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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2014, Volume 55, Issue 6, Pages 186–194
(Mi pmtf1020)
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This article is cited in 5 scientific papers (total in 5 papers)
Accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation: using an exact formulation of the beam curvature
H. M. Sedighi, K. H. Shirazi Shahid Chamran University, PO box 61357-43337, Ahvaz, Iran
Abstract:
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve 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. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
Keywords:
quintic nonlinearity, parameter expansion method, elastic foundation, nonlinear vibrations of the beam.
Received: 03.12.2012 Revised: 11.02.2013
Citation:
H. M. Sedighi, K. H. Shirazi, “Accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation: using an exact formulation of the beam curvature”, Prikl. Mekh. Tekh. Fiz., 55:6 (2014), 186–194; J. Appl. Mech. Tech. Phys., 55:6 (2014), 1066–1074
Linking options:
https://www.mathnet.ru/eng/pmtf1020 https://www.mathnet.ru/eng/pmtf/v55/i6/p186
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