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Nonlinear dynamics and chaos in coupled shape memory oscillators. (English) Zbl 1060.70512

Summary: Shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations, presented by shape memory alloys. This contribution concerns with the dynamical response of coupled shape memory oscillators. Equations of motion are formulated by assuming a polynomial constitutive model to describe the restitution force of the oscillators and, since they are associated with a five-dimensional system, the analysis is performed by splitting the state space in subspaces. Free and forced vibrations are analyzed showing different kinds of responses. Periodic, quasi-periodic, chaos and hyperchaos are all possible in this system. Numerical investigations show interesting and complex behaviors. Dynamical jumps in free vibration and amplitude variation when temperature characteristics are changed are some examples. This article also shown some characteristics related to chaos–hyperchaos transition.

MSC:

70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74N20 Dynamics of phase boundaries in solids
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