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

Mahmoud Bayat, Mahdi Bayat, Mehdi Kia, Hamid Ahmadi and Iman Pakar

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 4th technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

Key Words

elastic foundation; max-min approach; analytical method; Runge-Kutta 4th

Address

Mahmoud Bayat: Young Researchers and Elite club, Roudehen Branch, Islamic Azad University, Roudehen, Iran Mahdi Bayat: Department of Civil Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran Mehdi Kia: Department of Civil and Environmental Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran Hamid Ahmadi: Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran Iman Pakar: Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

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