Title: Mathematical modelling and parametric resonances of a nonlinear RLC series circuit

Authors: Yélomè Judicaël Fernando Kpomahou; Clément Hodévèwan Miwadinou; Laurent Amoussou Hinvi

Addresses: Department of Industrial and Technical Sciences, University of Abomey, ENSET-Lokossa, Benin ' Department of Physics, University of Abomey, ENS-Natitingou, Benin ' Département de Génie Électrique et Informatique Industrielle, Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques d'Abomey, IUT-Lokossa, Benin

Abstract: In order to study nonlinear parametric oscillations of a RLC series circuit consisting of a nonlinear resistor, a nonlinear inductor and a nonlinear capacitor subjected to mixed-frequency voltage, a class of nonlinear ordinary differential equations is generated. From this class, a generalised mixed Rayleigh-Liénard oscillator used to describe the steady-state oscillations is derived. Applying the method of multiple scales to this specific equation, six resonances states are obtained whose four cases of resonances such as Ω = 3 ω₀, Ω = 5 ω₀, Ω = 7 ω₀ and 2Ω = ω₀ are studied. The modulation equations in the amplitude and the phase of these four cases of resonances are determined. The corresponding frequency-response equations and stability analysis of steady-state solutions are investigated. The frequency response curves and stability analysis of each steady-state solution are plotted. As results, bistability, hysteresis, bifurcation and jump phenomena are obtained. Finally, some effects of the nonlinear damping parameters and excitation voltage amplitudes are investigated numerically and results are presented graphically and discussed.

Keywords: nonlinear RLC circuit; generalised mixed Rayleigh-Liénard oscillator; multiple scales method; nonlinear resonances; stability.

DOI: 10.1504/IJNDC.2018.093625

International Journal of Nonlinear Dynamics and Control, 2018 Vol.1 No.2, pp.133 - 153

Received: 30 Dec 2017
Accepted: 24 Feb 2018
Published online: 30 Jul 2018 *

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