Analysis of chaotic non-isothermal solutions of thermomechanical shape memory oscillators
1 Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland
2 Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Universita di Roma, via Antonio Gramsci 53, 00197 Roma, Italy
Received: 4 June 2013
Revised: 2 August 2013
Published online: 30 September 2013
Shape memory materials exhibit strong thermomechanical coupling, so that temperature variations occur during mechanical loading and unloading. In previous works the nonlinear dynamics of pseudoelastic oscillators subject to an harmonic force has been studied and the possibility of non-regular chaotic responses has been thoroughly documented. Instead of the standard Lyapunov exponent treatment, the statistical 0–1 test based on the asymptotic properties of a Brownian motion chain was successively applied to reveal the chaotic nature of trajectories in the special case in which temperature variations were neglected. In this work, the 0–1 test is applied to fully non-isothermal trajectories. To improve its reliability the test has been applied to the time-histories of maxima and minima of each trajectory, in each component. The obtained results have been validated and confirmed by the corresponding Fourier spectra. Non-regular solutions with different levels of chaoticity have been analyzed and their qualitative difference is reflected by the different values to which the control parameter K asymptotically converge.
© EDP Sciences, Springer-Verlag, 2013