On the monotonicity of the relaxation spectrum of fractional Maxwell model of viscoelastic materials

• Autorzy: Stankiewicz A.
• Języki publikacji: EN

Abstrakty

EN

This article focuses on the relaxation spectrum of fractional Maxwell model, which is a generalization of classic viscoelastic Maxwell model to non-integer order derivatives. The analytical formula for the spectrum of relaxation frequencies is derived. Theoretical analysis of the relaxation spectrum monotonicity is conducted by using simple analytical methods and illustrated by means of numerical examples. The necessary and sufficient conditions for the existence and uniqueness of the maximum of relaxation spectrum are stated and proved. The analytical formulas for minimum and maximum of the relaxation spectrum are derived. Also, a few useful properties concerning the relaxation spectrum monotonicity and concavity are given in the mathematical form of simple inequalities expressed directly in terms of the fractional Maxwell model parameters, which can be used to simplify the calculations and analysis.

Słowa kluczowe

EN

fractional calculus; viscoelasticity; fractional Maxwell model; relaxation spectrum; maximum of relaxation spectrum

• Wydawca: Polish Academy of Sciences, Branch in Lublin
• Czasopismo: ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
• Rocznik: 2018
• Tom: Vol. 7, No 1
• Strony: 117--125
• Opis fizyczny: Bibliogr. 25 poz., rys., wz.

Twórcy

autor

Stankiewicz A.

• Department of Technology Fundamentals, University of Life Sciences in Lublin, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).