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Theoretical and Applied Mechanics, 2020, Volume 47, Issue 2, Pages 221–239
DOI: https://doi.org/10.2298/TAM201006017O
(Mi tam87)
 

Free vibrations of planar serial frame structures in the case of axially functionally graded materials

Aleksandar Obradovića, Slaviša Šalinićb, Aleksandar Tomovića

a Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia
b Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia
References:
Abstract: This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler–Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.
Keywords: free vibrations, planar serial frame structures, axially functionally graded materials.
Funding agency Grant number
Ministry of Education, Science and Technical Development of Serbia 451-03-68/2020-14/200105
451-03-68/2020-14/200108
Support for this research was provided by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grants Nos. 451-03-68/2020-14/200105 and 451-03-68/2020-14/200108.
Received: 06.10.2020
Revised: 11.12.2020
Bibliographic databases:
Document Type: Article
MSC: Primary 70J10; Secondary 74K10, 74H45
Language: English
Citation: Aleksandar Obradović, Slaviša Šalinić, Aleksandar Tomović, “Free vibrations of planar serial frame structures in the case of axially functionally graded materials”, Theor. Appl. Mech., 47:2 (2020), 221–239
Citation in format AMSBIB
\Bibitem{ObrSalTom20}
\by Aleksandar~Obradovi\'c, Slavi{\v s}a~{\v S}alini\'c, Aleksandar~Tomovi\'c
\paper Free vibrations of planar serial frame structures in the case of axially functionally graded materials
\jour Theor. Appl. Mech.
\yr 2020
\vol 47
\issue 2
\pages 221--239
\mathnet{http://mi.mathnet.ru/tam87}
\crossref{https://doi.org/10.2298/TAM201006017O}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000607924500005}
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  • https://www.mathnet.ru/eng/tam87
  • https://www.mathnet.ru/eng/tam/v47/i2/p221
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