arXiv subjects

Jan Kyziol

Publications and source records attributed to Jan Kyziol.

4 recordsLinked to original sources

arXiv2024

Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance

We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the $1:2$ resonance and its interaction with the primary resonance.

nlin.CD↗

arXiv2012

Exact nonlinear fourth-order equation for two coupled nonlinear oscillators: metamorphoses of resonance curves

We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-Bogoliubov-Mitropolsky approach - we compute the amplitude profiles, which from mathematical point of view are algebraic curves. In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.

nlin.CD↗

arXiv2011

Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance

We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(Ω)$. In the present paper we investigate metamorphoses of the function $A(Ω)$ induced by changes of the control parameters in the case of 1:3 resonances.

nlin.CD↗

arXiv2010

Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation

We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to get the amplitude profiles $AOmega) $. Dependence of the amplitude $A$ of nonlinear resonances on the frequency $ Ω$ is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function $A(Ω) $ induced by changes of the control parameters.

nlin.CD↗