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Shock and Vibration
Volume 11, Issue 2, Pages 67-80

Bifurcations and Crises in a Shape Memory Oscillator

Luciano G. Machado,1 Marcelo A. Savi,2 and Pedro M.C.L. Pacheco3

1Instituto Militar de Engenharia, Department of Mechanical and Materials Engineering, 22.290.270, Rio de Janeiro, RJ, Brazil
2Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, 21.945.970, Rio de Janeiro, RJ, Caixa Postal 68.503, Brazil
3CEFET/RJ, Department of Mechanical Engineering, 20.271.110, Rio de Janeiro, RJ, Brazil

Received 5 May 2003; Accepted 24 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.