Numerical Characterization of the Chaotic Nonregular Dynamics of Pseudoelastic Oscillators

Previous studies on the nonlinear dynamics of pseudoelastic oscillators showed the occurrence of chaotic responses in some ranges of the system parameters [1,2]. The restoring force was modeled by a thermomechanically consistent model with four state variables [3]. In comparison with the simpler polynomial constitutive laws considered for example in [4], the present model is characterized by more governing parameters and it is therefore interesting to understand whether nonregular responses only occur in isolated zones or are actually robust outcomes. The relevant analyses need to be carried out through some synthetic measure of non-regularity that has to be reliable and computationally simple in order to allow for systematic investigations in meaningful parameter spaces.

Whereas the numerical characterization of chaos in smooth dynamical systems is often carried out via the computation of Lyapunov exponents, in the present case the computation of such exponents, following, for example [5], does not seem to be a convenient strategy.


Lyapunov Exponent Shape Memory Bifurcation Diagram Chaotic Motion Excitation Amplitude 
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  1. 1.
    Bernardini D, Rega G (2005) Thermomechanical modeling, nonlinear dynamics and chaos in shape memory oscillators, Mathematical and Computer Modelling of Dynamical Systems 11, 291–314.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bernardini D, Rega G (2007) On the characterization of the chaotic response in the nonlinear dynamics of pseudoelastic oscillators, Proceedings of the 18th AIMETA Conference, Brescia (Italy), September 11–14.Google Scholar
  3. 3.
    Bernardini D, Pence TJ (2002) Models for one-variant shape memory materials based on dissipation functions, International Journal of Non-linear Mechanics 37, 1299–1317.MATHCrossRefGoogle Scholar
  4. 4.
    Savi MA, Pacheco PMCL (2002) Chaos and hyperchaos in shape memory systems, International Journal of Bifurcation and Chaos 12, 645–667.CrossRefGoogle Scholar
  5. 5.
    Müller PC (1995) Calculation of Lyapunov exponents for dynamic systems with discontinuities, Chaos Solitons and Fractals 5, 1671–1681.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Awrejcewicz J, Dzyubak L, Grebogi C (2004) A direct numerical method for quantifying regular and chaotic orbits, Chaos Solitons Fractals 19, 503–507.MATHCrossRefGoogle Scholar
  7. 7.
    Awrejcewicz J, Dzyubak L, Grebogi C (2005) Estimation of chaotic and regular (stick-slip and slip-slip) oscillations exhibited by coupled oscillators with dry friction, Nonlinear Dynamics 42, 383–394.MATHCrossRefMathSciNetGoogle Scholar

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© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Strutturale e GeotecnicaSapienza Università di RomaRomaItaly

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