Dynamics of thermally activated shape memory alloy autoparametric systems with two pendulums

Sado, Danuta; Pietrzakowski, M.

doi:10.1016/j.ijnonlinmec.2009.11.014

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…1,2 The non-linear dynamics of shape memory oscillators (SMOs) has been intensively studied in recent years. [3][4][5][6][7][8][9][10][11][12] Shape memory materials exhibit a complex thermomechanical behaviour and various approaches are possible for their constitutive modelling 1,2,13 The study of the non-linear dynamics of SMOs has been undertaken essentially by means of two of them. On one hand, polynomial constitutive models inspired to Falk model 2 have been used in several works.…”

Section: Introductionmentioning

confidence: 99%

“…On one hand, polynomial constitutive models inspired to Falk model 2 have been used in several works. 3,4,10,11 This type of modelling has the advantage to permit a direct use of all the standard tools of smooth nonlinear dynamics, whereas it provides a simplified, indirect description of hysteresis at a fixed constant temperature. On the other hand, fully thermomechanical models based on one or more internal variables associated with the fraction or the type of martensite have been used in many works.…”

Section: Introductionmentioning

confidence: 99%

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Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Bernardini

Rega

Litak

et al. 2012

Proceedings of the Institution of Mechanical Engineers, Part K:

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Shape memory oscillators are thermomechanical hysteretic systems that, in a wide range of model parameters, can exhibit complex non-periodic non-linear dynamic responses under the excitation of a periodic force. In this study, the statistical 0-1 test based on the asymptotic properties of a Brownian motion chain is applied to periodic and nonperiodic isothermal trajectories to examine the type of motion. The analysis is based on the computation of the control parameter K that approaches asymptotically 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent of the integration procedure, being based on the characteristic sampling distance between the points of the analysed time series. The numerical results show that the test is able to unambiguously distinguish periodic from chaotic trajectories.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Bernardini

Rega

Litak

et al. 2012

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…When employed in dynamical systems, superelastic SMA elements may induce non-regular chaotic responses, as shown for example in [3][4][5][6][7][8][9][10][11]. The eventual presence of such chaotic motions may be an important aspect considered in the design of application and, for this reason, it is very important to be able to detect them.…”

Section: Introductionmentioning

confidence: 99%

Recurrence analysis of regular and chaotic motions of a superelastic shape memory oscillator

et al. 2017

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Abstract. The recurrence analysis is a promising tool for diagnostics of periodic and chaotic solutions, as well as identifying bifurcations. This paper deals with the application of this analysis for the first time to identify regular and non-regular motions of a superelastic shape memory alloy oscillator. The numerical analyses show that the method is capable of distinguishing periodic and chaotic trajectories. Recurrence quantities are applied, showing that different approaches are possible to establish the distinction between periodic and chaotic signals. Basically, recurrence entropy, trapping time, and characteristic recurrence time are considered.

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“…-those which studies the mathematical pendulum which is hanged by an element (rod, cable) of negligible mass; the pendulum can be excited or not, with or without damping [1,2,3,4];…”

Section: Introductionmentioning

confidence: 99%

The Study of the Pendulum with Heavy Neo-Hookean Rod

Stănescu

Popa

2013

AMM

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The present paper is a generalization of the problem of a rubber spring pendulum discussed by Bhattacharyya in 2000 and Stănescu in 2011, which studied the case of the neo-Hookean rod without mass. In our paper we consider that the mass of the neo-Hookean rod is not negligible and its deformation is realized such that at any moment of time the rod can be treated as a homogeneous rigid bar of variable length. Using the second order Lagrange equations we obtained the equations of motion in the most general case and we identified as particular cases the situations presented in the bibliography. We also performed a study of the equilibrium positions and their stability. A study of the small oscillations about the stable equilibrium positions is realized too. The theoretical results are finally compared to those obtained by numerical simulation.

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Dynamics of thermally activated shape memory alloy autoparametric systems with two pendulums

Cited by 7 publications

References 11 publications

Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Recurrence analysis of regular and chaotic motions of a superelastic shape memory oscillator

The Study of the Pendulum with Heavy Neo-Hookean Rod

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