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Vibration Analysis of a Beam with Embedded Shape Memory Alloy Wires

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Abstract

In this study, analytical relations for evaluating the exact solution of natural frequency and mode shape of beams with embedded shape memory alloy (SMA) wires are presented. Beams are modeled according to Euler-Bernoulli, Timoshenko and third order beam (Reddy) theories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities, the effect of different mechanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.

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References

  1. Sohn, J.W., Han, Y.M., Choi, S.B., Lee, Y.S. and Han, M.S., Vibration and position tracking control of a flexible beam using SMA wire actuators. Journal of Vibration and Control, 2009, 15: 263–281.

    Article  MathSciNet  Google Scholar 

  2. Kang, K.W., Kim, H.J. and Kim, J.K., The role of shape memory alloy on impact response of glass/epoxy laminates under low temperature. Journal of Mechanical Science and Technology, 2007, 21: 1682–1688.

    Article  Google Scholar 

  3. Brinson, L.C., Huang, M.S., Boiler, C. and Brand, W., Analysis of controlled beam deflections using SMA wires. Journal of Intelligent Material Systems and Structures, 1997, 8: 12–25.

    Article  Google Scholar 

  4. Jun, L., Xiaobin, L. and Hongxing, H., Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method. Archive of Applied Mechanics, 2009, 79: 1083–1098.

    Article  Google Scholar 

  5. Raghavan, J., Bartkiewicz, T., Boyko, S., Kuprianov, M., Rajapakse, N. and Yu, B., Damping, tensile, and impact properties of superelastic shape memory alloy (SMA) fiber-reinforced polymer composites. Composites: Part B, 2010, 41: 214–222.

    Article  Google Scholar 

  6. Ni, Q.Q., Zhang, R.X., Natsuki, T. and Iwamoto, M., Stiffness and vibration characteristics of SMA/ER3 composites with shape memory alloy short fibers. Composite Structures, 2007, 79: 501–507.

    Article  Google Scholar 

  7. Du, X.W., Sun, G. and Sun, S.S., A study on the deflection of shape memory alloy (SMA) reinforced thermo-viscoelastic beam. Composites Science and Technology, 2004, 64: 1375–1381.

    Article  Google Scholar 

  8. Li, J. and Hua, H., The Effects of shear deformation on the free vibration of elastic beams with general boundary conditions. Journal of Mechanical Engineering Science: Part C, 2010, 224: 71–84.

    Article  Google Scholar 

  9. Vo, T.P. and Lee, J., Free vibration of axially loaded thin-walled composite timoshenko beams. Archive of Applied Mechanics, 2011, 81: 1165–1180.

    Article  Google Scholar 

  10. Su, X. and Cartmell, M.P., Modifications to the response of a parametrically excited cantilever beam by means of smart active elements. Journal of Mechanical Engineering Science: Part C, 2010, 224: 1573–1591.

    Google Scholar 

  11. Lee, S.K. and Kim, B., Design parametric study based fabrication and evaluation of in-pipe moving mechanism using shape memory alloy actuators. Journal of Mechanical Science and Technology, 2008, 22: 96–102.

    Article  Google Scholar 

  12. Brinson, L.C., One-dimensional constitutive behavior of shape memory alloys: thermo-mechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures, 1993 , 4: 229–242.

    Article  Google Scholar 

  13. Liang, C. and Rogers, C.A., One-dimensional thermo-mechanical constitutive relations for shape memory materials. Journal of Intelligent Material Systems and Structures, 1990, 1: 207–234.

    Article  Google Scholar 

  14. Brinson, L.C., Huang, M.S., Simplifications and comparisons of shape memory alloy constitutive models. Journal of Intelligent Material Systems and Structures, 1995, 7: 108–114.

    Article  Google Scholar 

  15. Rao, S.S., Vibration of Continuous Systems. Wiley, New Jersey, 2007.

    Google Scholar 

  16. Wang, C.M., Reddy, J.N. and Lee, K.H., Shear Deformable Beams and Plates. Elsevier, Amsterdam, 2000.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    Mehdi Barzegari, Morteza Dardel & Alireza Fathi

Authors
  1. Mehdi Barzegari
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  2. Morteza Dardel
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  3. Alireza Fathi
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Correspondence to Morteza Dardel.

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Barzegari, M., Dardel, M. & Fathi, A. Vibration Analysis of a Beam with Embedded Shape Memory Alloy Wires. Acta Mech. Solida Sin. 26, 536–550 (2013). https://doi.org/10.1016/S0894-9166(13)60048-8

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  • DOI: https://doi.org/10.1016/S0894-9166(13)60048-8

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