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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Mizhidon A. D.
,
Kharakhinov А. V.
HYBRID SYSTEM OF DIFFERENTIAL EQUATIONS DESCRIBING SYSTEMS OF SOLIDS ATTACHED TO A TIMOSHENKO BEAM // BSU bulletin. Mathematics, Informatics. - 2019. №1. . - С. 65-77.
Title:
HYBRID SYSTEM OF DIFFERENTIAL EQUATIONS DESCRIBING SYSTEMS OF SOLIDS ATTACHED TO A TIMOSHENKO BEAM
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-1-65-77UDK: 51-7
Annotation:
The article proposes a generalized mathematical model described by a hybrid sys- tem of differential equations of a prescribed structure for one class of mechanical systems consisting of a system of connected solids, elastically attached to a Ti- moshenko beam. Theoretical background of the study of free vibrations has been developed for a generalized mathematical model, in particular, an analytical and numerical method for constructing a frequency equation based on the consideration of a boundary value problem for the corresponding hybrid system of differential equations. In this case, natural frequencies are in fact eigenvalues for which there exists a solution to a boundary value problem. A calculated example is given that shows the reliability and versatility of the proposed method for studying free vibra- tions of mechanical systems, which are systems of connected solids elastically at- tached to a Timoshenko beam.
Keywords:
Timoshenko beam; boundary value problem; mathematical model; solid; hybrid system of differential equations.
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