Duhem histeresisin Riemann-Liouville kesirli türevi ile modellenmesi

Bu çalışma, histerisisin hafıza etkisini göz önüne alarak, doğrusal olmayan histeresis davranışının hafıza ve kalıtım özelliğine sahip tekil olmayan Riemann-Liouville kesirli türevi açısından yorumlamayı amaçlamaktadır. Bunun için, birinci mertebeden diferansiyel denklem ile tanımlanan bir model olan Duhem histeresis göz önüne alınmış ve kesirli mertebeden bir diferansiyel denkleme uyarlanmıştır. Kesirli mertebeden Duhem histeresis analitik bir yöntem ile çözülemeyeceğinden, nümerik çözümleri elde etmek için Grünwald-Letnikov yaklaşımı kullanılmıştır. Böylece, kesirli mertebeden türevin modele etkisi bu yaklaşım göre elde edilen ve MATLAB kullanılarak çizdirilen grafikler ile gösterilmiştir. Sonuç olarak, kesirli mertebeden modelin 1 den küçük mertebeler için histerisis etkisi gösterdiği gözlemlenmiştir.

Modeling of Duhem hysteresis with Riemann-Liouville fractional derivative

In the view of memory effect of hysteresis, this work aims to interpret hysteresis nonlinearities in terms of Riemann-Liouville fractional derivative which is a singular operator with memory and hereditary properties. For this purpose, Duhem hysteresis, a model defined by a first order differential equation, is considered and adapted to a fractional order differential equation. Since the fractional order Duhem hysteresis cannot be solved by an analytical scheme, Grünwald-Letnikov approximation is used to obtain numerical solutions. Thus, the effect of fractional order derivative to Duhem hysteresis is demonstrated with graphics obtained by this approximation and plotting using MATLAB. As a result, it is observed that the fractional order model exhibits hysteresis behavior for the orders that are smaller than 1.

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Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi-Cover
  • ISSN: 1301-7985
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 1999
  • Yayıncı: Balıkesir Üniversitesi