Innovation science and technologiy 2-том 8-сан (2026) · 124-130-беттер
INVESTIGATION OF THE MAXWELL RHEOLOGICAL MODEL USING MIKUSINSKI OPERATIONAL ALGEBRA
Mirzoev, Akmal, Isomova, Sabohat, Abdulfatto, Raximjon, Ahmadov, Ilhom
Аннотация
This paper investigates the classical Maxwell rheological model using Mikusiński operational algebra anddevelops its operator-algebraic representation. The relevance of the study is motivated by the need for a unified mathematicalframework for describing the constitutive behavior of complex rheological media. The methodology is based onMikusiński operational calculus, operator algebra, and the theory of operator polynomials. In the proposed approach, thetime-derivative operator in the Maxwell model is treated as an algebraic element, enabling the constitutive equation tobe transformed into an operator-polynomial form and an operator solution to be obtained. Based on this formulation, therelationship between stress and strain is analyzed from an operator-algebraic perspective. Furthermore, the applicabilityof the proposed formalism to the unified representation of the Kelvin–Voigt, Standard Linear Solid, and other linear viscoelasticmodels in operator-polynomial form is demonstrated. The results provide a mathematical basis for developingadvanced modeling and operator-algebraic analysis methods for rheological models
Maxwell model, Mikusiński operational algebra, operational calculus, operator algebra, operator polynomial, rheological model, constitutive equation, linear viscoelasticity
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