Nonlinear Dynamics in Mechanics: State of the Art and Expected Future Developments

Abstract

Starting from a recent classification of the development stages of nonlinear dynamics in mechanics, this review builds on the idea that the level of scientific maturity of the area is now such as to involve a gradual shift of its core interests from the inherent theoretical and practical findings to the application benefits that they can bring to solving dynamic problems in a variety of technological environments. First, an overview of the current state of knowledge and the achievements of the community of relevant scholars in about the last ten years is presented, distinguishing between traditional and emerging themes fully inherent to mechanics, and more hybridized scientific contexts. Then, a “vision” of expected future developments is attempted, by organizing the presentation along some main lines. (i) Identifying modeling, methodological, and computational advancements needed to address challenging, new or updated, research issues, with a view to deepening and further expanding the ranges of theoretical development and practical interest of nonlinear dynamics. (ii) Overviewing directions toward which promoting full exploitation of intrinsic or intentionally added nonlinearities, to the aim of improving and possibly optimizing specific behaviors and general operating conditions of actual systems/structures in a variety of dynamic environments, by also referring to the uncertainty quantification issue. (iii) Pursuing “novel” lines of developments of nonlinear dynamics in a fully hybridized and cross-disciplinary framework, with also possible expectation of new related phenomenologies.