Nonlinear Dynamic Characteristics of Giant Magnetostrictive Nanofilm-SMA Composite Beam in Axial Stochastic Excitation

Abstract:

In this paper, nonlinear dynamic characteristics of giant magnetostructive nanofilm-shape memory alloy (SMA) composite beam in axial stochastic excitation were studied. Von del Pol nonlinear difference item was introduced to interpret the hysteresis phenomenon of the strain-stress curve of SMA, and the hysteretic nonlinear dynamic model of giant magnetostructive nanofilm-SMA composite beam in axial stochastic excitation was developed. The steady-state probability density function and the joint probability density function of the system were obtained in quasi-nonintegrable Hamiltonian system theory. The result of simulation shows that the stability of the trivial solution varies with bifurcation parameter, and stochastic Hopf bifurcation appears in the process. The result is helpful to stochastic bifurcation control to giant magnetostructive nanofilm-SMA composite beam.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 173-177
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.173
• Online since: January 2013
• Authors: Zhi Wen Zhu, Wei Guo, Jia Xu
• Keywords: Giant Magnetostrictive Nanofilm, Hysteretic Nonlinearity, Shape Memory Alloy (SMA), Stochastic Bifurcation, Stochastic Optimal Control

References

[1] K. T. Lau, Vibration characteristics of SMA composite beams with different boundary conditions, Mat. Des. 23 (2002) 741-749.

DOI: 10.1016/s0261-3069(02)00069-9

[2] K. M. Liew, J. Ren, S. Kitipornchai, Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method, Eng. Ana. Bou. Ele. 28 (2004) 497-507.

DOI: 10.1016/s0955-7997(03)00103-6

[3] A. Zbiciak, Dynamic analysis of pseudoelastic SMA beam, Int. J. Mech. Sci. 52 (2010) 56-64.

[4] F. Scarpa, M. Ruzzene, M. R. Hassan, Spectral element formulation for SMA beams under random vibration excitation, Sma. Str. Mat. 5387 (2004) 286-293.

DOI: 10.1117/12.545968

[5] S. M. T. Hashemi, S. E. Khadem, Modeling and analysis of the vibration behavior of a shape memory alloy beam, Int. J. Mech. Sci. 48 (2006) 44-52.

DOI: 10.1016/j.ijmecsci.2005.09.011

[6] M. Collet, E. Foltete, C. Lexcellent, Analysis of the behavior of a shape memory alloy beam under dynamical loading, Euro. J. Mech. A. 20 (2001) 615-630.

DOI: 10.1016/s0997-7538(01)01159-7

[7] Z. Y. Jia, W. Liu, Y. S. Zhang, A nonlinear magnetomechanical coupling model of giant magnetostrictive thin films at low magnetic fields, Sen. Act. A. 128 (2006) 158-164.

DOI: 10.1016/j.sna.2006.01.018

[8] H. Y. Chen, Q. X. Yang, S. Z. Liu, Element-free Galerkin modeling of giant magnetostrictive thin films, IEEE Trans. Mag. 41 (2005) 1512-1515.

DOI: 10.1109/tmag.2005.845075

[9] Q. X. Yang, H. Y. Chen, S. Z. Liu, Dynamic modeling of a magnetic system constructed with giant magnetostrictive thin film using element-free Galerkin method, IEEE Trans. Mag. 42 (2006) 939-942.

DOI: 10.1109/tmag.2006.871669

[10] S. Masuda, Y. Matsumura, Y. Nishi, High responsiveness composite mover device constructed with positive and negative giant magnetostrictive films, J. Jap. Ins. Met. 70 (2006) 166-168.

DOI: 10.2320/jinstmet.70.166

[11] W. Liu, X. H. Jia, F. J. Wang, An in-pipe wireless swimming microrobot driven by giant magnetostrictive thin film, Sen. Act. A. 160 (2010) 101-108.

DOI: 10.1016/j.sna.2010.04.014

[12] N. Tiercelin, P. Pernod, V. Preobrazhensky, Non-linear actuation of cantilevers using giant magnetostrictive thin films, Ultras. 38 (2000) 64-66.

DOI: 10.1016/s0041-624x(99)00061-x

[13] N. Tiercelin, V. Preobrazhensky, P. Pernod, Sub-harmonic excitation of a planar magneto-mechanical system by means of giant magnetostrictive thin films, J. Mag. Mag. Mat. 210 (2000) 302-308.

DOI: 10.1016/s0304-8853(99)00658-7

[14] K. Tanaka, A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior, Res. Mech. 18 (1986) 251-263.

[15] J. G. Boyd, D. C. Lagoudas, Thermodynamical constitutive model for shape memory materials, Int. J. Pla. 12 (1996) 805-842.

DOI: 10.1016/s0749-6419(96)00030-7

[16] L. C. Brinson, One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with nonconstant material functions and redefined martensite internal variable, J. Int. Mat. Sys. Str. 4 (1993) 229-242.

DOI: 10.1177/1045389x9300400213

[17] E.J. Graesser, F.A. Cozzarelli, A proposed three-dimensional constitutive model for Shape memory alloys, J. Int. Mat. Sys. Str. 5 (1994) 78-89.

DOI: 10.1177/1045389x9400500109

[18] Y. Ivshin, T. J. Pence, Thermomechanical model for a one variant shape memory material, J. Int. Mat. Sys. Str. 5 (1994) 455-473.

DOI: 10.1177/1045389x9400500402

[19] F. Auricchio, J. Lubliner, Uniaxial model for shape-memory alloys, Int. J. Sol. Str. 34 (1997) 3601-3618.

DOI: 10.1016/s0020-7683(96)00232-6

[20] Z. W. Zhu, J. Wang, J. Xu, Modeling of shape memory alloy based on hysteretic nonlinear theory, App. Mech. Mat. 44 (2010) 537-541.

DOI: 10.4028/www.scientific.net/amm.44-47.537

[21] M. A. Savi, P. M. Pacheeo, M. B. Braga, Chaos in shape memory two-bar truss, Int. J. Non. Mech. 37 (2002) 1387-1395.

DOI: 10.1016/s0020-7462(02)00029-x

[22] A. S. Kumar, S. M. Sivakumar, Numerical simulation of shape memory effect and superelasticity in SMA wires and beam, Sma. Mat. Str. Sys. 5062 (2003) 936-943.

DOI: 10.1117/12.514376

[23] M. S. Speicher, R. DesRoches, R. T. Leon, Experimental results of a NiTi shape memory alloy (SMA)-based recentering beam-column connection, Eng. Str. 33 (2011) 2448-2457.

DOI: 10.1016/j.engstruct.2011.04.018