This paper contains review of the theory and applications of nonlinear normal modes, which are developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers of the same authors (Mikhlin Y.V., Avramov K.V.: Nonlinear normal modes for vibrating mechanical systems. Review of Theoretical Developments. Appl. Mech. Rev. 63, 060802 (2010); Avramov, K.V., Mikhlin, Yu.V.: Review of applications of nonlinear normal modes for vibrating mechanical systems. Appl. Mech. Rev. 65, 020801 (2013)). The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal forms theory for nonlinear modes construction; nonlinear modes in finite degrees of freedom systems; resonances and bifurcations; reduced-order modelling; 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.

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