Self-synchronized phenomena generated in rotor-type oscillators (2nd report, investigation using nonlinear normal modes)

In the previous report, the overall properties of self-synchronized phenomena generated in rotortype self-excited oscillators were experimentally and analytically clarified using two types of system constructed from oscillators and coupled mass-blocks. The relationship between stable self-synchronized solutions and the linear natural frequencies of a spring-mass system in each system was also examined. For clarification of the occurrence mechanism, it is important to undertake an investigation that is based on the nonlinear vibration characteristics of the systems. Nonlinear normal modes have the potential to be useful tools for such an investigation, because the nonlinear normal modes and the self-synchronized phenomena are both periodic vibrations in nonlinear systems with many degrees of freedom. However, there is a very important difference, in that the former are free vibrations in conservative systems and the latter are self-excited vibrations in nonconservative systems, so that a definite relationship between them is not obvious. This report examines the relationship using the same systems treated in the previous report. Computational results demonstrate that many characteristics of the self-synchronized phenomena can be explained by the nonlinear normal modes.