INVESTIGATION OF THE MAXWELL RHEOLOGICAL MODEL USING MIKUSINSKI OPERATIONAL ALGEBRA
DOI:
https://doi.org/10.5281/zenodo.22090985Abstract
This paper investigates the classical Maxwell rheological model using Mikusiński operational algebra and
develops its operator-algebraic representation. The relevance of the study is motivated by the need for a unified mathematical
framework for describing the constitutive behavior of complex rheological media. The methodology is based on
Mikusiński operational calculus, operator algebra, and the theory of operator polynomials. In the proposed approach, the
time-derivative operator in the Maxwell model is treated as an algebraic element, enabling the constitutive equation to
be transformed into an operator-polynomial form and an operator solution to be obtained. Based on this formulation, the
relationship between stress and strain is analyzed from an operator-algebraic perspective. Furthermore, the applicability
of the proposed formalism to the unified representation of the Kelvin–Voigt, Standard Linear Solid, and other linear viscoelastic
models in operator-polynomial form is demonstrated. The results provide a mathematical basis for developing
advanced modeling and operator-algebraic analysis methods for rheological models
Keywords
Maxwell model, Mikusiński operational algebra, operational calculus, operator algebra, operator polynomial, rheological model, constitutive equation, linear viscoelasticityReferences
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