Rotating vector solving method applied for nonlinear oscillator
Doctoral School of Safety and Security Sciences, Obuda University, Budapest, Hungary
2 Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
3 Faculty of Engineering, University of Szeged, Szeged, Hungary
Accepted: 7 July 2021
Published online: 2 August 2021
Significant number of procedures for solving of the finite degree-of-freedom forced nonlinear oscillator are developed. For all of them it is common that they are based on the exact solution of the corresponding linear oscillator. For technical reasons, the aim of this paper is to develop a simpler solving procedure. The rotating vector method, developed for the linear oscillator, is adopted for solving of the nonlinear finite degree-of-freedom oscillator. The solution is assumed in the form of trigonometric functions. Assuming that the nonlinearity is small all terms of the series expansion of the function higher than the first are omitted. The rotating vectors for each mass are presented in the complex plane. In the paper, the suggested rotating vector procedure is applied for solving of a three-degree-of-freedom periodically excited oscillator. The influence of the nonlinear stiffness of the flexible elastic beam, excited with a periodical force, on the resonant properties of the system in whole is investigated. It is obtained that the influence of nonlinearity on the amplitude and phase of vibration is more significant for smaller values of the excitation frequency than for higher ones.
© The Author(s) 2021
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