ARTICLE
Steady state vibration of the periodically forced and damped pure nonlinear two-degrees-of-freedom oscillator
1
University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia
2
Óbuda University, Doctoral School of Safety and Security Sciences, Budapest, Hungary
3
Remming, Novi Sad, Serbia
Submission date: 2018-06-13
Acceptance date: 2019-01-23
Publication date: 2019-04-15
Journal of Theoretical and Applied Mechanics 2019;57(2):445-460
KEYWORDS
non-harmonic excitationforce identificationsteady-state motionvan der Pol oscillatorDuffing oscillator
ABSTRACT
In the paper, a pure nonlinear and damped two-mass oscillator excited with a periodical
force is considered. The oscillator is modelled with a system of two coupled second order
nonlinear and non-homogenous equations. Using the model, two problems are investigated:
one, identification of the excitation force for the known vibrating response of the system,
and the second, determination of vibrations of the system excited with the known periodical
force. Using the steady-state motion of the nonlinear oscillator, a method for identification
of the excitation force is developed. For the pure nonlinear oscillator, it is obtained that
the forcing function has the form of the Ateb function. However, if the excitation force is
known, the procedure for computing the steady-state vibration of the system is introduced.
The solution corresponds to steady-state vibrations of the free oscillator, but the amplitude
and phase are assumed to be time variable. The averaged solutions are obtained for the
pure nonlinear oscillator with an additional linear elastic force and for the van der Pol
oscillator. Analytically obtained solutions are compared with numerical ones. They are in
good agreement.
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| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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