In the last few decades, global nonlinear dynamics has been evolving in a revolutionary way, with applications to a wide variety of mechanical/structural systems made possible by the use of sophisticated analytical, geometrical, and computational techniques employing powerful concepts and tools of dynamical systems,
bifurcation, and chaos theory, properly updated and complemented with a view to
engineering aims and with meaningful experimental verifications.
The achievements occurred in the area entail a substantial change of perspective
when dealing with vibration problems and are ready to meaningfully affect the
analysis, control, and design of systems at different scales in applied mechanics and
structural dynamics.
In this context, attention has to be paid, in particular, to the evolution and update
of the classical concept of stability, as ensuing from consideration of global
dynamical effects. Local and global dynamics, bifurcation and complexity, theoretical and practical stability play an extremely important—yet still generally overlooked—role as regards understanding and suitably controlling nonlinear
phenomena, as well as reliably determining the load carrying capacity and safety of
engineering systems.