Journal of Theoretical
and Applied Mechanics

54, 4, pp. 1197-1204, Warsaw 2016
DOI: 10.15632/jtam-pl.54.4.1197

Metamorphoses of resonance curves in systems of coupled oscillators

Jan Kyzioł, Andrzej Okniński
We study dynamics of two coupled periodically driven oscillators in a general case and compare it with two simplified models. Periodic steady-state solutions to these system equations are determined within the Krylov-Bogoliubov-Mitropolsky approach. Amplitude profiles are computed. These two equations, each describing a surface, define a 3D curve – intersection of these surfaces. In the present paper, we analyse metamorphoses of amplitude profiles induced by changes of control parameters in three dynamical systems studied. It is shown
that changes of the dynamics occur in the vicinity of singular points of these 3D curves.
Keywords: coupled oscillators, amplitude profiles, singular points