Free vibration analysis of quintic nonlinear beams by using the equivalent linearization method with a weighted averaging

	Free vibration analysis of quintic nonlinear beams by using the equivalent linearization method with a weighted averaging
Articles in Press, Accepted Manuscript , Available Online from 06 April 2018
Document Type: Research Paper
DOI: 10.22055/jacm.2018.24919.1217
Authors
Dang Hieu ¹; N.Q. Hai²
¹Thai Nguyen University of Technology, Thai Nguyen, Viet Nam
²Ha Noi Architechtural University, Ha Noi, Viet Nam
Abstract
In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyse the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to the axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, which are compared with the previous analytical solutions and the exact solutions. Comparisons show the accuracy of the present solutions. The impact of nonlinear terms on dynamical behavior of beams and the effect of the initial amplitude on frequencies of beams are investigated. Futhermore, the effect of the axial force and the length of beams on frequencies are studied.
Keywords
Equivalent linearization method; Weighted averaging; Non-linear vibration; Euler-Bernoulli beam
Main Subjects
Dynamics and Vibration


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