Search for Periodic Regimes in an Energy-Harvester Model by Simulation
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I. MATHEMATICAL MODELING SEARCH FOR PERIODIC REGIMES IN AN ENERGY-HARVESTER MODEL BY SIMULATION V. V. Fomichev,1 A. V. Il’in,2 A. I. Rogovskii,3 G. D. Todorov,4 and Ya. P. Sofronov5
UDC 517.926
A model of an energy harvester is considered a system intended for the conversion of residual thermal energy into electric energy. Periodic motions are a key factor in the operation of the harvester. We search for model parameters that produce self-oscillations in the systems. The problem is solved by numerical simulation and evolutionary computation. Keywords: nonlinear systems, self-oscillations, evolutionary computation.
Introduction An energy harvester is a device that converts the residual energy of a process into useful energy. Currently, energy harvesters are widely used in engineering applications and their design is discussed in numerous publications (see, e.g., [1, 2, 3, 4, 5] and the references therein). Useful energy is generally supplied in the form of electric energy. The initial energy for harvesting may take different forms, such as solar energy [6, 7, 8], vibration energy [9, 10, 11], thermal energy [12, 13, 14, 15], and other forms [16]. Energy harvesters often use so-called shape memory alloys (SMA) [14, 17, 15]. In the present article, we consider a mathematical model of an SMA harvester proposed in [14]. We determine the model parameters for which the harvester generates useful energy. Statement of the Problem We consider a thermo-electromechanical device that converts thermal energy into electrical energy. The device consists of a shape-memory wire, a piezoelectric cantilever beam, and a hot plate. The hot plate is attached to a moving hinge and may rotate (see Fig. 1). This design was proposed in [14]. To generate useful energy, the system must operate in a periodic regime: first the cold wire (see Fig. 1a) is heated and contracts (due to its SMA properties), rotating the hot plate (see Fig. 1b). The rotation of the plate reduces the quantity of heat transmitted from the plate to the wire, the wire cools off, and the plate returns to its initial position. Then the process is repeated. Our objective is to determine what parameters support such periodic motion in the model. 1
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia; e-mail: fomichev@ cs.msu.ru. 2 Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia; e-mail: [email protected]. 3 Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia; e-mail: [email protected]. 4 Sofia Technical University, Sofia, Bulgaria; e-mail: [email protected]. 5 Sofia Technical University, Sofia, Bulgaria; e-mail: [email protected]. Translated from Prikladnaya Matematika i Informatika, No. 63, 2020, pp. 5–21. 1046-283X/20/3103–0293
© 2020
Springer Science+Business Media, LLC
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V. V. F OMICHEV, A. V. I L’ IN , A. I. ROGOVSKII , G. D. T ODOROV, AND YA . P. S OFRONOV
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(a)
(b) Fig. 1
Consider the
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