Dorji Banzarov Buryat state University
LoginРУСENG

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:
Mizhidon A. D., Dabaeva M. Zh. (Tsytsyrenova M. Zh.) Obobshchennaya matematicheskaya model sistemy tverdykh tel, ustanovlennykh na uprugom sterzhne [A Generalized Mathematical Model of the System of Solids Mounted on an Elastic Rod]. Vestnik Vostochno-Sibirskogo gosudarstvennogo tekhnicheskogo universiteta. 2013. No. 6. Pp. 5–12.

Mizhidon A. D. Teoreticheskie osnovy issledovaniya odnogo klassa gibridnykh sistem differentsialnykh uravnenii [Theoretical Background for the Study of One Class of Hybrid Systems of Differential Equations]. Itogi nauki i tekhniki. Matematicheskii analiz. Ser. Sovremennaya matematika i ee prilozheniya. 2018. V. 155. Pp. 38–64.

Mizhidon A. D., Mizhidon K. A. Sobstvennye znacheniya dlya odnoi sistemy gibridnykh differentsialnykh uravnenii [Eigenvalues for One System of Hybrid Differ- ential Equations]. Siberian Electronic Mathematical Reports. 2016. V. 13. Pp. 911– 922.

Vladimirov V. S. Obobshchennye funktsii v matematicheskoi fizike [Generalized Functions in Mathematical Physics]. Moscow: Nauka Publ., 1976. 280 p.

Garmaeva V. V. Algoritmicheskoe obespechenie issledovaniya svobodnykh kolebanii balki Eilera—Bernulli s prikreplennymi telami [Algorithmic Support for the Study of Free Vibrations of an Euler—Bernoulli Beam with Attached Bodies]. Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika. 2016. No. 1. Pp. 79–87.

Mizhidon A. D., Barguev S. G., Dabaeva M. Zh., Garmaeva V. V. Raschet sobstvennykh chastot balki Eilera—Bernulli s prikreplennymi tverdymi telami [Calcula- tion of Natural Frequencies of an Euler—Bernoulli beam with Attached Solids]. Svide- telstvo o gosudarstvennoi registratsii programmy dlya EVM no. 2015612387. 18.02.2015.