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.
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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)
Q. Wang, X.U. Zhiwei, Q. Zhu, Structural design of morphing trailing edge actuated by SMA. Front. Mech. Eng. 8(3), 268–275 (2013)
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)
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)
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)
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)
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)
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)
G. Song, N. Ma, H.N. Li, Application of shape memory alloys in civil structures. Eng. Struct. 28, 1266–1274 (2006)
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)
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)
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)
L. Wang, R.V.N. Melnik, Nonlinear dynamics of shape memory alloy oscillators in tuning structural vibration frequencies. Mechatronics 22(8), 1085–1096 (2012)
G.L. McGavin, G. Guerin, Real-time seismic damping and frequency control of steel structures using Nitinol wire. Proc SPIE 4696, 176–184 (2002)
S.S. Oueini, A.H. Nayfeh, J.R. Pratt, A nonlinear vibration absorber for flexible structures. Nonlinear Dyn. 15(3), 259–282 (1998)
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)
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)
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)
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)
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)
H.G.D. Goyder, R.G. White, Vibrational power flow from machines into built-up structures. J. Sound Vib. 68(1), 59–117 (1980)
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)
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
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
N. Bubner, Landau-Ginzburg model for a deformation-driven experiment on shape memory alloys. Continu Mech. Therm. 8(5), 293–308 (1996)
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)
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)
This work was supported by the National Natural Science Foundation of China (Grant No. 51575478 and Grant No. 61571007).
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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
- Shape memory alloy
- Analytical solution
- Amplitude–frequency characteristics
- Power flow analysis