Normal Vibrations in Near-Conservative Self-Excited and Viscoelastic Nonlinear Systems

A perturbation methodology and power series are utilizedto the analysis of nonlinear normal vibration modes in broadclasses of finite-dimensional self-excited nonlinear systems closeto conservative systems taking into account similar nonlinear normal modes.The analytical construction is presented for some concretesystems. Namely, two linearly connected Van der Pol oscillatorswith nonlinear elastic characteristics and a simplesttwo-degrees-of-freedom nonlinear model of plate vibrations in agas flow are considered.Periodical quasinormal solutions of integro-differentialequations corresponding to viscoelastic mechanical systems areconstructed using a convergent iteration process. One assumesthat conservative systems appropriate for the dominant elasticinteractions admit similar nonlinear normal modes.