The influence of damping on the limit cycles for a self-exciting mechanism

Abstract

The objective of the present work is to investigate qualitative aspects of mode-coupling instability of self-excited friction-induced oscillations in the presence of structural damping and a cubic nonlinearity. In a previous study, Sinou and Jezequel demonstrated the effects of structural damping in determining stable and unstable zones and indicated that the damping ratio of the coupling modes may be a key factor for avoiding bad design. In this paper, we propose to complete this study by examining the influence of structural damping on limit cycle amplitudes in order to achieve a complete design including not only the evolution of stable/unstable areas but also the evolution of limit cycle amplitudes as functions of the structural damping and nonlinear system parameter. For the sake of simplicity, a two-degree-of-freedom minimal model is constructed and analysed to examine the effects of structural damping and cubic nonlinearity on the limit cycles. The nonlinear behaviour and stable limit cycle amplitudes are determined through a Complex Nonlinear Modal Analysis which makes use of the nonlinear unstable mode governing the nonlinear dynamics of structural systems in unstable areas. Based on this nonlinear modal approach, we will produce and explain qualitative and quantitative results of limit cycle evolutions in the presence of structural damping and nonlinearity.