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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Mizhidon A. D.
,
Garmaeva V. V.
EQUILIBRIUM POSITION OF THE SYSTEM OF SOLIDS ATTACHED TO AN EULER—BERNOULLY BEAM, DESCRIBED BY A HYBRID SYSTEM OF DIFFERENTIAL EQUATIONS // BSU bulletin. Mathematics, Informatics. - 2019. №1. . - С. 56-64.
Title:
EQUILIBRIUM POSITION OF THE SYSTEM OF SOLIDS ATTACHED TO AN EULER—BERNOULLY BEAM, DESCRIBED BY A HYBRID SYSTEM OF DIFFERENTIAL EQUATIONS
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-1-56-64UDK: 51-7
Annotation:
The article considers a refined generalized mathematical model that allows us to de- scribe a wider class of systems of interconnected solids elastically attached to an Euler—Bernoulli beam. The model is described by a non-uniform linear hybrid sys- tem of differential equations with coefficients depending on the Dirac delta func- tions. Nonhomogeneity in the system necessitates finding the initial conditions cor- responding to the position of bodies and beam deflection in a state of equilibrium. The equilibrium position of a mechanical system is understood as a solution of the initial hybrid system of differential equations that doesn’t vary with time. It is pro- posed an approach to find the equilibrium position of the system of solids attached to an Euler—Bernoulli beam in the chosen coordinate system.
Keywords:
solid; Euler—Bernoulli beam; hybrid system of differential equations; equilibrium position.
List of references:
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