Discreteness effects in the forced dynamics of a string on a periodic array of nonlinear supports (Q1390111)

The authors analyze forced oscillations of an infinite string supported by a periodic array of nonlinear elastic bodies. To eliminate the singularities from the equations of motion that arise due to the discrete nature of the supports, the authors introduce non-smooth transformations of the spatial variable. The problem then reduces to a set of two non-homogeneous nonlinear boundary value problems which are solved by means of perturbation theory. The boundary conditions for these problems arise from `smoothness conditions' that are imposed to guarantee sufficient differentiability of the results. An application is presented of forced localized vibrations of the string with analytically computed discreteness effects of the forced dynamics.