Abstract
Hysteresis, quasi-periodicity and chaoticity in a nonlinear dissipative hybrid oscillator are studied. The modified Rayleigh-Duffing oscillator is considered. We simultaneously take into account the new nonlinear cubic, pure quadratic and hybrid dissipative terms which modify the classical Rayleigh-Duffing oscillator. The influence of each of these new parameters on the dynamics of the oscillator has been seriously studied and interesting results are obtained. It is clear that each of these new dissipation terms can be used to control the dynamics of this oscillator. Some may be used to reduce or eliminate hysteresis, amplitude jump and resonance phenomena; others may accentuate them. Similarly, these new parameters can be used to impose on the systems modeled by this oscillator, a regular, quasi-periodic or even chaotic behavior according to their field of application. Thus, one of the original results obtained is the equation of the curve delimiting the zone of instabilities of the amplitudes of harmonic oscillations. This equation thus makes it possible to know the zone of amplitude permitted or of the amplitude jump for the systems and thus to control and predict the loss or gain of energy during this jump. Finally, the second stability of the oscillations of the system is studied as well as the influence of the dissipation parameters on this stability. It should be noted that the influence of some of these parameters depends on the simultaneous presence of these parameters.
Highlights
In recent years, a twofold interest has attracted theoretical, numerical, and experimental investigations to understand the behaviour of nonlinear oscillators
We propose to study in this paper hysteresis, quasiperiodicity and chaoticity in a system modeled by a modified Rayleigh
Regular and chaotic behaviours of a physical system modelled by a modified Rayleigh-Duffing oscillator are investigated
Summary
Assuming that the fundamental component of the solution and the external excitation have the same period, the amplitude of harmonic oscillations can be tackled using the harmonic balance method [5, 21, 22, 23]. Fig. shows the amplitude-response curve where hysteresis and jump phenomena appear. Figs. (a) and (b) illustrate the effect of the pure cubic damping and pure quadratic damping on amplitude-response curve respectively Through these figures, we notice that jump and hysteresis phenomena appear when each damping coefficient increases. These two phenomena always exist whatever the value of α and become more and more accentuated when α increases. Hysteresis and jump phenomena, and multistability oscillations are observed and are affected by the nonlinearities parameters and parametrical excitation amplitude. Eq (8) describes the two loci of the jump points
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Basic and Applied Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
