Analytic solution of transversal oscillation of quintic non-linear beam with energy balance method and global residue harmonic balance method

Beams are very important element in structures because of its widespread usage in steel construction such as buildings, bridges, aircraft arm, aerospace vehicles and many other industrial usages. To attain a proper design of the beam structures, it is essential to realize how the beam vibrates in it...

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Bibliographic Details
Published in:Moscow University physics bulletin 2017-03, Vol.72 (2), p.157-162
Main Authors: Akbarzade, M., Farshidianfar, A.
Format: Article
Language:English
Subjects:
Aerospace engineering
Aerospace vehicles
Aircraft components
Beams (structural)
Bridge construction
Harmonic balance method
Mathematical and Computational Physics
Nonlinearity
Physics
Physics and Astronomy
Steel construction
Theoretical
Theoretical and Mathematical Physics
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Summary:Beams are very important element in structures because of its widespread usage in steel construction such as buildings, bridges, aircraft arm, aerospace vehicles and many other industrial usages. To attain a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system. The main objective of present study is to obtain highly accurate analytical solutions for vibrations of a beam with quintic nonlinearity. Two new analytical methods are the improved energy balance method, and the global residue harmonic balance method. Subsequently, the analytical results are compared with the numerical solution of the exact equation in order to evaluate the correctness of the applied approaches.
ISSN:0027-1349
1934-8460
DOI:10.3103/S0027134917020035