Analysis of shape memory alloy vibrator using harmonic balance method

Abstract

Shape memory alloy (SMA) is a very important smart material, which has been widely used in many fields, especially in vibration. Phase transformation can be induced by changing temperature and its stiffness changes accordingly. In this paper, the primary resonance vibration of a one-dimensional SMA oscillator is analyzed using the harmonic balance (HB) method. The amplitude-frequency curves of the SMA oscillator with different temperatures are drawn, and the effect of temperature and frequency on the amplitude is discussed. Then, the energy flow of SMA in the vibration process is researched by the power flow analysis (PFA) approach. The time-averaged input power (TAIP) is calculated using the analytical and numerical method, respectively, and the calculation time is compared. It is found that the difference between the analytical and numerical solutions is not significant in most cases, but the calculation time of analytical solution is only about one-tenth of that of the numerical solution, which is very important in saving computational cost, real-time control and so on. Finally, some other characteristics of energy flow in the SMA oscillator are identified.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    L.X. Wang, R.V.N. Melnik, Numerical model for vibration damping resulting from the first-order phase transformations. Appl. Math. Model. 31(9), 2008–2018 (2007)

    Article  Google Scholar 

  2. 2.

    Q. Wang, X.U. Zhiwei, Q. Zhu, Structural design of morphing trailing edge actuated by SMA. Front. Mech. Eng. 8(3), 268–275 (2013)

    ADS  Article  Google Scholar 

  3. 3.

    G. Borchert, C. Lochte, G. Carbone et al., A modular design kit for task-adaptable low-cost robots based on BaPaMan design. Front. Mech. Eng. 8(1), 33–41 (2013)

    Article  Google Scholar 

  4. 4.

    P.B.C. Leal, M.A. Savi, D.J. Hartl, Aero-structural optimization of shape memory alloy-based wing morphing via a class/shape transformation approach. Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 232(15), 2745–2759 (2018)

    Article  Google Scholar 

  5. 5.

    M.H. Moghadam, M.R. Zakerzadeh, M. Ayati, Development of a cascade position control system for an SMA-actuated rotary actuator with improved experimental tracking results. J. Braz. Soc. Mech. Sci. Eng. 41(10), 407 (2019)

    Article  Google Scholar 

  6. 6.

    Y. Zhishan, L. Dezhi, C. Yue, F. Zhaowei, L. Juntao, S. Zaiyan, Z. Ming, X. Xiaodong, W. Xingquan, Grikin Advanced Materials Co. Ltd, Research progress on the phase transformation behavior, microstructure and property of NiTi based high temperature shape memory alloys. Rare Metal Mater. Eng. 47(7), 2269–2274 (2018)

    Google Scholar 

  7. 7.

    X. Wang, S. Kustov, J. Van Humbeeck, A short review on the microstructure, transformation behavior and functional properties of NiTi shape memory alloys fabricated by selective laser melting. Materials 11(9), 1683 (2018)

    ADS  Article  Google Scholar 

  8. 8.

    C.A. Canbay, A. Tataroğlu, W.A. Farooq, A. Dere, A. Karabulut, M. Atif et al., CuAlMnV shape memory alloy thin film based photosensitive diode. Mater. Sci. Semicond. Process. 107, 104858 (2020)

    Article  Google Scholar 

  9. 9.

    G. Song, N. Ma, H.N. Li, Application of shape memory alloys in civil structures. Eng. Struct. 28, 1266–1274 (2006)

    Article  Google Scholar 

  10. 10.

    X. He, Z. Tong, H. Du et al., Modeling microstructure evolution in shape memory alloy rods via Legendre wavelets collocation method. J. Mater. Sci. 54(23), 14400–14413 (2019)

    ADS  Article  Google Scholar 

  11. 11.

    C.A. Canbay, T. Polat, Thermal and structural alternations in CuAlMnNi shape memory alloy by the effect of different pressure applications. Phys. B Phys. Condens. Matter 521, 331–338 (2017)

    ADS  Article  Google Scholar 

  12. 12.

    C.A. Canbay et al., Investigation of thermoelastical martensitic transformations and structure in new composition of CuAlMnTi shape memory alloy. J. Mater. Electron. Dev. 1(1), 60–64 (2019)

    Google Scholar 

  13. 13.

    L. Wang, R.V.N. Melnik, Nonlinear dynamics of shape memory alloy oscillators in tuning structural vibration frequencies. Mechatronics 22(8), 1085–1096 (2012)

    Article  Google Scholar 

  14. 14.

    G.L. McGavin, G. Guerin, Real-time seismic damping and frequency control of steel structures using Nitinol wire. Proc SPIE 4696, 176–184 (2002)

    ADS  Article  Google Scholar 

  15. 15.

    S.S. Oueini, A.H. Nayfeh, J.R. Pratt, A nonlinear vibration absorber for flexible structures. Nonlinear Dyn. 15(3), 259–282 (1998)

    Article  Google Scholar 

  16. 16.

    J. Yang, Y.P. Xiong, J.T. Xing, Dynamics and power flow behavior of a nonlinear vibration isolation system with a negative stiffness mechanism. J. Sound Vib. 332(1), 167–183 (2013)

    ADS  Article  Google Scholar 

  17. 17.

    A. Masuda, M. Noori, Optimisation of hysteretic characteristics of damping devices based on pseudoelastic shape memory alloys. Int. J. Nonlinear Mech. 37, 1375–1386 (2002)

    ADS  Article  Google Scholar 

  18. 18.

    E. Rustighi, M.J. Brennan, B.R. Mace, A shape memory alloy adaptive tuned vibration absorber: design and implementation. Smart Mater. Struct. 14, 19–28 (2005)

    ADS  Article  Google Scholar 

  19. 19.

    S. Saadat, J. Salichs, M. Noori, Z. Hou, H. Davoodi, I. Bar-on et al., An overview of vibration and seismic applications of NiTi shape memory alloy. Smart Mater. Struct. 11, 218–229 (2002)

    ADS  Article  Google Scholar 

  20. 20.

    J. Yang, Y.P. Xiong, J.T. Xing, Nonlinear power flow analysis of the Duffing oscillator. Mech. Syst. Signal Process 45(2), 563–578 (2014)

    ADS  Article  Google Scholar 

  21. 21.

    H.G.D. Goyder, R.G. White, Vibrational power flow from machines into built-up structures. J. Sound Vib. 68(1), 59–117 (1980)

    ADS  Article  Google Scholar 

  22. 22.

    Y.P. Xiong, J.T. Xing, W.G. Price, A power flow mode theory based on a system’s damping distribution and power flow design approach. Proc. R. Soc. A: Math. Phys. Eng. Sci. 461(2063), 3381–3411 (2005)

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

    J. Yang, Y.P. Xiong, J.T. Xing, Investigations on a nonlinear energy harvesting device consisting of a flapping foil and an electro-magnetic generator using power flow analysis, in 23th Biennial Conference on Mechanical Vibration and Noise, ASME IDETC/CIE Conferences, Washington, DC, USA, August 29–21, Washington (2011), pp. 1–8

  24. 24.

    J. Yang, Y.P. Xiong, J.T. Xing, Examinations of nonlinear isolators using power flow approach. in 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012), International Union of Theoretical and Applied Mechanics (IUTAM), Beijing, China, August 19–24, Beijing (2012), pp. 1–2

  25. 25.

    N. Bubner, Landau-Ginzburg model for a deformation-driven experiment on shape memory alloys. Continu Mech. Therm. 8(5), 293–308 (1996)

    Article  Google Scholar 

  26. 26.

    L.X. Wang, R.V.N. Melnik, Thermo-mechanical wave propagation in shape memory alloy rod with phase transformations. Mech. Adv. Mater. Struct. 14(8), 665–676 (2007)

    Article  Google Scholar 

  27. 27.

    S. Fan, A new extracting formula and a new distinguishing means on the one variable cubic equation. Nat. Sci. J. Hainan Teach. Coll. 2(2), 91–98 (1989)

    MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51575478 and Grant No. 61571007).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Linxiang Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Du, H., He, X., Wang, L. et al. Analysis of shape memory alloy vibrator using harmonic balance method. Appl. Phys. A 126, 568 (2020). https://doi.org/10.1007/s00339-020-03740-x

Download citation

Keywords

  • Shape memory alloy
  • Analytical solution
  • Amplitude–frequency characteristics
  • Power flow analysis