On the Optimal Damping of a Vibrating Shape Memory Alloy Rod

[+] Author and Article Information
Eduard R. Oberaigner, Franz D. Fischer

Institute of Mechanics, Montanuniversität Leoben, Leoben, Austria

Kikuaki Tanaka

Department of Aerospace Engineering, Tokyo Metropolitan Institute of Technology, Hino/Tokyo, Japan

J. Eng. Mater. Technol 124(2), 97-102 (Mar 26, 2002) (6 pages) doi:10.1115/1.1310306 History: Received December 03, 1999; Revised March 17, 2000; Online March 26, 2002
Copyright © 2002 by ASME
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George, P. E., Takashashi, S., Trolier-McKinstry, S., Uchino, K., and Wun-Fogle, M., 1995, “Materials for Smart Systems,” MRS.
George, P. E., Gotthardt, R. Kazuhiro, O., Trolier-McKinstry and Wun-Fogle, M., 1997, “Materials for Smart Systems II”, MRS.
Birman,  V., 1997, “Review of Mechanics of Shape Sputter-Deposited Ti-Ni Thin Films,” J. Phys. IV, Coll. 5–8, pp. 5–8,677.
Skrobanek, K. D., Kohl, M., and Miyazaki, S., eds., 1996, “Stress-Optimized Shape Memory Microactuators,” Proceedings of Third ICIM/ECSSM.
Miyazaki,  S., , 1995, “Shape Memory Effects Associated with the Martensitic and R-Phase Transformations in Sputter-Deposited Ti-Ni Thin Films,” J. Phys. IV, Coll. 5–8, pp. 677–682.
Miyazaki, S., 1996, “Development and Characterization of Shape Memory Alloys,” Shape Memory Alloys, Fremond, M., and Miyazaki, S., eds., Springer-Verlag, Wien, New York, pp. 69–147.
Tanaka,  K., 1986, “A Thermomechanical Sketch of Shape Memory Effect: One-dimensional Tensile Behavior,” Res. Mech., 18, pp. 251–263.
Tanaka,  K., Kobayashi,  S., and Sato,  Y., 1986, “Thermomechanics of Transformation Pseudoelasticity and Shape Memory Effect in Alloys,” Int. J. Plast., 2, pp. 59–72.
Fischer,  F. D., Berveiller,  M., Tanaka,  K., and Oberaigner,  E. R., 1994, “Continuum Mechanical Aspects of Phase Transformations in Solids,” Arch. Appl. Mech.,64, pp. 54–85.
Fischer,  F. D., Sun,  Q. P., and Tanaka,  K., 1996, “Transformation-Induced Plasticity,” Appl. Mech. Rev., 49, pp. 317–364.
Tanaka,  K., Nishimura,  F., Tobushi,  H., Oberaigner,  E. R., and Fischer,  F. D., 1995, “Thermomechanical Behavior of an Fe-based Shape Memory Alloy: Transformation Conditions and Hystereses,” J. Phys. IV Coll. C8, p. 5, pp. 463–468.
Brinson,  L. C., and Huang,  M. S., 1996, “Simplifications and Comparisons of Shape Memory Alloy Constitutive Models,” J. Intell. Mater. Syst. Struct., 7, pp. 108–114.
Liang,  C., and Rogers,  C. A., 1997a, “One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials,” J. Intell. Mater. Syst. Struct., 8, pp. 285–302.
Liang,  C., and Rogers,  C. A., 1997b, “Design Of Shape Memory Alloy Actuators,” J. Intell. Mater. Syst. Struct., 8, pp. 303–313.
Wu,  K., Yang,  F., Pu,  Z., and Shi,  J., 1996, “The Effect of Strain Rate on Detwinning and Superelastic Behavior of NiTi Shape Memory Alloys,” J. Intell. Mater. Syst. Struct., 7, pp. 138–144.
Miyazaki,  S., , 1981, “Lüders-like Deformation Observed in the Transformation Pseudoelasticity of a Ti-Ni Alloy,” Scr. Metall., 15, pp. 853–856.
Shaw,  J. A., and Kyriakides,  S., 1995, “Thermomechanical Aspects of NiTi,” J. Mech. Phys. Solids, 43, pp. 1243–1281.
Abeyaratne,  A., and Knowles,  J. K., 1993, “A Continuum Model of Thermoelastic Solids Capable of Undergoing Phase Transitions,” J. Mech. Phys. Solids, 41, pp. 541–571.
Raniecki,  B., and Tanaka,  K., 1994, “On the Thermodynamic Driving Force for Coherent Phase Transformations,” Int. J. Eng. Sci., 32, pp. 1845–1858.
Bruno,  O. P., Leo,  P. H., and Reitich,  F., 1995, “Free Boundary Conditions at Austenite Martensite Interfaces,” Phys. Rev. Lett., 74, pp. 746–749.
Zhong,  S. G., and Batra,  R. C., 1996, “Modeling of Macroscopic Response of Phase Transforming Materials under Quasi-Static Loading,” J. Elast., 44, pp. 145–160.
Bekker,  A., and Brinson,  L. C., 1997, “Temperature-Induced Phase Transformation in a Shape Memory Alloy: Phase Diagram Based Kinetics Approach,” J. Mech. Phys. Solids, 54, pp. 949–988.
Bhattacharyya,  A., Lagoudas,  D. C., Wang,  Y., and Kinra,  V., 1995, “On the Role of Thermoelectric Heat Transfer in the Design of SMA Activators: Theoretical Modeling and Experiment,” Smart Mater. Struct., 4, pp. 252–263.
Oberaigner,  E. R., Tanaka,  K., and Fischer,  F. D., 1996, “Investigation of the Damping Behavior of a Vibrating Shape Memory Alloy Rod using a Micromechanical Model,” Smart Mater. Struct., 3, pp. 456–463.
Oberaigner, E. R., Tanaka, K., and Fischer, F. D., 1999, “Damping of a Vibrating SMA Rod through Phase Transformation,” Proceedings IUTAM Symposium on “Variations of Domains and Free Boundary Problems,” Argoul, P., et al., ed., Kluwer Academic, pp. 35–44.
Oberaigner,  E. R., Fischer,  F. D., and Tanaka,  K., 1993, “A New Micromechanical Formulation of Martensite Kinetics Driven by Temperature and/or Stress,” Arch. Appl. Mech.,63, pp. 522–533.
Oberaigner,  E. R., Fischer,  F. D., and Tanaka,  K., 1994, “The Influence of Transformation Kinetics on Stress-Strain Relations of Shape Memory Alloys in Thermomechanical Processes,” J. Intell. Mater. Syst. Struct., 5, pp. 474–486.
Butkovskiy, A. G., 1982, Green’s Functions and Transfer Functions Handbook, Ellis Harwood Limited, Chichester.
Golberg, M. A., ed., 1990, Numerical Solution of Integral Equations, Plenum, New York.
Pipkin, A. C., 1991, A Course on Integral Equations, Springer-Verlag, New York.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986, Numerical Recipes, Cambridge University Press, Cambridge.
Pouchtchaenko, O. V., 2000, personal communication.
Belyaev,  S. P., Volkov,  A. E., and Voronkov,  A. V., 1999, “Mechanical Oscillations in TiNi Under Synchronized Martensite Transformations,” ASME J. Eng. Mater. Technol., 21, pp. 105–107.
Likhachev,  V. A., and Pouchtchaenko,  O. V., 1996, “Calculations for a Thermomechanical Coupling by the Methods of the Structure-Analytical Theory,” Tech. Phys., 41, pp. 1127–1131.
Banks, H. T., Smith, R. C., and Wang, Y., 1996, Smart Materials Structures: Modeling, Estimation and Control, Wiley, Chichester, pp. 225–238.


Grahic Jump Location
Elastic rod under initial stress Σ0
Grahic Jump Location
Stress-temperature plane
Grahic Jump Location
Elastic and inelastic domain on the damped rod. Schematically.
Grahic Jump Location
Schematic stress-strain curve
Grahic Jump Location
E/Ei=Emech(t)/Emech(0) in dependence of the reduced time t/tr. Circles: T(x=0,t)=237 K. Squares: Topt(t=0)=241 K. Triangles: Topt(t=0)=237 K.
Grahic Jump Location
Topt(t) for two starting values and a constant temperature at the fixed end of the rod. Circles: T(x=0,t)=237 K. Squares: Topt(t=0)=241 K. Triangles: Topt(t=0)=237 K.
Grahic Jump Location
Domains along the rod for different time steps. Elastic domains are white, inelastic domains are gray.




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