Normal Modes of Chaotic Vibrations and Transient Normal Modes in Nonlinear Systems

Abstract

Nonlinear normal modes of forced chaotic vibrations can be found in models which are obtained by discretization of some elastic systems that have lost stability under external compressive force. Transient nonlinear normal modes, which exist only for some specific values of the system energy, appear in nonlinear dissipative systems in vicinity of external or internal resonance. These dissipative systems under resonance conditions are analyzed by transformation to reduced systems stated with respect to the parameter which characterizes the system energy, the arctangent of the amplitudes ratio and the phase difference.