Metamorphoses of resonance curves for two coupled oscillators: The case of small non-linearities in the main mass frame

摘要

We study dynamics of two coupled periodically driven oscillators in general case. Periodic steady-state solutions of the system of two equations are determined within the Krylov-Bogoliubov-Mitropolslcy approach. The corresponding amplitude profiles, A(omega),B(omega), which are given by two implicit equations, F (A,B, omega) = 0, G (A,B, omega) = 0, where omega is frequency of the driving force, are computed. These two equations, each describing a surface, define a 3D curve-intersection of these surfaces. In the present paper we carry out preliminary investigation of metamorphoses of this curve, induced by changes of control parameters. The corresponding changes of dynamics near singular points of the curve are studied. (C) 2015 Elsevier Ltd. All rights reserved.