In this paper vibration damping of a shape memory alloy rod is studied. The mathematical model includes the heat conduction equation, the stress wave equation, a kinetic law and a constitutive law. As kinetic law the Likhachev model is used, which describes the one-way effect, pseudoelasticity properties and thermal loading cycles. It is observed that the vibration amplitude of the rod decreases in this model very quickly. Results are in good agreement with earlier investigations, where other kinetic laws have been used.
Belyaev, S. P. , Vdovin, E. D., Volkov, A. E. and Voronkov, A. V.1999a. “Experimental Study and Simulation of Vibrations in TiNi Controlled by Periodic Martensitic Transformations,”Optimiz. and Control in Civil and Struct. Eng., pp. 169-173, Civil-Comp Press, Edinburgh.
2.
Belyaev, S. P. , Volkov, A. E. and Voronkov, A. V.1999b. “Mechanical Oscillations in TiNi under Synchronized Martensite Transformations,”ASME J. Eng. Mat. Technol., 121:105-107.
3.
Butkovsky, A. G.1982. “Greens Functions and Transfer Functions Handbook,”Ellis Harwood Limited Publishers, Chicester.
4.
Erglis, I. V. , Ermolaev, V. A. and Volkov, A. E.1995. “A Model of Martensitic Unelasticity Accounting for the Crystal Symmetry of the Material,”J. de Phys., IVC8:239-244.
5.
Evard, M. E. and Volkov, A. E. 1998. “Computer Simulation of the Shape Memory Effects in Fe-Mn Type Alloys Accounting for the Features of the fcc-hcp Phase Transformation,” In: Melker, A. I. (ed.), Nondestructive Testing and Computer Simulations in Mat. Science and Eng., Proceedings of SPIE, Vol. 3345, pp. 178-183.
6.
Evard, M. E. , Volkov, A. E.1999. “Modeling of Martensite Accommodation Effect on Mechanical Behaviour of Shape Memory Alloys,”ASME J. Eng. Mat. Technol., 121:102-104.
7.
Knowles, K. M. and Smith, D. A.1981. “The Crystallography of the Martensitic Transformation in Equiatomic Nickel-Titanium,”Acta metall., 29:101-110.
8.
Likhachev, V. A.1995. “Structure Analytical Theory of Martensitic Unelasticiy,”J. de Phys., IV, C8-5: 137-142.
9.
Likhachev, V. A.1996. “Theory of Martensitic Unelasticity of Crystals,”J. de Phys., IVC1:321-333.
10.
Liu, Y. and van Humbeek, J.1997. “On the Damping Behavior NiTi Shape Memor Alloy,”J. de Phys., IVC5:519-524.
11.
Oberaigner, E. R. , Tanaka, K. and Fischer, F. D. 1999. “Damping of a Vibrating SMA Rod through Phase Transformation,” In: Argoul P.et al. (eds.), Proceedings IUTAM Symposium on Variations of Domains and Free Boundary Problems, pp. 35-44, Kluwer Acad. Publ. Dordrecht, The Netherlands.
12.
Prahlad, H. and Chopra, I.2000. “Experimental Characterization of NiTi Shape Memory Alloy Wires under Uniaxial Loading Conditions,”J. Intel. Mat. Syst. Struct., 11:272-282.
13.
Tanaka, K. , Kobayashi, S. and Sato, Y.1986. “Thermomechanics of Transformation Pseudoelasticity and Shape Memory Effect in Alloys,”Iny. J. Plasticity, 2:59-72.
14.
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. de Phys., IVC8:463-468.
15.
Volkov, A. E. , Evard, M. E., Kurzeneva, L. N., Likhachev, V. A., Sakharov, V. Y. and Ushakov, V. V.1996. “Mathematical Modelling of Martensitic Inelasticity and Shape Memory Effects,”Tech. Phys., 41:1084-1101.
16.
Wu, K. , Dalip, S. K., Liu, Y. and Pu, Z.1995. “Damping Characteristics of R-Phase NiTi Shape Memory Alloys,”Proceedings SPIE, Smart Struct. Mat., Vol. 2441, pp. 139-148.
