Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh's legacy

Nonlinear dynamics of engineering systems has reached the stage of full maturity in which it makes sense to critically revisit its past and present in order to establish an historical perspective of reference and to identify novel objectives to be pursued. This paper makes a first step in this direction, focusing on the mechanics of machines, solids and structures, with applications in both classical and novel technological areas. This is accomplished first by identifying some main stages of scientific development over the last four decades, with the characterizing features as regards addressed systems, underlying mathematical tools, and phenomenological aspects. These are substantiated in terms of topics and involved people with also an archival, and tentatively comprehensive, list of related activities. The second part of the study deals with Ali Nayfeh’s contributions as a scientist and a scholar, embedding his research achievements within the identified four stages of development, and highlighting some qualifying methodological features of his activity as a book author. His legacy is framed within an overall scenario of expected future developments of nonlinear dynamics.