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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Garmaeva V. V.
Algorithmic solution for research of natural oscillations of an Euler- Bernoulli beam with attached solids // BSU bulletin. Mathematics, Informatics. - 2016. №1. . - С. 79-87.
Title:
Algorithmic solution for research of natural oscillations of an Euler- Bernoulli beam with attached solids
Financing:
Работа выполнена при финансовой поддержке РФФИ, проект № 15-08-00973-а
Codes:
DOI: 10.18101/2304-5728-2016-1-79-87UDK: 519.62, 519.63
Annotation:
The article deals with the algorithmic solution for research of mechanical systems with lumped and distributed parameters. This class of systems is described by the generalized mathematical model. Generalized mathematical model is understood as a system of hybrid differential equations with the given structure, it describes the dynamics of an Euler-Bernoulli beam with the attached system of interconnected solids. Algorithmic solution is implemented as a set of programs in the Fortran language.
Keywords:
Euler-Bernoulli beam, the system of solids, mathematical model, algorithmic solution.
List of references:
1. Mizhidon A. D., Dabaeva M. Zh. (Tsytsyrenova M. Zh.). Obobshchennaya matematicheskaya model' sistemy tverdykh tel, ustanovlennykh na upru- gom sterzhne [Generalized Mathematical Model of the System of Solids Mounted on Elastic Rod]. Vestnik VSGUTU – Bulletin of ESSUTM. 2013. – No. 6. Pp. 5–12.

2. Mizhidon A. D., Barguev S. G. Kraevaya zadacha dlya odnoi gibridnoi sistemy differentsial'nykh uravnenii [A Boundary Value Problem for the Hybr- id System of Differential Equations]. Vestnik Buryatskogo gosudarstvennogo universiteta – Bulletin of Buryat State University. 2013. No. 9. Pp. 130–137.

3. Kukla S., Posiadala B. Free Vibrations of Beams with Elastically Mounted Masses. Journal of Sound and Vibration. 1994. No. 175(4). Pp. 557- 564.

4. Philip D. Cha. Free Vibrations of a Uniform Beam with Multiple Elasti- cally Mounted Two-Degree-of-Freedom Systems. Journal of Sound and Vibra- tion. 2007. No. 307. Pp. 386–392.

5. Wu J.-J., Whittaker A. R. The Natural Frequencies and Mode Shapes of a Uniform Cantilever Beam with Multiple Two-DOF Spring-Mass Systems. Journal of Sound and Vibration. 1999. No. 227. Pp. 361–381.

6. Wu J. S., Chou H. M. A New Approach for Determining the Natural Fre- quancies and Mode Shape of a Uniform Beam Carrying Any Number of Spring Masses. Journal of Sound and Vibration. 1999. No. 220. Pp. 451–468.

7. Wu J. S. Alternative Approach for Free Vibration of Beams Carrying a Number of Two-Degree-of-Freedom Spring-Mass Systems. Journal of Structural Engineering. 2002. No. 128. Pp. 1604–1616.

8. Naguleswaran S. Transverse Vibration of an Euler-Bernoulli Uniform Beam Carrying Several Particles. International Journal of Mechanical Sciences. 2002. No. 44. Pp. 2463–2478.

9. Naguleswaran S. Transverse Vibration of an Euler-Bernoulli Uniform Beam on Up a Five Resilient Supports Including End. Journal of Sound and Vibration. 2003. No. 261. Pp. 372–384.

10. Su H., Banerjee J. R. Exact Natural Frequencies of Structures Consist- ing of Two Part Beam-Mass Systems. Structural Engineering and Mechanics. 2005. No. 19 (5). Pp. 551–566.

11. Lin H. Y., Tsai Y. C. Free Vibration Analysis of a Uniform Multi-Span Beam Carrying Multiple Spring-Mass Systems. Journal of Sound and Vibra- tion. 2007. No. 302. Pp. 442–456.

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

13. Mizhidon A. D., Barguev S. G., Dabaeva M. Zh., Garmaeva V. V. Ras- chet sobstvennykh chastot balki Eilera-Bernulli s prikreplennymi tverdymi telami [Calculation of the Natural Frequencies of the Euler-Bernoulli Beam with Attached Solids]. State Registration Certificate of Computer Program No. 2015612387. February 18, 2015.