Spatially-oscillating structures

Abstract

This chapter illustrates applications of nonsmooth argument substitutions to modeling spatially oscillating structures such as one-dimensional elastic rods with periodic discrete inclusions, and two- or three-dimensional acoustic media with periodic nonsmooth boundary sources of waves. Whenever the corresponding global spatial domains are infinite or cyclical, the related analytical manipulations are similar to those conducted with dynamical systems. The idea of averaging is implemented through the two-variable expansions, where the fast scale is represented by the triangular periodic wave. Such an approach results in closed form analytical solutions despite of the presence discrete inclusions or external discontinuous loads.