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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Mizhidon A. D.
,
Kharakhinov A. V.
A frequency equation of a Timoshenko beam carrying a two-degree of freedom spring-mass system // BSU bulletin. Mathematics, Informatics. - 2016. №4. . - С. 61-68.
Title:
A frequency equation of a Timoshenko beam carrying a two-degree of freedom spring-mass system
Financing:
Работа выполнена при финансовой поддержке РФФИ в рамках научного проекта № 15-08-00973а
Codes:
DOI: 10.18101/2304-5728-2016-4-61-68UDK: 519.62, 519
Annotation:
In paper construct a frequency equation for a mechanical system that con- sist of a rigid two degree of freedom mass that was attached by two springs to the Timoshenko beam. The system that we considered described a hybrid sys- tem of differential equations that with help a harmonic substitute transform into an algebraic-differential system relatively amplitude parameters. The fre- quency equation was obtained by review of conditions of the solution existence of the boundary problem for the algebraic differential equation.
Keywords:
eigenvalue problem, Timoshenko beam, hybrid system of differential equations, boundary problem.
List of references:
1. Mizhidon A.D., Harahinov A.V. K issledovaniju kraevoj zadachi dlja

balki Timoshenko s uprugo prikrepljonnym tvjordym telom // Vestnik Burjat- skogo gosudarstvennogo universiteta. Matematika, informatika. — 2016. — № 1. — S. 88 – 101.

2. Vladimirov V.S. Obobshhennye funkcii v matematicheskoj fizike. — M.: Nauka, 1976. — 280 s.

3. Mizhidon A.D., Mizhidon K.A. Sobstvennye znachenija dlja odnoj sis-

temy gibridnyh differencial'nyh uravnenij // Sibirskie jelektronnye mate- maticheskie izvestija. — 2016. — T. 13. — S. 911 – 922.