On the Existence of a Periodic Mode in a Nonlinear System

Fursov, A. S.; Mitrev, Rosen; Крылов, П. А.; Todorov, T.

doi:10.1134/s0012266121080127

Cited by 9 publications

(1 citation statement)

References 2 publications

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“…A peculiarity of thermomechanical models with SMAs are the nonlinearities arising from the hysteresis in the stress-strain, stress-temperature, and temperature-strain relationships. The existence conditions of oscillatory modes of nonlinear thermomechanical self-excited systems with hysteresis are a challenge for modern research in the field of differential equations and control theory [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Study of Self-Excited Thermomechanical Oscillator with Shape Memory Alloys

Yotov,

Todorov,

Todorov

2024

Preprint

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In this paper, a new type of self-excited thermomechanical oscillator containing an oscillating shape memory alloy (SMA) filament with two symmetrically arranged spheres is investigated. The self-excitation of the oscillations is due to a heater of constant temperature, which causes periodic contractions of the filament when it approaches it. The contracted filament moves away from the heater a distance sufficient to cool it. Under the action of the weight of the spheres, the cooled filament re-approaches the heater, causing the above processes to repeat periodically. On the basis of experimental studies, approximating functions of the heater's heat field distribution are derived. A dynamic model of the oscillator has been created, in which the minor and major hysteresis in the SMA alloy and the distribution of the heat field around the heater have been taken into account. By numerical solutions of the differential equations, the laws of motion of the spheres are obtained. The displacements of the spheres in two perpendicular directions were measured using an experimental system. The obtained experimental results validate the proposed dynamic model and its assumptions with a high degree of confidence. Conclusions are drawn about the stochastic nature of the oscillations due to the hysteresis properties of the SMA and the temperature variation of the natural frequency of the oscillating system.

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Section: Introductionmentioning

confidence: 99%