works the fluid models with Various assumptions and boundary conditions are discussed. The most important assumptions are those ones which take into account the compressibility, viscosity, surface waves influence on structure vibrations and adoption about an identity of natural modes in the fluid and vacuum. The fluid compressibility and pressibiity influence on vertical cylindrical pile vibration is considered by Sheinin (1966, 1967a), Shulman and Gordeyeva (1973), Chandrasekaran et al.(1970), Liaw and Chopra (1970). The influence of the viscosity was studied in the works of Sheinin (1967a), Sheinin and Kalicheva (1983). The problem of small offshore - structure vibrations in fluid is usually solved on the assumption that the waves induced by the vibration of a structure on the free surface may be ignored. In reference to single cylindrical structures this assumption was studied by Sakurai (1964) and Liaw (1974).