Investigation of the Damping Performance of a Shape Memory Alloy Beam

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, University of Texas at Arlington, Arlington, TX, USA

2 Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

3 Department of Mechanical Engineering, Babol Noushirvani University of Technology, Babol, Iran

Abstract

The aim of this research is to introduce a semi-analytical approach for the analysis of the free and forced nonlinear vibrations of a bending shape memory alloy (SMA) beam; while, considering the effect of its pseudo-elastic behavior. In order to create a primary deflection, an appropriate pre-strain is applied to the SMA beam using a compression spring. A new material model was utilized to simulate the nonlinear hysteric behavior of the SMA beam, while the differential equations of motion of the beam were derived based on Euler–Bernoulli beam theory and Hamilton principle. The extracted nonlinear partial differential equations of motion are semi-analytically solved by utilizing the Galerkin method. The pseudo-elastic behavior and energy dissipation of the SMA beam were studied in the free and forced nonlinear vibration regimes. Finally, the influences of the system parameters such as the spring constant, amplitude, and frequency of the excitation force on the absorber efficiency were investigated, and its stability was studied. The numerical results depict that the SMA beam exhibits a highly nonlinear dynamical behavior, and can be used as an actuator for energy dissipation.

Keywords

Main Subjects


  1. Kabla, M., Ben-David, E. and Shilo, D., "A novel shape memory alloy microactuator for large in-plane strokes and forces", Smart Materials and Structures, Vol. 25, No. 7, (2016). doi: 10.1088/0964-1726/25/7/075020.
  2. Barzegari, M.M., Dardel, M., Fathi, A. and Ghadimi, M., "Aeroelastic characteristics of cantilever wing with embedded shape memory alloys", Acta Astronautica, Vol. 79, (2012), 189-202. doi: 10.1016/j.actaastro.2012.04.023.
  3. Pittaccio, S., Garavaglia, L., Ceriotti, C. and Passaretti, F., "Applications of shape memory alloys for neurology and neuromuscular rehabilitation", Journal of Functional Biomaterials, Vol. 6, No. 2, (2015), 328-344. doi: 10.3390/jfb6020328.
  4. Sohn, J., Han, Y., Choi, S., Lee, Y. and Han, M., "Vibration and position tracking control of a flexible beam using sma wire actuators", Journal of Vibration and Control, Vol. 15, No. 2, (2009), 263-281. doi: 10.1177/1077546308094251.
  5. She, Y., Chen, J., Shi, H. and Su, H.-J., "Modeling and validation of a novel bending actuator for soft robotics applications", Soft Robotics, Vol. 3, No. 2, (2016), 71-81. doi: 10.1089/soro.2015.0022.
  6. Bellini, A., Colli, M. and Dragoni, E., "Mechatronic design of a shape memory alloy actuator for automotive tumble flaps: A case study", IEEE Transactions on Industrial Electronics, Vol. 56, No. 7, (2009), 2644-2656. doi: 10.1109/TIE.2009.2019773.
  7. Burugupally, S.P., Koppolu, B., Danesh, N., Lee, Y., Indeewari, V. and Li, B., "Enhancing the performance of dielectric elastomer actuators through the approach of distributed electrode array with fractal interconnects architecture", Journal of Micromechanics and Microengineering, Vol. 31, No. 6, (2021), 064002. doi: 10.1088/1361-6439/abf632.
  8. Kang, Z. and James, K.A., "Multiphysics design of programmable shape-memory alloy-based smart structures via topology optimization", Structural and Multidisciplinary Optimization, Vol. 65, No. 1, (2022), 24. doi: 10.1007/s00158-021-03101-z.
  9. Ozturk, B., Cetin, H., Dutkiewicz, M., Aydin, E. and Noroozinejad Farsangi, E., "On the efficacy of a novel optimized tuned mass damper for minimizing dynamic responses of cantilever beams", Applied Sciences, Vol. 12, No. 15, (2022), 7878. doi: 10.3390/app12157878.
  10. Aydin, E., Öztürk, B. and Dutkiewicz, M., "Analysis of efficiency of passive dampers in multistorey buildings", Journal of Sound and Vibration, Vol. 439, (2019), 17-28. doi: 10.1016/j.jsv.2018.09.031.
  11. Aydin, E., Dutkiewicz, M., Öztürk, B. and Sonmez, M., "Optimization of elastic spring supports for cantilever beams", Structural and Multidisciplinary Optimization, Vol. 62, (2020), 55-81. doi: 10.1007/s00158-019-02469-3.
  12. Coşkun, S.B., Atay, M.T. and Öztürk, B., "Transverse vibration analysis of euler-bernoulli beams using analytical approximate techniques", Advances in Vibration Analysis Research, Vol. 1, (2011), 22. doi: 10.5772/15891.
  13. Rogers, C.A., "Active vibration and structural acoustic control of shape memory alloy hybrid composites: Experimental results", The Journal of the Acoustical Society of America, Vol. 88, No. 6, (1990), 2803-2811. doi: 10919/52280.
  14. Peyroux, R., Chrysochoos, A., Licht, C. and Löbel, M., "Thermomechanical couplings and pseudoelasticity of shape memory alloys", International Journal of Engineering Science, Vol. 36, No. 4, (1998), 489-509. doi: doi:10.1016/S0020-7225(97)00052-9.
  15. Grabe, C. and Bruhns, O.T., "On the viscous and strain rate dependent behavior of polycrystalline niti", International Journal of Solids and Structures, Vol. 45, No. 7-8, (2008), 1876-1895. doi: 10.1016/j.ijsolstr.2007.10.029.
  16. Müller, C. and Bruhns, O., "A thermodynamic finite-strain model for pseudoelastic shape memory alloys", International Journal of Plasticity, Vol. 22, No. 9, (2006), 1658-1682. doi: 10.1016/j.ijplas.2006.02.010.
  17. Christ, D. and Reese, S., "A finite element model for shape memory alloys considering thermomechanical couplings at large strains", International Journal of Solids and Structures, Vol. 46, No. 20, (2009), 3694-3709. doi: 10.1016/j.ijsolstr.2009.06.017.
  18. Andani, M.T. and Elahinia, M., "A rate dependent tension–torsion constitutive model for superelastic nitinol under non-proportional loading; a departure from von mises equivalency", Smart Materials and Structures, Vol. 23, No. 1, (2013), 015012. doi: 10.1088/0964-1726/23/1/015012.
  19. Chatziathanasiou, D., Chemisky, Y., Chatzigeorgiou, G. and Meraghni, F., "Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading", International Journal of Plasticity, Vol. 82, (2016), 192-224. doi: 10.1016/j.ijplas.2016.03.005.
  20. Jani, J.M., Leary, M., Subic, A. and Gibson, M.A., "A review of shape memory alloy research, applications and opportunities", Materials & Design (1980-2015), Vol. 56, (2014), 1078-1113. doi: 10.1016/j.matdes.2013.11.084.
  21. Chemisky, Y., Chatzigeorgiou, G., Kumar, P. and Lagoudas, D.C., "A constitutive model for cyclic actuation of high-temperature shape memory alloys", Mechanics of materials, Vol. 68, (2014), 120-136. doi: 10.1016/j.mechmat.2013.07.020.
  22. Plietsch, R., Bourauel, C., Drescher, D. and Nellen, B., "Analytical description of the bending behaviour of niti shape-memory alloys", Journal of Materials Science, Vol. 29, No. 22, (1994), 5892-5902. doi: 10.1007/BF00366873.
  23. Auricchio, F. and Sacco, E., "A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite", International Journal of Non-Linear Mechanics, Vol. 32, No. 6, (1997), 1101-1114. doi: 10.1016/S0020-7462(96)00130-8.
  24. Rajagopal, K.R. and Srinivasa, A.R., "On the bending of shape memory wires", Mechanics of Advanced Materials and Structures, Vol. 12, No. 5, (2005), 319-330. doi: 10.1080/15376490590953581.
  25. Eshghinejad, A. and Elahinia, M., "Exact solution for bending of shape memory alloy superelastic beams", in ASME conference proceedings. Vol. 54723, (2011), 345-352.
  26. Rizzoni, R., Merlin, M. and Casari, D., "Shape recovery behaviour of niti strips in bending: Experiments and modelling", Continuum Mechanics and Thermodynamics, (2013), 1-21. doi: 10.1007/s00161-012-0242-0.
  27. Mirzaeifar, R., DesRoches, R., Yavari, A. and Gall, K., "On superelastic bending of shape memory alloy beams", International Journal of Solids and Structures, Vol. 50, No. 10, (2013), 1664-1680. doi: 10.1016/j.ijsolstr.2013.01.035.
  28. Ostadrahimi, A., Arghavani, J. and Poorasadion, S., "An analytical study on the bending of prismatic sma beams", Smart Materials and Structures, Vol. 24, No. 12, (2015), 125035. doi: 10.1088/0964-1726/24/12/125035.
  29. Atanacković, T. and Achenbach, M., "Moment-curvature relations for a pseudoelastic beam", Continuum Mechanics and Thermodynamics, Vol. 1, No. 1, (1989), 73-80. doi: 10.1007/BF01125887.
  30. Liu, M.X., J. Li, Q. , "Design and experiment of piezoelectric-shape memory alloy composite shock absorber", Materials Letters, Vol. 304, (2021). doi: 10.1016/j.matlet.2021.130538.
  31. Sattari, M.K., M. Akbarzadeh, S.  Gholami, R.  Beheshti, A.  , "Wear in superelastic shape memory alloys: A thermomechanical analysis", Wear (2022), 488-489. doi: 10.1016/j.wear.2021.204139.
  32. De la Flor, S., Urbina, C. and Ferrando, F., "Asymmetrical bending model for niti shape memory wires: Numerical simulations and experimental analysis", Strain, Vol. 47, No. 3, (2011), 255-267. doi: 10.1111/j.1475-1305.2009.00679.x.
  33. Hartl, D., Lagoudas, D., Calkins, F. and Mabe, J., "Use of a ni60ti shape memory alloy for active jet engine chevron application: I. Thermomechanical characterization", Smart Materials and Structures, Vol. 19, No. 1, (2009), 015020. doi: 10.1088/0964-1726/19/1/015021.
  34. Hartl, D., Mooney, J., Lagoudas, D., Calkins, F. and Mabe, J., "Use of a ni60ti shape memory alloy for active jet engine chevron application: Ii. Experimentally validated numerical analysis", Smart Materials and Structures, Vol. 19, No. 1, (2009), 015021. doi: 10.1088/0964-1726/19/1/015021.
  35. Razavilar, R., Fathi, A., Dardel, M. and Arghavani Hadi, J., "Dynamic analysis of a shape memory alloy beam with pseudoelastic behavior", Journal of Intelligent Material Systems and Structures, Vol. 29, No. 9, (2018), 1835-1849. doi: 10.1177/1045389X17754268.
  36. Hashemi, S. and Khadem, S., "Modeling and analysis of the vibration behavior of a shape memory alloy beam", International Journal of Mechanical Sciences, Vol. 48, No. 1, (2006), 44-52. doi: 10.1016/j.ijmecsci.2005.09.011.
  37. Jose, S., Chakraborty, G. and Bhattacharyya, R., "Coupled thermo-mechanical analysis of a vibration isolator made of shape memory alloy", International Journal of Solids and Structures, Vol. 115, (2017), 87-103. doi: 10.1016/j.ijsolstr.2017.03.001.
  38. Pan, Q. and Cho, C., "The investigation of a shape memory alloy micro-damper for mems applications", Sensors, Vol. 7, No. 9, (2007), 1887-1900. doi: 10.3390/s7091887.
  39. Damanpack, A., Bodaghi, M., Aghdam, M. and Shakeri, M., "On the vibration control capability of shape memory alloy composite beams", Composite Structures, Vol. 110, No., (2014), 325-334. doi: 10.1016/j.compstruct.2013.12.002.
  40. Panico, M. and Brinson, L., "A three-dimensional phenomenological model for martensite reorientation in shape memory alloys", Journal of the Mechanics and Physics of Solids, Vol. 55, No. 11, (2007), 2491-2511. doi: 10.1016/j.jmps.2007.03.010.
  41. Brinson, L., Huang, M., Boller, C. and Brand, W., "Analysis of controlled beam deflections using sma wires", Journal of Intelligent Material Systems and Structures, Vol. 8, No. 1, (1997), 12-25. doi: 10.1177/1045389X9700800103.
  42. Moallem, M., "Deflection control of a flexible beam using shape memory alloy actuators", Smart Materials and Structures, Vol. 12, No. 6, (2003), 1023. doi: 10.1088/0964-1726/12/6/022.
  43. Sayyaadi, H. and Zakerzadeh, M., "Nonlinear analysis of a flexible beam actuated by a couple of active sma wire actuators", International Journal of Engineering, Transactions A: Basics, Vol. 25, No. 3, (2012), 249-264. doi: 10.5829/idosi.ije.2012.25.03a.07.
  44. Andrade, B.H., Silva, D.D., Brito, I.C., Caluête, R.E., Sousa, A.R., Gomes, R.M. and Oliveira, D.F., "Influence of strain rate on mechanical properties of a cualmntib shape memory alloy", Journal of Materials Research and Technology, Vol. 16, No., (2022), 1667-1672. doi: 10.1016/j.jmrt.2021.12.100.
  45. Billah, A.M., Rahman, J. and Zhang, Q., "Shape memory alloys (smas) for resilient bridges: A state-of-the-art review", in Structures, Elsevier. Vol. 37, (2022), 514-527.
  46. Bellini, C., Berto, F., Di Cocco, V. and Iacoviello, F., "A cyclic integrated microstructural-mechanical model for a shape memory alloy", International Journal of Fatigue, Vol. 153, (2021), 106473. doi: 10.1016/j.ijfatigue.2021.106473.
  47. Souza, A.C., Mamiya, E.N. and Zouain, N., "Three-dimensional model for solids undergoing stress-induced phase transformations", European Journal of Mechanics-A/Solids, Vol. 17, No. 5, (1998), 789-806. doi: 10.1016/S0997-7538(98)80005-3.
  48. Paik, J.K., Hawkes, E. and Wood, R.J., "A novel low-profile shape memory alloy torsional actuator", Smart Materials and Structures, Vol. 19, No. 12, (2010), 125014. doi: 10.1088/0964-1726/19/12/125014.
  49. Chung, J.-H., Heo, J.-S. and Lee, J.-J., "Modeling and numerical simulation of the pseudoelastic behavior of shape memory alloy circular rods under tension–torsion combined loading", Smart Materials and Structures, Vol. 15, No. 6, (2006), 1651. doi: 10.1088/0964-1726/15/6/018.
  50. Viet, N. and Zaki, W., "Analytical investigation of the behavior of concrete beams reinforced with multiple circular superelastic shape memory alloy bars", Composite Structures, Vol. 210, (2019), 958-970. doi: 10.1016/j.compstruct.2018.11.080.
  51. Viet, N. and Zaki, W., "Bending model for functionally graded porous shape memory alloy/poroelastic composite cantilever beams", Applied Mathematical Modelling, Vol. 97, (2021), 398-417. doi: 10.1016/j.apm.2021.03.058.
  52. Auricchio, F., Taylor, R.L. and Lubliner, J., "Shape-memory alloys: Macromodelling and numerical simulations of the superelastic behavior", Computer methods in applied mechanics and engineering, Vol. 146, No. 3-4, (1997), 281-312. doi: 10.1016/S0045-7825(96)01232-7.
  53. Sun, Q.P. and Hwang, K.C., "Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys—i. Derivation of general relations", Journal of the Mechanics and Physics of Solids, Vol. 41, No. 1, (1993), 1-17. doi: 10.1016/0022-5096(93)90060-S.
  54. Auricchio, F., Bonetti, E., Scalet, G. and Ubertini, F., "Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation", International Journal of Plasticity, Vol. 59, (2014), 30-54. doi: 10.1016/j.ijplas.2014.03.008.
  55. Arghavani, J., Auricchio, F. and Naghdabadi, R., "A finite strain kinematic hardening constitutive model based on hencky strain: General framework, solution algorithm and application to shape memory alloys", International Journal of Plasticity, Vol. 27, No. 6, (2011), 940-961. doi: 10.1016/j.ijplas.2010.10.006.
  56. Gao, X., Huang, M. and Brinson, L.C., "A multivariant micromechanical model for smas part 1. Crystallographic issues for single crystal model", International Journal of Plasticity, Vol. 16, No. 10, (2000), 1345-1369. doi: 10.1016/S0749-6419(00)00013-9.
  57. Patoor, E., Lagoudas, D.C., Entchev, P.B., Brinson, L.C. and Gao, X., "Shape memory alloys, part i: General properties and modeling of single crystals", Mechanics of Materials, Vol. 38, No. 5, (2006), 391-429. doi: 10.1016/j.mechmat.2005.05.027.
  58. Lagoudas, D.C., Entchev, P.B., Popov, P., Patoor, E., Brinson, L.C. and Gao, X., "Shape memory alloys, part ii: Modeling of polycrystals", Mechanics of Materials, Vol. 38, No. 5, (2006), 430-462. doi: 10.1016/j.mechmat.2005.08.003.
  59. Boyd, J.G. and Lagoudas, D.C., "Thermomechanical response of shape memory composites", Journal of Intelligent Material Systems and Structures, Vol. 5, No. 3, (1994), 333-346. doi: 10.1177/1045389X9400500306.
  60. Tanaka, K. and Nagaki, S., "A thermomechanical description of materials with internal variables in the process of phase transitions", Archive of Applied Mechanics, Vol. 51, No. 5, (1982), 287-299. doi: 10.1007/BF00536655.
  61. Liang, C. and Rogers, C.A., "One-dimensional thermomechanical constitutive relations for shape memory materials", Journal of Intelligent Material Systems and Structures, Vol. 8, No. 4, (1997), 285-302. doi: 10.1177/1045389X9000100205.
  62. Brinson, L.C., "One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable", Journal of Intelligent Material Systems and Structures, Vol. 4, No. 2, (1993), 229-242. doi: 10.1177/1045389X9300400213.
  63. Ivshin, Y. and Pence, T.J., "A thermomechanical model for a one variant shape memory material", Journal of Intelligent Material Systems and Structures, Vol. 5, No. 4, (1994), 455-473. doi: 10.1177/1045389X9400500402.
  64. Ivshin, Y. and Pence, T.J., "A constitutive model for hysteretic phase transition behavior", International Journal of Engineering Science, Vol. 32, No. 4, (1994), 681-704. doi: 10.1016/0020-7225(94)90027-2.
  65. Simo, J. and Taylor, R., "A return mapping algorithm for plane stress elastoplasticity", International Journal for Numerical Methods in Engineering, Vol. 22, No. 3, (1986), 649-670. doi: 10.1002/nme.1620220310.
  66. Bertram, A., "Thermo-mechanical constitutive equations for the description of shape memory effects in alloys", Nuclear Engineering and Design, Vol. 74, No. 2, (1983), 173-182. doi: 10.1016/0029-5493(83)90054-7.
  67. Leclercq, S., Bourbon, G. and Lexcellent, C., "Plasticity like model of martensite phase transition in shape memory alloys", Le Journal de Physique IV, Vol. 5, No. C2, (1995), C2-513-C512-518. doi: 10.1051/jp4:1995279.
  68. Courant, R. and Hilbert, D., "Methods of mathematical physics: Partial differential equations, John Wiley & Sons, (2008).
  69. Brigham, E.O. and Morrow, R., "The fast fourier transform", IEEE Spectrum, Vol. 4, No. 12, (1967), 63-70. doi: 10.1109/MSPEC.1967.5217220.