Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress

Abstract This paper contains a review of the theory and applications of nonlinear normal modes, which have been developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers by the same authors. The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal form theory for nonlinear modes construction; nonlinear modes in finite degrees-of-freedom systems; resonances and bifurcations; reduced-order modeling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.