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Computational Mechanics

, Volume 63, Issue 1, pp 121–136 | Cite as

Computational and experimental investigation of free vibration and flutter of bridge decks

  • Tore A. HelgedagsrudEmail author
  • Yuri Bazilevs
  • Kjell M. Mathisen
  • Ole A. Øiseth
Original Paper
  • 260 Downloads

Abstract

A modified rigid-object formulation is developed, and employed as part of the fluid–object interaction modeling framework from Akkerman et al. (J Appl Mech 79(1):010905, 2012.  https://doi.org/10.1115/1.4005072) to simulate free vibration and flutter of long-span bridges subjected to strong winds. To validate the numerical methodology, companion wind tunnel experiments have been conducted. The results show that the computational framework captures very precisely the aeroelastic behavior in terms of aerodynamic stiffness, damping and flutter characteristics. Considering its relative simplicity and accuracy, we conclude from our study that the proposed free-vibration simulation technique is a valuable tool in engineering design of long-span bridges.

Keywords

Flutter Numerical methods Solid–fluid interaction Rigid bodies Wind 

Notes

Acknowledgements

This work was carried out with financial support from the Norwegian Public Roads Administration. All simulations were performed on resources provided by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data Storage in Norway. YB was partially supported through AFOSR Award No. FA9550-16-1-0131. The authors greatly acknowledge this support.

References

  1. 1.
    Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79(1):010905.  https://doi.org/10.1115/1.4005072 Google Scholar
  2. 2.
    Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21(4):481–508.  https://doi.org/10.1007/s11831-014-9113-0 MathSciNetzbMATHGoogle Scholar
  3. 3.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces. The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94(3):353–371.  https://doi.org/10.1016/0045-7825(92)90060-W MathSciNetzbMATHGoogle Scholar
  4. 4.
    Mittal S, Tezduyar TE (1992) A finite element study of incompressible flows past oscillating cylinders and aerofoils. Int J Numer Methods Fluids 15(9):1073–1118.  https://doi.org/10.1002/fld.1650150911 Google Scholar
  5. 5.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130.  https://doi.org/10.1007/BF02897870 zbMATHGoogle Scholar
  6. 6.
    Ed Akin J, Tezduyar TE, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36(1):2–11.  https://doi.org/10.1016/j.compfluid.2005.07.008 zbMATHGoogle Scholar
  7. 7.
    Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230(11):4137–4152.  https://doi.org/10.1016/j.jcp.2010.11.044 MathSciNetzbMATHGoogle Scholar
  8. 8.
    Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50(6):719–727.  https://doi.org/10.1007/s00466-012-0770-2 Google Scholar
  9. 9.
    Kees CE, Akkerman I, Farthing MW, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230(12):4536–4558.  https://doi.org/10.1016/j.jcp.2011.02.030 MathSciNetzbMATHGoogle Scholar
  10. 10.
    R. P. Selvam, S. Govindaswamy, H. Bosch, Aeroelastic analysis of bridges using FEM and moving grids, Wind and Structures 5 (2\_3\_4) (2002) 257–266.  https://doi.org/10.12989/was.2002.5.2_3_4.257. http://koreascience.or.kr/journal/view.jsp?kj=KJKHCF&py=2002&vnc=v5n2_3_4&sp=257
  11. 11.
    Frandsen JB (2004) Numerical bridge deck studies using finite elements. Part I: Flutter. J Fluids Struct 19(2):171–191.  https://doi.org/10.1016/j.jfluidstructs.2003.12.005 Google Scholar
  12. 12.
    Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp02):1230002.  https://doi.org/10.1142/S0218202512300025 zbMATHGoogle Scholar
  13. 13.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid-structure interaction. Math Models Methods Appl Sci 23(02):215–221.  https://doi.org/10.1142/S0218202513400010 MathSciNetzbMATHGoogle Scholar
  14. 14.
    Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21(4):359–398.  https://doi.org/10.1007/s11831-014-9119-7 MathSciNetzbMATHGoogle Scholar
  15. 15.
    Bazilevs Y, Takizawa K, Tezduyar TE (2015) New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods. Math Models Methods Appl Sci 25(12):2217–2226.  https://doi.org/10.1142/S0218202515020029 MathSciNetzbMATHGoogle Scholar
  16. 16.
    Bazilevs Y, Korobenko A, Yan J, Pal A, Gohari SMI, Sarkar S (2015) ALEVMS formulation for stratified turbulent incompressible flows with applications. Math Models Methods Appl Sci 25(12):2349–2375.  https://doi.org/10.1142/S021820251540011 MathSciNetzbMATHGoogle Scholar
  17. 17.
    Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196(49–52):4853–4862.  https://doi.org/10.1016/j.cma.2007.06.026 MathSciNetzbMATHGoogle Scholar
  18. 18.
    Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36(1):12–26.  https://doi.org/10.1016/j.compfluid.2005.07.012 MathSciNetzbMATHGoogle Scholar
  19. 19.
    Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229(9):3402–3414.  https://doi.org/10.1016/j.jcp.2010.01.008 MathSciNetzbMATHGoogle Scholar
  20. 20.
    Bazilevs Y, Tezduyar TE (2013) Computational fluid structure interaction methods and application. Wiley, Hoboken.  https://doi.org/10.1002/9781118483565 zbMATHGoogle Scholar
  21. 21.
    Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALEVMS: validation and the role of weakly enforced boundary conditions. Comput Mech 50(4):499–511.  https://doi.org/10.1007/s00466-012-0686-x MathSciNetGoogle Scholar
  22. 22.
    Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54(4):1055–1071.  https://doi.org/10.1007/s00466-014-1059-4 MathSciNetzbMATHGoogle Scholar
  23. 23.
    Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid structure interaction with application to floating offshore wind turbines. Computers & Fluids 141:155–174.  https://doi.org/10.1016/j.compfluid.2016.03.008. http://linkinghub.elsevier.com/retrieve/pii/S0045793016300536
  24. 24.
    Scotta R, Lazzari M, Stecca E, Cotela J, Rossi R (2016) Numerical wind tunnel for aerodynamic and aeroelastic characterization of bridge deck sections. Comput Struct 167:96–114.  https://doi.org/10.1016/j.compstruc.2016.01.012 Google Scholar
  25. 25.
    Helgedagsrud TA, Mathisen KM, Bazilevs Y, Øiseth O, Korobenko A (2017) Using ALE-VMS to compute wind forces on moving bridge decks. In: Skallerud B, Andersson HI (eds.) Proceedings of MekIT’17 ninth national conference on computational mechanics, CMIME, Barcelona, Spain, pp. 169–189Google Scholar
  26. 26.
    Helgedagsrud TA, Bazilevs Y, Korobenko A, Mathisen KM, Øiseth OA (2018) Using ALE-VMS to compute aerodynamic derivatives of bridge sections, Computers Fluids, published online.  https://doi.org/10.1016/j.compfluid.2018.04.037. http://linkinghub.elsevier.com/retrieve/pii/S0045793018302330
  27. 27.
    Takizawa K, Tezduyar TE (2011) Multiscale spacetime fluid structure interaction techniques. Comput Mech 48(3):247–267.  https://doi.org/10.1007/s00466-011-0571-z MathSciNetzbMATHGoogle Scholar
  28. 28.
    Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001.  https://doi.org/10.1142/S0218202512300013 MathSciNetzbMATHGoogle Scholar
  29. 29.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Spacetime interface-tracking with topology change (ST-TC). Comput Mech 54(4):955–971.  https://doi.org/10.1007/s00466-013-0935-7 MathSciNetzbMATHGoogle Scholar
  30. 30.
    Takizawa K, Tezduyar TE, Buscher A (2015) Spacetime computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55(6):1131–1141.  https://doi.org/10.1007/s00466-014-1095-0 Google Scholar
  31. 31.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Spacetime fluid mechanics computation of heart valve models. Comput Mech 54(4):973–986.  https://doi.org/10.1007/s00466-014-1046-9 zbMATHGoogle Scholar
  32. 32.
    Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017) Heart valve flow computation with the integrated SpaceTime VMS. Slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176–188.  https://doi.org/10.1016/j.compfluid.2016.11.012. http://linkinghub.elsevier.com/retrieve/pii/S0045793016303681
  33. 33.
    Takizawa K, Tezduyar TE, Kuraishi T, Tabata S, Takagi H (2016) Computational thermo-fluid analysis of a disk brake. Comput Mech 57(6):965–977.  https://doi.org/10.1007/s00466-016-1272-4 MathSciNetzbMATHGoogle Scholar
  34. 34.
    Takizawa K, Tezduyar TE, Hattori H (2017) Computational analysis of flow-driven string dynamics in turbomachinery. Comput Fluids 142:109–117.  https://doi.org/10.1016/j.compfluid.2016.02.019 MathSciNetzbMATHGoogle Scholar
  35. 35.
    Takizawa K, Tezduyar TE, Otoguro Y, Terahara T, Kuraishi T, Hattori H (2017) Turbocharger flow computations with the spacetime isogeometric analysis (ST-IGA). Comput Fluids 142:15–20.  https://doi.org/10.1016/j.compfluid.2016.02.021 MathSciNetzbMATHGoogle Scholar
  36. 36.
    Otoguro Y, Takizawa K, Tezduyar TE (2017) Spacetime VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method. Comput Fluids 158:189–200.  https://doi.org/10.1016/j.compfluid.2017.04.017 MathSciNetzbMATHGoogle Scholar
  37. 37.
    Takizawa K, Tezduyar TE, Asada S, Kuraishi T (2016) SpaceTime method for flow computations with slip interfaces and topology changes (ST-SI-TC). Comput Fluids 141:124–134.  https://doi.org/10.1016/j.compfluid.2016.05.006 MathSciNetzbMATHGoogle Scholar
  38. 38.
    Šarkić A, Fisch R, Höffer R, Bletzinger KU (2012) Bridge flutter derivatives based on computed, validated pressure fields. J Wind Eng Ind Aerodyn 104–106:141–151.  https://doi.org/10.1016/j.jweia.2012.02.033 Google Scholar
  39. 39.
    Brusiani F, Miranda SD, Patruno L, Ubertini F, Vaona P (2013) On the evaluation of bridge deck flutter derivatives using RANS turbulence models. J Wind Eng 119:39–47Google Scholar
  40. 40.
    Bai Y, Yang K, Sun D, Zhang Y, Kennedy D, Williams F, Gao X (2013) Numerical aerodynamic analysis of bluff bodies at a high Reynolds number with three-dimensional CFD modeling. Sci China Phys Mech Astron 56(2):277–289.  https://doi.org/10.1007/s11433-012-4982-4 Google Scholar
  41. 41.
    de Miranda S, Patruno L, Ubertini F, Vairo G (2014) On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms. Eng Struct 76:359–370.  https://doi.org/10.1016/j.engstruct.2014.07.027 Google Scholar
  42. 42.
    Nieto F, Owen JS, Hargreaves DM, Hernández S (2015) Bridge deck flutter derivatives: efficient numerical evaluation exploiting their interdependence. J Wind Eng Ind Aerodyn J 136:138–150Google Scholar
  43. 43.
    Patruno L (2015) Accuracy of numerically evaluated flutter derivatives of bridge deck sections using RANS: effects on the flutter onset velocity. Eng Struct 89:49–65.  https://doi.org/10.1016/j.engstruct.2015.01.034 Google Scholar
  44. 44.
    Diana G, Rocchi D, Belloli M (2015) Wind tunnel : a fundamental tool for long-span bridge design. Struct Infrastruct Eng Maint Manag Life Cycle Des Perform 11(4):533–555.  https://doi.org/10.1080/15732479.2014.951860 Google Scholar
  45. 45.
    Siedziako B, Øiseth O, Rønnquist A (2017) An enhanced forced vibration rig for wind tunnel testing of bridge deck section models in arbitrary motion. J Wind Eng Ind Aerodyn 164:152–163.  https://doi.org/10.1016/j.jweia.2017.02.011 Google Scholar
  46. 46.
    Scanlan RH, Tomko J (1971) Airfoil and bridge deck flutter derivatives. J Eng Mech Div 97(6):1717–1737Google Scholar
  47. 47.
    Svend Ole Hansen APS, The Hardanger bridge: static and dynamic wind tunnel tests with a section model. Technical report, prepared for Norwegian Public Roads Administration, Tech. rep. (2006)Google Scholar
  48. 48.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349.  https://doi.org/10.1016/0045-7825(81)90049-9 MathSciNetzbMATHGoogle Scholar
  49. 49.
    Hughes T, Tezduyar T (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible euler equations. Comput Methods Appl Mech Eng 45(1–3):217–284.  https://doi.org/10.1016/0045-7825(84)90157-9 MathSciNetzbMATHGoogle Scholar
  50. 50.
    Hughes TJ, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics. : V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59(1):85–99.  https://doi.org/10.1016/0045-7825(86)90025-3 zbMATHGoogle Scholar
  51. 51.
    Tezduyar T, Park Y (1986) Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59(3):307–325.  https://doi.org/10.1016/0045-7825(86)90003-4 zbMATHGoogle Scholar
  52. 52.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430.  https://doi.org/10.1016/S0045-7825(00)00211-5 zbMATHGoogle Scholar
  53. 53.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43(5):555–575.  https://doi.org/10.1002/fld.505 MathSciNetzbMATHGoogle Scholar
  54. 54.
    Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45(2):539–557.  https://doi.org/10.1137/050645646 MathSciNetzbMATHGoogle Scholar
  55. 55.
    Hsu M-C, Bazilevs Y, Calo V, Tezduyar T, Hughes T (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time step. Comput Methods Appl Mech Eng 199(13–16):828–840.  https://doi.org/10.1016/j.cma.2009.06.019 MathSciNetzbMATHGoogle Scholar
  56. 56.
    Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale spacetime methods for thermo-fluid analysis of a ground vehicle and its tires. Math Models Methods Appl Sci 25(12):2227–2255.  https://doi.org/10.1142/S0218202515400072 MathSciNetzbMATHGoogle Scholar
  57. 57.
    Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015) Spacetime VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25(12):2377–2406.  https://doi.org/10.1142/S0218202515400126 MathSciNetzbMATHGoogle Scholar
  58. 58.
    K. Takizawa, T. E. Tezduyar, Y. Otoguro, Stabilization and discontinuity-capturing parameters for spacetime flow computations with finite element and isogeometric discretizations, Comput Mech.published online (2018).  https://doi.org/10.1007/s00466-018-1557-x
  59. 59.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43(1):3–37.  https://doi.org/10.1007/s00466-008-0315-x MathSciNetzbMATHGoogle Scholar
  60. 60.
    Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech 70(1):58.  https://doi.org/10.1115/1.1530635 zbMATHGoogle Scholar
  61. 61.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressiblke flows and massively parallel implementations. New Methods Transient Anal 246:7–24Google Scholar
  62. 62.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36.  https://doi.org/10.1109/2.237441 zbMATHGoogle Scholar
  63. 63.
    Johnson A, Tezduyar T (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119(1–2):73–94.  https://doi.org/10.1016/0045-7825(94)00077-8 zbMATHGoogle Scholar
  64. 64.
    Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15(12):1862–1867.  https://doi.org/10.1002/nme.1620151210 MathSciNetzbMATHGoogle Scholar
  65. 65.
    Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319MathSciNetzbMATHGoogle Scholar
  66. 66.
    Kuhl E, Hulshoff S, de Borst R (2003) An arbitrary lagrangian eulerian finite-element approach for fluid-structure interaction phenomena. Int J Numer Methods Eng 57(1):117–142.  https://doi.org/10.1002/nme.749 zbMATHGoogle Scholar
  67. 67.
    Dettmer WG, Peric D (2006) A computational framework for fluid-structure interaction: finite element formulation and applications. Comput Methods Appl Mech Eng 195:5754–5779zbMATHGoogle Scholar
  68. 68.
    Øiseth O, Rönnquist A, Sigbjörnsson R (2010) Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study. J Wind Eng Ind Aerodyn 98(12):730–741.  https://doi.org/10.1016/j.jweia.2010.06.009 Google Scholar
  69. 69.
    Scanlan RH (1993) Problematics in formulation of wind force models for bridge decks. J Eng Mech 119(7):1353–1375.  https://doi.org/10.1061/(ASCE)0733-9399(1993)119:7(1353) Google Scholar
  70. 70.
    Bartoli G, Contri S, Mannini C, Righi M (2009) Toward an improvement in the identification of bridge deck flutter derivatives. J Eng Mech 135(8):771–785.  https://doi.org/10.1061/(ASCE)0733-9399(2009)135:8(771) Google Scholar
  71. 71.
    Tezduyar TE (2001) Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces. In: Proceedings of the ASME symposium on fluid-physics and heat transfer for macro- and micro-scale gas-liquid and phase-change flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New York, New YorkGoogle Scholar
  72. 72.
    Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193(21–22):2019–2032.  https://doi.org/10.1016/j.cma.2003.12.046 zbMATHGoogle Scholar
  73. 73.
    Hsu MC, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids 49(1):93–100.  https://doi.org/10.1016/j.compfluid.2011.05.002 MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tore A. Helgedagsrud
    • 1
    Email author
  • Yuri Bazilevs
    • 2
  • Kjell M. Mathisen
    • 1
  • Ole A. Øiseth
    • 1
  1. 1.Department of Structural EngineeringNTNU - Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.School of EngineeringBrown UniversityProvidenceUSA

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