Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads
Abstract
:1. Introduction
2. Determination of Wave Loads with Nonlinear Morison Equation
3. Explicit Formulation of Dynamic Responses
3.1. Equation of Motion
3.2. Explicit Time-Domain Expressions of Structural Responses
4. Random Vibration Analysis with MCS Based on ETDM
4.1. Digital Simulation of Wave-Particle Velocities and Accelerations
4.2. ETDM-Based MCS
5. Numerical Example
5.1. Finite Element Model
5.2. Wave-Particle Velocities and Accelerations
5.3. Deterministic Time-History Analysis with ETDM
5.4. Random Vibration Analysis with ETDM-Based MCS
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Morison, J.R.; O’Brien, M.P.; Johnson, J.W.; Schaaf, S.A. The force exerted by surface waves on piles. J. Pet. Technol. 1950, 2, 149–154. [Google Scholar] [CrossRef]
- Det Norske Veritas. Environmental Conditions and Environmental Loads; DNV-RP-C205: Oslo, Norway, 2014. [Google Scholar]
- Boccotti, P.; Arena, F.; Fiamma, V.; Barbaro, G. Field experiment on random wave forces acting on vertical cylinders. Prob. Eng. Mech. 2012, 28, 39–51. [Google Scholar] [CrossRef]
- Boccotti, P.; Arena, F.; Fiamma, V.; Romolo, A. Two small-scale field experiments on the effectiveness of Morison’s equation. Ocean Eng. 2013, 57, 141–149. [Google Scholar] [CrossRef]
- Santo, H.; Taylor, P.H.; Williamson, C.H.K.; Choo, Y.S. The relative-velocity version of the Morison equation for obstacle arrays in combined steady, low and high frequency motion. J. Fluid Mech. 2018, 842, 188–214. [Google Scholar] [CrossRef]
- Santo, H.; Taylor, P.H.; Day, A.H.; Nixon, E.; Choo, Y.S. Current blockage and extreme forces on a jacket model in focused wave groups with current. J. Fluids Struct. 2018, 78, 24–35. [Google Scholar] [CrossRef] [Green Version]
- Taylor, R.E.; Rajagopalan, A. Load spectra for slender offshore structures in waves and currents. Earthq. Eng. Struct. Dyn. 2010, 11, 831–842. [Google Scholar] [CrossRef]
- Silva, L.S.P.D.; Cazzolato, B.S.; Sergiienko, N.Y.; Ding, B.; Morishita, H.M.; Pesce, C.P. Statistical linearization of the Morison’s equation applied to wave energy converters. J. Ocean Eng. Mar. Energy 2020, 6, 157–169. [Google Scholar] [CrossRef]
- Borgman, L.E. Random hydrodynamic forces on objects. Ann. Math. Stat. 1967, 38, 37–51. [Google Scholar] [CrossRef]
- Borgman, L.E. Spectral analysis of ocean wave forces on piling. J. Waterw. Harb. Div. 1967, 93, 129–156. [Google Scholar]
- Brouwers, J.J.H.; Verbeek, P.H.J. Expected fatigue damage and expected extreme response for Morison-type wave loading. Appl. Ocean Res. 1983, 5, 129–133. [Google Scholar] [CrossRef]
- Wolfram, J. On alternative approaches to linearization and Morison’s equation for wave forces. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 1999, 455, 2957–2974. [Google Scholar] [CrossRef]
- Su, C.; Xu, R. Random vibration analysis of structures by a time-domain explicit formulation method. Struct. Eng. Mech. 2014, 52, 239–260. [Google Scholar] [CrossRef]
- Su, C.; Huang, H.; Ma, H.T. Fast equivalent linearization method for nonlinear structures under nonstationary random excitations. J. Eng. Mech. 2016, 142, 4016049. [Google Scholar] [CrossRef]
- Su, C.; Li, B.M.; Chen, T.C.; Dai, X. Stochastic optimal design of nonlinear viscous dampers for large-scale structures subjected to non-stationary seismic excitations based on dimension-reduced explicit method. Eng. Struct. 2018, 175, 217–230. [Google Scholar] [CrossRef]
- Su, C.; Liu, X.L.; Li, B.M.; Huang, Z. Inelastic response analysis of bridges subjected to non-stationary seismic excitations by efficient MCS based on explicit time-domain method. Nonlinear Dyn. 2018, 94, 2097–2114. [Google Scholar] [CrossRef]
- Shinozuka, M. Monte-Carlo solution of structural dynamics. Comput. Struct. 1972, 2, 855–874. [Google Scholar] [CrossRef]
- Santo, H.; Taylor, P.H.; Day, A.H.; Nixon, E.; Choo, Y.S. Blockage and relative velocity Morison forces on a dynamically-responding jacket in large waves and current. J. Fluids Struct. 2018, 81, 161–178. [Google Scholar] [CrossRef] [Green Version]
- Borgman, L.E. Computation of the ocean-wave forces on inclined cylinders. Trans. Am. Geophys. Union 1958, 39, 885–888. [Google Scholar] [CrossRef]
- Charkrabarti, S.K. Laboratory generated waves and wave theories. J. Waterw. Port. Coast. Ocean Eng. Div. 1980, 106, 349–368. [Google Scholar]
- Su, C.; Han, D.J.; Yan, Q.S.; Au, F.T.K.; Tham, L.G.; Lee, P.K.K.; Lam, K.M.; Wong, K.Y. Wind-induced vibration analysis of the Hong Kong Ting Kau Bridge. Proc. Inst. Civ. Eng.-Struct. Build. 2003, 156, 263–272. [Google Scholar] [CrossRef]
- Wang, D.J. Hydrodynamic Behavior of Large Moored Offshore Structures during Adverse Weather Conditions. Ph.D. Thesis, Hong Kong Polytechnic, Hong Kong, China, 1993. [Google Scholar]
- American Bureau of Shipping. Guidance Notes on Dynamic Analysis Procedure for Self-Elevating Drilling Units; American Bureau of Shipping: Houston, TX, USA, 2004. [Google Scholar]
- Wheeler, J.D. Method for calculating forces produced by irregular waves. J. Pet. Technol. 1970, 22, 359–367. [Google Scholar] [CrossRef]
Method | Elapsed Time (s) |
---|---|
ETDM-based MCS | 200 + 100 = 300 |
Traditional MCS | 106 |
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Lin, W.; Su, C.; Tang, Y. Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads. J. Mar. Sci. Eng. 2020, 8, 1001. https://doi.org/10.3390/jmse8121001
Lin W, Su C, Tang Y. Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads. Journal of Marine Science and Engineering. 2020; 8(12):1001. https://doi.org/10.3390/jmse8121001
Chicago/Turabian StyleLin, Wei, Cheng Su, and Youhong Tang. 2020. "Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads" Journal of Marine Science and Engineering 8, no. 12: 1001. https://doi.org/10.3390/jmse8121001
APA StyleLin, W., Su, C., & Tang, Y. (2020). Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads. Journal of Marine Science and Engineering, 8(12), 1001. https://doi.org/10.3390/jmse8121001