Nonlinear Waves and Interaction with an External Field in the Models of Acoustic Metamaterials

In the first part of the diploma we consider the fundamental problem of nonlinear wave propagation in the damped-driven granular lattice mounted on a linear elastic foundation. The problem formulation assumes general type of strongly nonlinear inter-site potential and subject to an external harmonic forcing in the form of a traveling wave. In the present part of the work we focus on the analysis of moving "breather" and "kink" solutions forming in the damped-driven chain. The second part is devoted to the problem of escape of a classical particle from a potential well under external harmonic forcing. We consider a system with "soft" type of nonlinearity - pendulum - with three different excitation modalities: application of periodic external angular momentum, horizontal and vertical drive of the suspension point. We consider two problems: finding escape threshold for zero initial conditions and defining the "safety basins" - sets of initial conditions from which the escape event does not occur.