Transient Resonant Regimes and Localized States of Essentially Nonlinear Media: Analytical Study

Theoretical characterization and control of transient, resonant responses of many real mechanical systems encounter significant challenges due to their essential nonlinearity. Strong nonlinearity manifests in systems with intermittently interacting components such as granular materials, structures with breathing cracks, interlocking materials, suspension bridges as well as in smooth systems such as for instance light and slender structures exhibiting high amplitude vibrations. Understanding their strongly nonlinear and highly nonstationary behavior under various loading conditions is crucial for successful engineering design in many applications. While many previous analytical studies primarily focused on the steady-state phase of the response of forced, essentially nonlinear media, transient responses play a crucial role in many real-life applications. My presentation covers three key aspects.