Jack-up platformunun deterministik titreşim analizi: et kalınlığının titreşim genlik ve rezonansına etkisi

Abstract

ÖZET Dinamik yüklere maruz kalan açık deniz yapılarının daya nıklılık analizi, yapının dizayn şekline bağlı olarak sta tik analiz ve dinamik analiz olmak üzere iki yolla yapıl maktadır (l). Hidrodinamik geçirgen açık deniz yapılarına gelen dalga nın analitik ifadesi lineer Airy teorisinden alınmıştır. Dalga nedeniyle oluşan atalet ve direnç kuvvetleri de Morison formülüyle biraraya getirilmiştir. Direnç kuvveti, dinamik analiz frekans bölgesinde yapılır ken lineerleştirilmiştir. Daha sonra yapının determinis tik ve stokastik konseptlerdeki davranışı incelenmiştir. Bu analizlere ait bilgisayar programları raysere ait bir örnek gözönüne alınarak denenmiş ve daha sonra Jack-Up platformuna uygulanmıştır. -vii-

THE DETERMINISTIC VIBRATION ANALYSE OF THE JACK-UP PLATFORMS : THE EFFECTS OF THE STRUCTURE THICKNESS ON THE AMPLITUDE AND RESONANCE OF VIBRATION SUMMARY The discovery of large deposits of oil and gas in deep - water regions has resulted in the construction of large production and drilling platforms, which often have to withstand severe environmental conditions in inhospital areas. It is important both the determine how far our present knowledge can be extrapolated in order to analyse deep - water structures, and to understand the most up-to-date methods of analysis, which can often produce better es - timates of the structural response [2]. The Offshore structures are affected by various environ mental effects than over other structures (Figure 1). These are the own weight, working loads, snow and ice because of the offshore constructions; and waves, maneuver ing forces, flows, ice, covered with moss, the gradient of temperature because of sea; and wind because of air; and the foundation deformation and the earthquake because of the construction base. These effects then need to be transformed into loads acting on tfte structures, and in this way new sources of uncertainty are introduced. The dynamic response of structures which are exposed to dyna mic loads can nowadays be very accurately determined, for linear systems, by using computational techniques. The main uncertainties occur when trying to estimate the soil properties the fatiques life of the structure. The structural response depends on both the magnitude, types and direction of loads, and the mass, stiffness, and damping of the system properties of the construction. The dynamic loads can be divided into three groups: the periodic loads, the stroke leads and the random loads. The response of offshore structures to wave loading is of fundamental importance in the analysis. Waves account for most of the structural loading and, because they are -viii-the own weight, working loads, snow, ice wind maneuvering forces 2y>5 temperature gradient foundation deformation Figure 1. Loads acting on an offshore structure. time dependent, produce dynamic effects tending to in crease the stresses and damage the long-term behaviour of the system. Wave forecasting techniques allow us to determine the sea states that will occur during the life of the struc ture. The long-term statistics are calculated by the knowledge of all the sea states. These are usually more important, since the maximum stresses occur only during a very short period in the life of the platform. From the wave scatter diagram one can pass to either a wave height exceedance diagram or several wave spectral den s i ty curve s. In the spectral approach, exceedance diagrams are not used. Instead each of the sea states shown in the wave scatter diagram is transformed into a spectrum. These spectra are then applied to stud` the response of the -ix-system in a probabilistic manner. The spectra are usually appliable to fully developed seas, although some of them are not. The waves are caused the most of loads affecting offshore structures. Waves that are uniform and break down by construction can be represented analitically according to different theories such as Airy* s, Stokes' and Gerstner's theories. But there are some difficulties in the finding wave forces. The both of them are slamming and slapping on the structural members. In addition, the waves and the construction are interacted one another : the potential of the incident waves is broken down with the energy ra diation resulting from reflecting waves. This event is known as the diffraction. From the offshore structure designer's point of view it is important to differentiate between the various force regimes resulting from the interaction between the st ructure and the waves. They can be summarised as follows: for d/X>l, (d = diameter or characteristic dimension and A = wavelength), conditions approximate to pure reflec tion? for d// > 0.2, diffraction is increasingly important; for d// > 0.2, diffraction is negligible. The determination of the forces resulting in any of these regimes can be formulated in two basic steps : first, computation of the kinematic flow field starting with the water elevations, using a wave theory j second determina tion of hydrodynamic forces applying Morison's equation or diffraction theory. Diffraction is neglected only for the hydrodynamic perme able construction. The inertia forces due to waves can always be calculated by a wave theory. The drag forces due to non- linear friction is calculate by ampirical formula. These two forces are combined with a important relation as known Morison equation. With help this formula, q forces coming per unit length of the slender, vertical, and cylindrical construction element is calculated like below. q (z,t) = q (z,t)w + q (z,t)D (1) -x-The inertia force and the drag force on the body per unit length can be written, q (z,t)M= y.A.ii0+ Ca.y.A. (u0-U) (2) and qMD- l/2.CD.j».D.û0-û. (ü0-ü) (3) respectively, where A cross-sectional area, D straight dimension (diameter) of the construction to the direction of coming waves, Ca hydrodynamic mass coefficient, C_ drag coefficient, û and ü are the horizontal velocity and accelaration of the water particles, û and ü are the construction's. oA shows the overflowing water mass from the construction element, Ca.oA is defined the hydrodyna mic water mass (or added mass). C and C_ are changeable dimensionless magnitudes rapidly. These magnitudes de pend on Reynolds number, the surface roughness, the cross- sectional form and the vibration foam of the structure. When the movement of the cylinders is to be taken into consideration, equation (1) is written as follows : q(z,t) = 5>.A.ü0 + Ca.j>.A. (ü0 - ü) + 7cD-?-D-k ` *!. Vû> (4) The first term is the inertial term representing the distortion of the streamlines in the fluid, and is con - sidered to be independent of the accelaration of the st ructure. The second term is the added or hydrodynamic mass term, and it depends on the motion of the member. The drag term is the only non-linear term in the above expression. In order to linearise it one-can assume that the velecities are distributed as a Gaussian process with zero mean. This gives q(z,t) = 5>.A.ü0+ Ca.j).A. (ü0-ü) + ch(û0-ü) (5) where & the hydrodynamic damping constant. This constant can be given two ways in deterministic concept and in probabilistic concept as follows -xx-h 3.TT ° ch = //§7ur.b.6r (z) (6) respectively, b is the drag constant per unit length and it equals CD.o.D/2.v (z) shows the amplitude of the rela tive velocity (u » û0~u). ^r is the standart deviation of the relative velocity. The simple linear Airy wave theory will be apply to cal culate the velocities and accelarations in Morison's equa tion. When the further sensitive wave theories are used, the differences between results using Airy' s theory and other theories are remained very small in the mean time. In the compact structures, the energy radiation of them are paid attention by diffraction theory. The methods of analysis are probably the more reliable part of the design process, owing to the many recent advances in computational mechanics. The most important of these possibilities are summarised in Figure 2. Methods of analysis Static analysis Dynamic analysis Frequency domain Tine domain Figure 2 Methods of analysis -xii-The first option is to use a static analysis. The loading and the structure are designed that the dynamic response of structure can not be affected by the forces of mass and damping at all. In that case, the equivalent static loads can be taken instead of dynamic loads. Then, the quasistatic analyse can be used. It is important to point out that even structures analysed statically will eventually require some dynamic consideration to analyse the effect of fatigue. If the inertia forces are comparatively important one uses dynamic analysis, and two possibilities exist. One can work in the frequency demain, in which case transient effects are neglected and one concentrates on steady-state solutions. In this study, the dynamic analyse is determined in the this domain. The method assumes a linear system. The other possibility is to analyse the system in the time domain by some step technique, in which case transient effects may be considered as well as non-linearities. Frequency domain methods can be divided into deterministic and probabilistic methods. Deterministic analysis applies a series of design waves and uses the long-term exceedance diagram for fatique. Spectral curves of wave height are the information needed to start probabilistic analysis (Figure 3). They are con verted into spectral estimates of forces by applying a transfer function, which is simply the square of the re sulting wave force per unit wave height. The new spectrum is then mult ip led by the ordinates of the structural trans fer function. This transfer function is the square of the dynamic response per unit wave force. The final response curve then can be integrated to produce the variance 6`2, for displacements or stresses. The drawback is that one analysis is required for each sea state in order to study cumulative damage. The main uncertainties in the analysis lie in the estima tion of the fatigue life of the structure and the soil - structure interaction effects. -XXil-Waive scatter diagr Ves Diffraction theory Morison equation 1 Force spectrum > Structural transfer function Di spl acement response Stress response Yes No Cumulative damage Maxima Fatigue curves Figure 3 Probabilistic analysis -xiv-