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

Abstract

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.