Analysis of nonlinear vibrations of two-degree-of-freedom systems
Department of Mechanics, Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of Technology, Thainguyen, Vietnam.
Research Article
World Journal of Advanced Engineering Technology and Sciences, 2023, 08(02), 293–304.
Article DOI: 10.30574/wjaets.2023.8.2.0104
Publication history:
Received on 24 February 2023; revised on 09 April 2023; accepted on 11 April 2023
Abstract:
In this paper, the motions of two-mass systems with two-degree-of-freedom are investigated by using an analytical approach. The masses are connected by linear and nonlinear springs. The motions of systems are described by systems of two coupled strong nonlinear differential equations. Nonlinear differential equations are transferred into a single equation by using some intermediate variables. An analytical method, the equivalent linearization method, is employed to analyze the free nonlinear vibration of systems. The oscillation systems with different values of the parameters are investigated in this paper. In order to verify the accuracy of the obtained results, the present solutions are compared with those achieved by the Hamiltonian approach and the exact solutions. The comparison results show that the obtained solutions are more accurate than those obtained by the Hamiltonian approach.
Keywords:
Nonlinear vibration; Two-degree-of-freedom; Equivalent linearization; Weighted averaging
Full text article in PDF:
Copyright information:
Copyright © 2023 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0