[503] Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems

The Colloquium aims at presenting the latest developments in the areas of Nonlinear Normal Modes, Dimension Reduction and Localization, and their applications in vibrating systems.
Nonlinear Normal Modes (NNMs) is a classical topic which is presently given a more modern interpretation mostly as regards their formulation for continuous or discontinuous systems, strongly nonlinear regimes, and discretized structures, as well as their use in various applications. They are also of major interest in the framework of Dimension Reduction of dynamical systems, an area where various methods are being formulated and compared with each other, along with the reduced order models – developed for different purposes/systems – based on just nonlinear (vs linear) normal modes or proper orthogonal modes or multi-modes ensuing from nonlinear finite element analyses. In turn, Localization is one major topic (to be possibly addressed via NNMs) in wave propagation and targeted energy transfer. In this context, there is special interest towards analyzing possible occurrence in mechanics of such dynamic phenomena as the discrete breathers highlighted in applied mathematics and physics, where they are paradigmatic solutions in periodic lattices. Cross-fertilization among such companion areas could allow to exploit results useful to describe analogous phenomena likely to occur in engineered materials and devices, with nontrivial effects in terms of efficient/robust energy focusing/transfer, and material/system design.