![ Nonlinearities
- Material
- Geometrical
- Hydrodynamic damping
Newton Rapson fixed load step method
Linear acceleration method
Rayleigh’s damping method
assume damping ratio r = r = 3%
[C]= [M]+ [K]
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𝑚∆ 𝑢𝑖 + 𝑐∆ 𝑢𝑖 + 𝑘𝑖∆𝑢𝑖 = ∆𝑃𝑖](https://image.slidesharecdn.com/reponsemitigationofoffshorefixedjacketplatform-170930072130/85/Reponse-mitigation-of-offshore-fixed-jacket-platform-7-320.jpg)
Reponse mitigation of offshore fixed jacket platform
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- 2. Fixed type offshore structures are very stiff( rigid) in nature . It has tendency to attract more forces But the forces are cyclic in nature with high magnitude. Response to wave loads is relatively less but if at all damage caused it will be very high. Expensive structural system 9/30/2017 2
- 3. Safety, serviceability and fatigue life of fixed offshore platforms. complex failure modes considered in addition to usual design requirements. special design considerations that are costly and time consuming to implement. Hydrodynamic Buoyant Mass Damper (HBMD) is introduced as an alternative 9/30/2017 3
- 4. employs both buoyancy and added mass in conjunction with the inertia force of its vibrating mass consists of a fully submerged vertical short closed cylinder. motion is restricted by a set of springs that attach it to the platform. 9/30/2017 4
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- 6. Linear wave theory (Airy’s theory) Stokes fifth order nonlinear wave theory Find velocity and acceleration fields given by Skjelbreia Morison equation to find wave force is, Added mass and drag coefficients are measured from Reynolds number and Kulegan Carpenter number. In this paper Ca = 1.6 and Cd =0.65 based on API recommendations 9/30/2017 6 F(t) = ρw V ü + Ca ρw V ( v̈ - ü ) + 1/2 Cd ρw A ( v̇ -u̇ ) 1 v̇-u̇ 1
- 7. Nonlinearities - Material - Geometrical - Hydrodynamic damping Newton Rapson fixed load step method Linear acceleration method Rayleigh’s damping method assume damping ratio r = r = 3% [C]= [M]+ [K] 9/30/2017 7 𝑚∆ 𝑢𝑖 + 𝑐∆ 𝑢𝑖 + 𝑘𝑖∆𝑢𝑖 = ∆𝑃𝑖
- 8. OJSAP (Offshore Jacket Structural Analysis Program ) It is based on stokes 5th order wave theory non linear dynamic equilibrium load increment method a)Modelling of jacket - four legged type platform - depth of water,(d) = 120 m - density of material, = 7849 kg/m3 9/30/2017 8
- 9. - young’s modulus, E = 2*1011 n/m2 - origin is fixed at centre of platform and at SWL - fixed to sea bed using pile strubs - Nodal masses each of 200 tonnes at +11m on top of each leg. - Remove bracings - Leg Do = 1.5 m ; t = 2 cm - Bracings Do = 1.0 m ; t = 2 cm - modelled as two node beam element9/30/2017 9
- 10. b) modelling of HBMD : - rigid closed cylinder fixed at -63.5 m - outer diameter, D = 10 m - thickness, t = 50 cm - connected with shear releases in wave direction and springs 9/30/2017 10
- 11. For different hydro dynamic conditions and for different spring stiffness values. Each model defined by a-b-c Example: model 1-5-1 1 shows wave parameters model 1 5-1 shows spring stiffness ks = 5*100+1*20 = 520 kN/m Model no Wave height (m) Wave period (sec) 1 4 6 2 6 7 3 8 8.5 9/30/2017 11
- 12. Displacement of deck in only x- direction is considered for response study Reduction in structural response is more influenced by HBMD’s buoyancy force, HBMD’s mass damper. To examine the performance of HBMD and arrive at optimal stiffness values for the spring connectors, i) Maximum displacement criterion (R1) ii) Total displacement criterion (R2) 9/30/2017 12
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- 16. COMSOL metaphysics software HBMD modelled as a moving boundary with its velocity extracted from analysis. 9/30/2017 16
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- 18. Model 3-2-2 is analysed again by considering hydrodynamic effects of HBMD New R1 and R2 factors are 0.577 and 0.409 Indicating that eddies formations can be beneficial to HBMD’s performance Shape and exact position of HBMD are important factors. 9/30/2017 18
- 19. A jacket type fixed platform is analysed for three types of wave loading along with HBMD. HBMD reduced the response to wave loading by doveloping reversal forces Buoyancy force and inertia force are the main reversal forces Eddy formation in the proximity of hbmd can reduce the response Suggesting wave harvesting devices instead of springs in controlling reposnse of platform 9/30/2017 19
- 20. M. Moharrami, M. Tootkaboni, 2014 Reducing response of offshore platforms to wave loads using hydrodynamic buoyant mass dampers, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300, USA. Chakrabarti SK. 1987 Hydrodynamics of offshore structures, Computational mechanics. Clough RW, Penzien J. 1975 Dynamics of structures, McGraw-Hill. API RP 2A, 2000. Recommended practice for planning, designing and constructing fixed offshore platforms. Washington: API Publishing Services. 9/30/2017 20
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