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Chaos in Autoparametric Three Degree of Freedom System with SMA Spring

Warianty tytułu
French-Polish Seminar of Mechanics (18 ; 31.05.2010 ; Warsaw, Poland)
Języki publikacji
In this paper is studied a three degree of freedom autoparametric system with two pendulums connected by shape memory alloys (SMA) spring in the neighborhood internal and external resonance. The system consists of the body of mass mi which is hung on a spring and a damper, and two connected by SMA spring pendulums of the length l₁ and l₂ and masses m₂ and m₃ mounted to the body of mass m₁. It is assumed, that the motion of the pendulums are damped by resistive forces. Shape memory alloys have ability to change their material properties. A polynomial constitutive model is assumed to describe the behavior of the SMA spring (it was assumed that the uniaxial stress σ is a fifth-degree polynomial of the strain). The equations of motion have been solved numerically and there were studied pseudoelastic effects associated with martensitic phase transformations. It was assumed that SMA presents two stable phases: austenite and martensite. Solutions for the system response are presented for specific values of the parameters of system. It was shown that in this type system one mode of vibrations may excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities (FFT), Poincare maps and exponents of Lyapunov maybe use.
Opis fizyczny
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