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http://dx.doi.org/10.12989/gae.2018.16.4.355

Nonlinear frequency analysis of beams resting on elastic foundation using max-min approach  

Bayat, Mahmoud (Young Researchers and Elite club, Roudehen Branch, Islamic Azad University)
Bayat, Mahdi (Department of Civil Engineering, Roudehen Branch, Islamic Azad University)
Kia, Mehdi (Department of Civil and Environmental Engineering, University of Science and Technology of Mazandaran)
Ahmadi, Hamid Reza (Department of Civil Engineering, Faculty of Engineering, University of Maragheh)
Pakar, Iman (Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University)
Publication Information
Geomechanics and Engineering / v.16, no.4, 2018 , pp. 355-361 More about this Journal
Abstract
In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.
Keywords
elastic foundation; max-min approach; analytical method; Runge-Kutta $4^{th}$;
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Times Cited By KSCI : 6  (Citation Analysis)
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