Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin solution

Abstract

This study continues the work of Forbes (1986) on periodic waves beneath an elastic sheet floating on the surface of an infinitely deep fluid. The solution is sought as a Fourier series with coefficients that are computed numerically. Waves of extremely large amplitude are found to exist, and results are presented for waves belonging to several different nonlinear solution branches, characterized by different numbers of inflexion points in the wave profiles. The existence of multiple solutions, conjectured in the previous paper (Forbes 1986), is confirmed here by direct numerical computation.