Applications for Shape Memory Alloys in Structural and Machine Dynamics

  • Matthew P. Cartmell
  • Arkadiusz J. Żak
  • Olga A. Ganilova
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 181)


This chapter presents a review of some of the fundamental science behind applications for shape memory alloys (SMAs) in mechanical engineering structures and machines in the context of an inexhaustive review of the literature. Following this three well known literature models are considered in some detail after which a summary investigation of the effect of SMAs on the dynamics of beams and plates is given. This leads into a discussion of applications in rotor dynamics for which SMA elements are shown to have considerable uses in the modification of resonant behaviour within the rotor. The chapter concludes with further work on plates, and the concept of antagonism as a means for the approximate equalisation of heating and cooling time constants.


Shape memory alloys vibration dynamics resonance nonlinearity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Armstrong, W.D., Lilgholt, H.: The time dependant, super-viscoelastic behavior of NiTi shape memory alloy fiber reinforced polymer matrix composites. Mater. Sci. Eng. B 68, 149–155 (2000)CrossRefGoogle Scholar
  2. 2.
    Basinski, Z.S., Christian, J.W.: Experiments on the martensitic transformation in single crystals of Indium-Thallium alloys. Acta Metallurgica 2, 148–166 (1954)CrossRefGoogle Scholar
  3. 3.
    Baz, A., Chen, T., Ro, J.: Shape control of NITINOL-reinforced composite beams. Composites B 31, 631–642 (2000)CrossRefGoogle Scholar
  4. 4.
    Baz, A., Poh, S., Ro, J., Gilheany: Control of natural frequencies of NITINOL-reinforced composite beams. Journal of Sound and Vibration 185, 171–185 (1995)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bekker, A., Brinson, L.C.: Phase diagram based description of the hysteresis behavior of shape memory alloys. Acta Materialia 46, 3649–3665 (1998)CrossRefGoogle Scholar
  6. 6.
    Bo, Z., Lagoudas, D.C.: Comparison of different thermomechanical models for shape memory alloys. Adaptive Structures and Composite Materials: Analysis and Application AD-45/MD-54 9-15 (1994)Google Scholar
  7. 7.
    Boyd, J.G., Lagoudas, D.C.: A theromdynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. International Journal of Plasticity 12, 805–842 (1996)zbMATHGoogle Scholar
  8. 8.
    Birman, V.: Stability of functionally graded shape memory alloy sandwich panel. Smart Materials and Structures 6, 278–286 (1997)CrossRefGoogle Scholar
  9. 9.
    Birman, V., Saravanos, D.A., Hopkins, D.A.: Micromechanics of composites with shape memory alloy fibers in uniform thermal fields. AIAA Journal 30, 1905–1912 (1996)CrossRefGoogle Scholar
  10. 10.
    Brinson, L.C.: One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions. Journal of Intelligent Material Systems and Structures 4, 229–242 (1993)CrossRefGoogle Scholar
  11. 11.
    Brocca, M., Brinson, L.C., Bažant, Z.P.: Three-dimensional constitutive model for shape memory alloys based on microplane model. Journal of the Mechanics and Physics of Solids 50, 1051–1077 (2002)zbMATHCrossRefGoogle Scholar
  12. 12.
    Buehler, W.J., Gilfrich, J.V., Wiley, R.C.: Effect of low-temperature phase change on the mechanical properties of alloys near composition. TiNi Journal of Applied Physics 34, 1475–1477 (1963)CrossRefGoogle Scholar
  13. 13.
    Burkart, M.W., Read, T.A.: Diffusionless phase change in the Indium-Thallium system Transactions of AIME. Journal of Metals 197, 1516–1524 (1953)Google Scholar
  14. 14.
    Cartmell, M.P., Inman, D.J., Lees, A.W., Ganilova, O.A., Atepor, L.: Smart materials applications to structural dynamics and rotating machines. In: Proc. Euromech., Kazimierz Dolny, Poland, May 21-24, vol. 498 (2008)Google Scholar
  15. 15.
    Chang, L.C., Read, T.A.: Plastic deformation and diffusionless phase change in metals - the Gold-Cadmium beta phase. Transactions of AIME Journal of Metals 191, 47–52 (1951)Google Scholar
  16. 16.
    Chen, C.W.: Some characteristics of the martensite transformation of Cu-Al-Ni alloys. Journal of Metals 9, 1202–1203 (1957)Google Scholar
  17. 17.
    Chen, Q., Levy, C.: Active vibration control of elastic beam by means of shape memory alloy layers. Smart Materials and Structures 5, 400–406 (1996)CrossRefGoogle Scholar
  18. 18.
    Chen, Q., Levy, C.: Vibration analysis and control of flexible beam by using smart damping structures. Composites: Part B 30, 395–406 (1999)CrossRefGoogle Scholar
  19. 19.
    Choi, S., Lee, J.J., Seo, D.C., Choi, S.W.: The active buckling control of laminated composite beams with embedded shape memory alloy wires. Composite Structures 47, 679–686 (1999)CrossRefGoogle Scholar
  20. 20.
    Epps, J., Chandra, R.: Shape memory alloy actuation for active tuning of composite beams. Smart Mater. Struct. 6, 251–264 (1997)CrossRefGoogle Scholar
  21. 21.
    Epps, J.J., Chopra, I.: Comparative evaluation of shape memory alloy constitutive models with test data. In: Proceedings of the 38th AIAA Structures Structural Dynamics and Materials Conference and Adaptive Forum, Kissimmee Florida, April 7-10 (1997)Google Scholar
  22. 22.
    Ford, D.S., White, S.R.: Thermomechanical behavior of 55Ni45Ti. Nitinol Acta Metallurgica 44, 2295–2307 (1996)Google Scholar
  23. 23.
    Gandhi, F., Wolons, D.: Characterization of the pseudoelastic damping behavior of shape memory alloy wires using complex modulus. Journal of Smart Material Structures 8, 49–56 (1999)CrossRefGoogle Scholar
  24. 24.
    Ganilova, O.A., Cartmell, M.P.: An analytical model for the vibration of a composite plate containing an embedded periodic shape memory alloy structure. Composite Structures 92, 39–47 (2010)CrossRefGoogle Scholar
  25. 25.
    Govindjee, S., Hall, G.J.: A computational model for shape memory alloys. International Journal of Solids and Structures 37, 375–760 (2000)CrossRefGoogle Scholar
  26. 26.
    Gristchak, V.Z., Ganilova, O.A.: A hybrid WKB-Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects. Journal of Sound and Vibration 317, 366–377 (2008)CrossRefGoogle Scholar
  27. 27.
    Hornbogen, E., Wassermann, G.: Über den Einfluβ von Spannungen und das Auftretten von Umwandlungsplastizitt bei Beta1-Beta-Umwandlung des Messings. Zeitschrift fr Metallkunde 47, 427–433 (1956)Google Scholar
  28. 28.
    Icardi, U.: Large bending actuator made with SMA contractile wires: theory numerical simulation and experiments. Composites B 32, 259–267 (2001)CrossRefGoogle Scholar
  29. 29.
    Inman, D.J., Cartmell, M.P., Lees, A.W., Leize, T., Atepor, L.: Proposals for controlling flexible rotor vibration by means of an antagonistic SMSA/composite smart bearing. In: Proc. MPSVA 2006, Bath, UK (September 2006)Google Scholar
  30. 30.
    Kustov, S., Van Humbeeck, J.: Damping properties of SMA Advances in Shape Memory Materials. Materials Science Forum 583, 85–109 (2008)CrossRefGoogle Scholar
  31. 31.
    Kwai, M.: Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composite. Int. J. Plast. 16, 263–282 (2000)CrossRefGoogle Scholar
  32. 32.
    Lau, K.-T.: Vibration characteristics of SMA composite beams with different boundary conditions. Mater. Des. 23, 741–749 (2002)CrossRefGoogle Scholar
  33. 33.
    Lau, K.-T., Zhou, L.-M., Tao, X.-M.: Control of natural frequencies of a clamped-clamped composite beam with embedded shape memory alloy wires. Compos. Struct. 58, 39–47 (2002)CrossRefGoogle Scholar
  34. 34.
    Lee, H.J., Lee, J.J.: A numerical analysis of the buckling and postbuckling behavior of laminated composite shells with embedded shape memory alloy wire actuators. Smart Mater. Struct. 9, 780–787 (2000)CrossRefGoogle Scholar
  35. 35.
    Lee, H.J., Lee, J.J.: Evaluation of the characteristics of a shape memory alloy spring actuator Smart. Materials and Strucutres 9, 817–823 (2000)Google Scholar
  36. 36.
    Lees, A.W., Jana, S., Inman, D.J., Cartmell, M.P.: The control of bearing stiffness using shape memory. In: Proc. ISCORMA-4, Calgary, Canada, August 27-30 (2007)Google Scholar
  37. 37.
    Lexcellent, C., Leclercq, S., Garbry, B., Bourbon, G.: The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological mode. International Journal of Plasticity 16, 1155–1168 (2000)zbMATHCrossRefGoogle Scholar
  38. 38.
    Lexcellent, C., Moyne, S., Ishida, A., Miyazaki, S.: Deformation behaviour associated with the stress-induced martensitic transformation in Ti-Ni thin films and their thermodynamical modelling. Thin Solid Films 324, 184–189 (1998)CrossRefGoogle Scholar
  39. 39.
    Liang, C., Rogers, C.A.: One-dimensional thermomechanical constitutive relations for shape memory material. Journal of Intelligent Materials and Structures 1, 207–234 (1990)CrossRefGoogle Scholar
  40. 40.
    Liew, K.M., Kitipornachai, S., Ng, T.Y., Zou, G.P.: Multi-dimensional superelastic behavior of shape memory alloys via nonlinear finite element method. Engineering Structures 24, 51–57 (2002)CrossRefGoogle Scholar
  41. 41.
    Nagaya, K., Takeda, S., Tsukui, Y., Kumaido, T.: Active control method for passing through critical speeds of rotating shafts by changing stiffnesses of the supports with the use of memory metals. Journal of Sound and Vibration 113(2), 307–315 (1987)CrossRefGoogle Scholar
  42. 42.
    Nishimura, F., Watanabe, N., Tanaka, K.: Back stress and shape recoverability during reverse transformation in an Fe-based shape memory alloy. Materials Science and Engineering A 247, 275–284 (1998)CrossRefGoogle Scholar
  43. 43.
    Oh, J.T., Park, H.C., Hwang, W.: Active shape control of a double-plate structures using piezoceramics and SMA wires. Smart Materials and Structures 10, 1100–1106 (2001)CrossRefGoogle Scholar
  44. 44.
    Ostachowicz, W.M., Kaczmarczyk, S.: Vibrations of composite plates with SMA fibres in a gas stream with defects of the type of delamination. Composite Structures 54, 305–311 (2001)CrossRefGoogle Scholar
  45. 45.
    Ostachowicz, W., Krawczuk, M., Żak, A.: Natural frequencies of a multilayer composite plate with shape memory alloy wires. Finite Element in Analysis and Design 32, 71–83 (1999)zbMATHCrossRefGoogle Scholar
  46. 46.
    Ostachowicz, W., Krawczuk, M., Żak, A.: Dynamics and buckling of a multilayer composite plate with embedded. SMA wires Composite Structures 48, 163–167 (2000)Google Scholar
  47. 47.
    Otsuka, K., Wayman, C.M.: Shape Memory Materials. University Press Cambridge, Cambridge (1998)Google Scholar
  48. 48.
    Pae, S., Lee, H., Park, H., Hwang, W.: Realization of higher-mode deformation of beam using shape memory alloy wires and piezoceramics. Smart Mater. Struct. 9, 848–854 (2000)CrossRefGoogle Scholar
  49. 49.
    Piedboeuf, M.C., Gauvin, R., Thomas, M.: Damping behaviour of shape memory alloys: strain amplitude frequency and temperature effects. Journal of Sound and Vibration 214, 885–901 (1998)CrossRefGoogle Scholar
  50. 50.
    Raniecki, B., Lexcellent, C., Tanaka, K.: Thermomechanical models of pseudoelastic behaviour of shape memory alloys. Archives of Mechanics 44, 261–284 (1992)zbMATHMathSciNetGoogle Scholar
  51. 51.
    Rogers, C.A., Baker, D.K., Jaeger, C.A.: Introduction to smart materials and structures Smart Materials Structures and Mathematical Issues, pp. 17–28. Technomic Publishing Company Inc. (1989)Google Scholar
  52. 52.
    Rogers, C.A., Liang, C., Baker, D.K.: Dynamic control concepts using shape memory alloy reinforced plates Smart Materials Structures and Mathematical Issues, pp. 39–62. Technomic Publishing Company Inc. (1989)Google Scholar
  53. 53.
    Roh, J.-H., Kim, J.-H.: Hybrid smart composite plate under low velocity impact. Composite Strucutres 56, 175–182 (2002)CrossRefGoogle Scholar
  54. 54.
    Shu, S.G., Lagoudas, D.C., Hughes, D., Wen, J.T.: Modeling of a flexible beam actuated by shape memory alloy wires. Smart Mater. Struct. 6, 265–277 (1997)CrossRefGoogle Scholar
  55. 55.
    Song, G., Kelly, B., Agrawal, B.N.: Active position control of a shape memory alloy wire actuated composite beam. Smart Materials and Structures 9, 711–716 (2000)CrossRefGoogle Scholar
  56. 56.
    Su, Z., Mai, H., Lu, M., Ye, L.: Thermo-mechanical behaviour of shape memory alloy reinforced composite laminate (Ni-Ti/glass-fibre/epoxy). Compos. Struct. 47, 705–710 (1999)CrossRefGoogle Scholar
  57. 57.
    Sun, G., Sun, S., Wu, X., Wu, J.: A study on thermomechanical deformation of elastic beam with embedded shape memory alloy wires. Mater. Des. 21, 525–528 (2000)CrossRefMathSciNetGoogle Scholar
  58. 58.
    Tanaka, K.: A thermomechanical sketch for shape memory effect: One-dimensional tensile behavior. Res. Mechanica 18, 251–263 (1986)Google Scholar
  59. 59.
    Tawfik, M., Ro, J.J., Mei, C.: Thermal post-buckling and aeroelastic behaviour of shape memory alloy reinforced plates. Smart Materials and Structures 11, 297–303 (2002)CrossRefGoogle Scholar
  60. 60.
    Thompson, S.P., Loughlan, J.: The control of the post-buckling response in thin composite plates using smart technology. Thin-walled Structures 36, 231–263 (2000)CrossRefGoogle Scholar
  61. 61.
    Tsai, X.-Y., Chen, L.-W.: Dynamic stability of a shape memory alloy wire reinforced composite beam. Compos. Struct. 56, 235–241 (2002); a double-plate structures using piezoceramics and SMA wires Smart Mater. Struct. 10,1100-1106CrossRefGoogle Scholar
  62. 62.
    Viderman, Z., Porat, I.: An optimal control method for passage of a flexible rotor through resonances. Journal of Dynamic Systems Measurement and Control 109(3), 216–223 (1987)zbMATHCrossRefGoogle Scholar
  63. 63.
    Vinson, J.R., Sierakowski, R.L.: The behavior of structures composed of composite materials. Martinus Nijhoff Publishers, Dordrecht (1986)zbMATHGoogle Scholar
  64. 64.
    Wu, X., Grummon, D.S., Pence, T.J.: Modeling phase fraction shakedown during thermomechanical cycling of shape memory materials. Materials Science and Engineering A, 273-275, 273–275 (1999)Google Scholar
  65. 65.
    Zhu, J., Liang, N., Huang, W., Liew, K.M., Liu, Z.: A thermodynamic constitutive model for stress induced phase transformation in shape memory alloys I. International Journal of Solids and Structures 39, 741–763 (2002)zbMATHCrossRefGoogle Scholar
  66. 66.
    Żak, A.J., Cartmell, M.P.: Analytical modelling of shape memory alloys and flat multi-layered composite beams and plates with shape memory alloy wires. 1st Research Report, Department of Mechanical Engineering, University of Glasgow (2000)Google Scholar
  67. 67.
    Żak, A.J., Cartmell, M.P.: Statics and dynamics of a sleeve-ring component with SMA strips. 3rd Research Report, Department of Mechanical Engineering, University of Glasgow (2002)Google Scholar
  68. 68.
    Żak, A.J., Cartmell, M.P.: Dynamics of a rotor system with a smart SMA-embedded sleeve-ring component. 4th Research Report, Department of Mechanical Engineering, University of Glasgow (2002)Google Scholar
  69. 69.
    Żak, A.J., Cartmell, M.P., Ostachowicz, W.M.: Dynamics of multi-layered composite beams and plates with SMA wires. 2nd Research Report, Department of Mechanical Engineering, University of Glasgow (2001)Google Scholar
  70. 70.
    Żak, A.J., Cartmell, M.P., Ostachowicz, W.M., Wiercigroch, M.: One-dimensional shape memory alloy models for use with reinforced composite structures. Smart Mater. Struct. 12, 338–346 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Matthew P. Cartmell
    • 1
  • Arkadiusz J. Żak
    • 2
  • Olga A. Ganilova
    • 1
  1. 1.School of EngineeringUniversity of GlasgowGlasgowScotland, United Kingdom
  2. 2.Szewalski Institute of Fluid Flow MachineryPolish Academy of SciencesGdaskPoland

Personalised recommendations