Skip to main content

Spectral Analysis of Offshore Structures Under Wave and Earthquake Loadings

  • Chapter
  • First Online:
Stochastic Analysis of Offshore Steel Structures

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

This chapter presents spectral analysis of offshore structures under wave and earthquake actions. It contains six sections. The first section explains problem description and gives some general information. In the second section, formulation of dynamic analysis of offshore structures in the frequency domain, transfer functions of wave, and earthquake forces are presented. The third section presents response transfer functions of wave and earthquake forces individually. Then, having presented hydrodynamic and inertia forces produced by earthquakes, response transfer functions of their combined effect are formulated. The fourth section explains calculation of response spectra of offshore structures under stochastic wave and earthquake forces. Then, the stochastic ground motion under earthquakes and its spectral representation are presented. It follows the calculation of transfer functions and response spectra of offshore structures under nonuniform earthquake ground motions. In section five, calculation of response statistical quantities is presented and. In section six, numerical demonstration of an example offshore structure is given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Biggs JM (1964) Introduction to structural dynamics. McGraw-Hill, New York

    Google Scholar 

  2. Bishop RED, Gladwell GML, Michaelson S (1965) The matrix analysis of vibration. Cambridge University Press, London

    MATH  Google Scholar 

  3. Meirovitch L (1967) Analytical methods in vibrations. Collier-McMillan, London

    MATH  Google Scholar 

  4. Clough RW, Penzien J (1993) Dynamics of structures, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  5. Chopra AK (2001) Dynamics of structures: theory and applications to earthquake engineering. Prentice-Hall, Upper Saddle River

    Google Scholar 

  6. Cheng FY (2001) Matrix analysis of structural dynamics: applications and earthquake engineering. Dekker, New-York

    Google Scholar 

  7. Humar JL (2002) Dynamics of structures, 2nd edn. Swets & Zeitlinger, Lisse

    MATH  Google Scholar 

  8. Wunderlich W, Pilkey WD (2003) Mechanics of structures: variational and computational methods. CRC, Boca Raton

    MATH  Google Scholar 

  9. Paz M, Leigh W (2004) Structural dynamics: theory and computation, 5th edn. Kluwer, Dordrecht

    Google Scholar 

  10. Craig RR, Kurdila AJ (2006) Fundamentals of structural dynamics. Wiley, Hoboken

    MATH  Google Scholar 

  11. Brebbia CA, Walker S (1979) Dynamic analysis of offshore structures. Butterworths, London

    Google Scholar 

  12. Barltrop NDP, Adams AJ (1991) Dynamics of fixed marine structures, 3rd edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  13. Han SM, Benaroya H (2002) Nonlinear and stochastic dynamics of compliant offshore structures. Kluwer, Dordrecht

    MATH  Google Scholar 

  14. Wilson JF (2003) Dynamics of offshore structures. Wiley, New-York

    Google Scholar 

  15. Soares D, Mansur WJ (2003) An efficient time/frequency domain algorithm for modal analysis of non-linear models discretized by the FEM. Comput Methods Appl Mech Eng 192:3731–3745

    Article  MATH  Google Scholar 

  16. Shinozuka M, Yun C, Vaicaitis R (1977) Dynamic analysis of fixed offshore structures subjected to wind generated waves. Mech Based Des Struct Mach 5(2):135–146

    Article  Google Scholar 

  17. Penzien J, Kaul MK, Berge B (1972) Stochastic response of offshore towers to random sea waves and strong motion earthquakes. Comput Struct 2:733–756

    Article  Google Scholar 

  18. Kirk CL (1985) Dynamic response of marine risers by single wave and spectral analysis methods. Appl Ocean Res 7(1):2–13

    Article  Google Scholar 

  19. Ahmad S, Datta TK (1989) Dynamic response of marine risers. Eng Struct 11:179–188

    Article  Google Scholar 

  20. Hartnett M (2000) The application of a spectral response model to fixed offshore structures. Comput Struct 78:355–364

    Article  Google Scholar 

  21. Bolt BA (1999) Earthquakes, 4th edn. Freeman, New-York

    Google Scholar 

  22. Manolis GD, Koliopoulos PK (2001) Stochastic structural dynamics in earthquake engineering. WIT Press, Southampton

    Google Scholar 

  23. Chen WF, Scawthorn C (2003) Earthquake engineering handbook. CRC, Boca Raton

    Google Scholar 

  24. Bolt BA (2003) Earthquakes. W.H. Freeman, New York

    Google Scholar 

  25. Bozorgnia Y, Bertero VV (2004) Earthquake engineering—from engineering seismology to performance-based engineering. CRC, Boca Raton

    Book  Google Scholar 

  26. Chen WF, Lui EM (2006) Earthquake engineering for structural design. CRC, Boca Raton

    Google Scholar 

  27. Sen TK (2009) Fundamentals of seismic loading on structures. Wiley, Chichester

    Book  Google Scholar 

  28. Chen WF, Lui EM (2006) Earthquake engineering for structural design. CRC, Boca Raton

    Google Scholar 

  29. Trifunac D, Brady AG (1975) A study on the duration of strong earthquake ground motion. Bull Seismol Soc Am 65(3):581–626

    Google Scholar 

  30. Zerva A (2009) Spatial variation of seismic ground motions-modeling and engineering applications. CRC, Boca Raton

    Book  Google Scholar 

  31. Laouami N, Labbe P (2001) Analytical approach for evaluation of the seismic ground motion coherency function. Soil Dyn Earthq Eng 21:727–733

    Article  Google Scholar 

  32. Nadim F, Vanmarcke EH, Gudmestad OT, Hetland S (1991) Influence of spatial variation of earthquake motion on response of gravity base platforms. Struct Saf 10:113–128

    Article  Google Scholar 

  33. Harichandran RS, Vanmarcke EH (1986) Stochastic variation of earthquake ground motion in space and time. J Eng Mech ASCE 112(2):154–174

    Article  Google Scholar 

  34. Ryu CS, Yun CB (1997) Non-stationary response analysis of offshore guyed tower subjected to earthquake loading. Eng Struct 19(1):63–70

    Article  Google Scholar 

  35. Gao W (2007) Random seismic response analysis of truss structures with uncertain parameters. Eng Struct 29:1487–1498

    Article  Google Scholar 

  36. Takewaki I (2004) Critical envelope functions for non-stationary random earthquake input. Comput Struct 82(20–21):1671–1683

    Article  Google Scholar 

  37. Shinozuka M, Deodatis G (1988) Stochastic process models for earthquake ground motion. Probab Eng Mech 3(3):114–123

    Article  Google Scholar 

  38. Karadeniz H (1999) Spectral analysis of offshore structures under combined wave and earthquake loadings. Proceedings of the 9th Internataional Offshore and Polar Engineering Conference, ISOPE, vol 4. pp 504–511

    Google Scholar 

  39. Richter CF (1935) An instrumental earthquake scale. Bull Seism Soc Am 25:1–32

    Google Scholar 

  40. Hwang H, Huo JR (1997) Attenuation relations of ground motion for rock and soil sites in eastern United States. Soil Dyn Earthq Eng 16:363–372

    Article  Google Scholar 

  41. Campbell KW (1981) Near-source attenuation of peak horizontal acceleration. Bull Seism Soc Am 71(6):2039–2070

    Google Scholar 

  42. Campbell KW, Bozorgnia Y (2003) Updated near-source ground motion (attenuation) relations for the horizontal and vertical components of peak ground acceleration and acceleration response spectra. Bull Seism Soc Am 93(1):314–331

    Article  Google Scholar 

  43. Campbell KW, Bozorgnia Y (2006) Campbell-Bozorgnia next generation attenuation (NGA) relations for PGA, PGV and Spectral acceleration: A progress report. Proceedings of the 8th US National Conference on Earthquake Engineering, Paper No.906

    Google Scholar 

  44. Oliveira CS, Hao H, Penzien J (1991) Ground motion modeling for multiple input structural analysis. Struct Saf 10:79–93

    Article  Google Scholar 

  45. Der Kiureghian A, Neuenhofer A (1992) Response spectrum method for multi-support seismic excitations. Earthq Eng Struct Dyn 21:713–740

    Article  Google Scholar 

  46. Heredia-Zavoni E, Vanmarcke EH (1994) Seismic random-vibration analysis of multi-support-structural systems. J Eng Mech 120:1107–1128

    Article  Google Scholar 

  47. Bai FL, Hao H, Li HN (2010) Seismic response of a steel trussed arch structure to spatially varying earthquake ground motions including site effect. Adv Struct Eng 13(6):1089–1103

    Article  Google Scholar 

  48. Chun-guang L, Hui-jun L (2010) A novel method to calculate the dynamic reliability of space structures subjected to multi-dimensional multi-support excitations. Int J Space Struct 25(1):25–34

    Article  Google Scholar 

  49. Zhang YH, Li QS, Lin JH, Williams FW (2009) Random vibration analysis of long-span structures subjected to spatially varying ground motions. Soil Dyn Earthq Eng 29:620–629

    Article  Google Scholar 

  50. Rambabu KV, Allam MM (2007) Response of an open-plane frame to multiple support horizontal seismic excitations with soil–structure interaction. J Sound Vib 299:388–396

    Article  Google Scholar 

  51. Boissieres HP, Vanmarcke EH (1995) Spatial correlation of earthquake ground motion: non-parametric estimation. Soil Dyn Earthq Eng 14:23–31

    Article  Google Scholar 

  52. Goda K, Hong HP (2008) Spatial correlation of peak ground motions and response spectra. Bull Seism Soc Am 98(1):354–365

    Article  Google Scholar 

  53. Luco JE, Wong HL (1986) Response of a rigid foundation to a spatially random ground motion. Earthq Eng Struct Dyn 14:891–908

    Article  Google Scholar 

  54. Harichandran RS (1991) Estimating the special variation of earthquake ground motion from dense array recordings. Struct Saf 10:219–233

    Article  Google Scholar 

  55. Zerva A (1994) On the spatial variation of seismic ground motions and its effects on lifelines. Eng Struct 16(7):534–546

    Article  Google Scholar 

  56. Zerva A (2002) Spatial variation of seismic ground motions: an overview. Appl Mech Rev 55(3):271–297

    Article  Google Scholar 

  57. Zembaty Z, Rutenberg A (2002) Spatial response spectra and site amplification effects. Eng Struct 24:1485–1496

    Article  Google Scholar 

  58. Cacciola P, Deodatis G (2011) A method for generating fully non-stationary and spectrum-compatible ground motion vector processes. Soil Dyn Earthq Eng 31:351–360

    Article  Google Scholar 

  59. Hong HP, Zhang Y, Goda K (2009) Effect of spatial correlation on estimated ground-motion prediction equations. Bull Seism Soc Am 99(2A):928–934

    Google Scholar 

  60. Price TE, Eberhard MO (1998) Effects of spatially varying ground motions on short bridges. J Struct Eng 124(8):948–955

    Article  Google Scholar 

  61. Dumanoglu AA, Soyluk K (2003) A stochastic analysis of long span structures subjected to spatially varying ground motions including the site-response effect. Eng Struct 25:1301–1310

    Article  Google Scholar 

  62. Bayraktar A, Bilici Y, Akkose M (2010) The effect of the spatially varying earthquake ground motion on random hydrodynamic pressures. Adv Struct Eng 13(6):1153–1165

    Article  Google Scholar 

  63. Sun J, Ye J, Cheng W, Zhang Q (2007) Application of the pseudo-excitation method with spatial coherence in random vibration analysis of long-span space structures. Adv Struct Eng 10:135–151

    Article  Google Scholar 

  64. Vanmarcke E (1983) Random fields: analysis and synthesis. MIT Press, Cambridge

    MATH  Google Scholar 

  65. Yeh CH, Wen YK (1990) Modeling of non-stationary ground motion and analysis of inelastic structural response. Struct Saf 8:281–298

    Article  Google Scholar 

  66. Priestley MB (1965) Evolutionary spectra and non-stationary processes. J Royal Stat Soc Ser B (Methodol) 27(2):204–237

    MathSciNet  MATH  Google Scholar 

  67. Priestley MB (1967) Power spectral analysis of non-stationary random processes. J. Sound Vib 6(I):86–97

    Google Scholar 

  68. Hammond JK (1968) On the response of single and multidegree of freedom systems to non-stationary random excitations. J Sound Vib 7(3):393–416

    Article  MATH  Google Scholar 

  69. Zhixin X (1988) On the stochastic modeling of earthquake strong ground motion. Nucl Eng Des 110:171–175

    Article  Google Scholar 

  70. Langley RS (1986) Structural response to non-stationary non-white stochastic ground motions. Earthq Eng Struct Dyn 14:909–924

    Article  Google Scholar 

  71. Der Kiureghian A, Crempien J (1989) An evolutionary model for earthquake ground motion. Struct Saf 6(1989):235–246

    Google Scholar 

  72. Iwan WD, Hou ZK (1989) Explicit solution for the response of simple systems subjected to non-stationary random excitation. Struct Saf 6:77–86

    Article  Google Scholar 

  73. Quek ST, Teo YP, Balendra T (1990) Non-stationary structural response with evaluationary spectra using seismological input model. Earthq Eng Struct Dyn 19:275–288

    Article  Google Scholar 

  74. Lin J, Zhang W, Williams FW (1994) Pseudo-excitation algorithm for non-stationary random seismic responses. Eng Struct 16(4):270–276

    Google Scholar 

  75. Deodatis G (1996) Non-stationary stochastic vector processes: seismic ground motion applications. Probab Eng Mech 11:149–168

    Article  Google Scholar 

  76. Conte JP, Peng BF (1997) Fully non-stationary analytical earthquake ground-motion model. J Eng Mech 123(1):15–24

    Article  Google Scholar 

  77. Fang T, Sun M (1997) A unified approach to two types of evolutionary random response problems in engineering. Arch Appl Mech 67:496–506

    Article  MATH  Google Scholar 

  78. Deodatis J, Shinozuka M (1988) Auto-regressive model for non-stationary stochastic processes. J Eng Mech 114(11):1995–2012

    Article  Google Scholar 

  79. Zembaty Z (1988) A note on non-stationary stochastic response and strong motion duration. Earthq Eng Struct Dyn 16:1189–1200

    Article  Google Scholar 

  80. Gupta ID, Trifunac MD (2000) A note on the nonstationarity of seismic response of structures. Eng Struct 22(11):1567–1577

    Article  Google Scholar 

  81. Rofooei FR, Mobarake A, Ahmadi G (2001) Generation of artificial earthquake records with a non-stationary Kanai–Tajimi model. Eng Struct 23:827–837

    Article  Google Scholar 

  82. Takewaki I (2001) Non-stationary random critical excitation for nonproportionally damped structural systems. Comput Methods Appl Mech Eng 190(31):3927–3943

    Article  MATH  Google Scholar 

  83. Gao W, Chen JJ, Ma J, Liang ZT (2004) Dynamic response analysis of stochastic frame structures under non-stationary random excitation. AIAA 42(9):1818–1822

    Article  Google Scholar 

  84. Xue SD, Wang S, Cao Z (2004) Multi-dimensional pseudo excitation method for non-stationary random seismic analysis of spatial lattice shells. Int J Space Struct 19(3):129–136

    Article  Google Scholar 

  85. Pousse G, Bonilla LF, Cotton F, Margerin L (2006) Non-stationary stochastic simulation of strong ground motion time histories including natural variability: application to the K-net Japanese Database. Bull Seism Soc Am 96(6):2103–2117

    Article  Google Scholar 

  86. Chaudhuri A, Chakraborty S (2006) Reliability of linear structures with parameter uncertainty under non-stationary earthquake. Struct Saf 28:231–246

    Article  Google Scholar 

  87. Rezaeian S, Der Kiureghian A (2008) A stochastic ground motion model with separable temporal and spectral nonstationarities. Earthq Eng Struct Dyn 37:1565–1584

    Article  Google Scholar 

  88. Bougioukou AP, Leros AP, Papakonstantinou V (2008) Modeling of non-stationary ground motion using the mean reverting stochastic process. Appl Math Modell 32:1912–1932

    Article  MathSciNet  MATH  Google Scholar 

  89. Cacciola P (2010) A stochastic approach for generating spectrum compatible fully non-stationary earthquakes. Comput Struct 88:889–901

    Article  Google Scholar 

  90. Jangid RS (2004) Response of SDOF system to non-stationary earthquake excitation. Earthq Eng Struct Dyn 33:1417–1428

    Article  Google Scholar 

  91. Senthilnathan A, Lutes LD (1991) Non-stationary maximum response statistics for linear structures. J Eng Mech ASCE 117(2):294–311

    Article  Google Scholar 

  92. Michaelov G, Sarkani S, Lutes LD (1999) Spectral characteristics of non-stationary random processes—a critical review. Struct Saf 21:223–244

    Article  Google Scholar 

  93. Michaelov G, Sarkani S, Lutes LD (1999) Spectral characteristics of non-stationary random processes - response of a simple oscillator. Struct Saf 21:245–267

    Article  Google Scholar 

  94. Sarkani S, Lutes LD, Michaelov G (2000) Extreme response of linear structures to non-stationary base excitation. Paper No.1293, Proceedings of the 12th WCEE, Auckland, New Zealand

    Google Scholar 

  95. Naprstek J, Fischer C (2000) Analysis of non-stationary response of structures due to seismic random processes of evolutionary type. Paper No.1110, Proceedings of the 12th. WCEE, Auckland, New Zealand

    Google Scholar 

  96. Fuentes M (2002) Spectral methods for non-stationary spatial processes. Biometrika 98(1):197–210

    Article  MathSciNet  Google Scholar 

  97. Barbato M, Conte JP (2008) Spectral characteristics of non-stationary random processes: theory and applications to linear structural models. Probab Eng Mech 23:416–426

    Article  Google Scholar 

  98. He J (2009) An approximation of the first passage probability of systems under non-stationary random excitation. Appl Math Mech Engl Ed 30(2):255–262

    Google Scholar 

  99. Karadeniz H (2009) SAPOS, Spectral analysis program of structures. Report, Structural Mechanics Division, Faculty of Civil Engineering and Geosciene, TUDelft, Delft, The Netherlands

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Halil Karadeniz .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag London

About this chapter

Cite this chapter

Karadeniz, H., Saka, M.P., Togan, V. (2013). Spectral Analysis of Offshore Structures Under Wave and Earthquake Loadings. In: Stochastic Analysis of Offshore Steel Structures. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-84996-190-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-84996-190-5_4

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-189-9

  • Online ISBN: 978-1-84996-190-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics