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Surface waves of large amplitude beneath an elastic sheet. II. Galerkin solution. (English) Zbl 0643.76013
This study continues the work of the author [(*) ibid. 169, 409-428 (1986; Zbl 0607.76015)] 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 (*), is confirmed here by direct numerical computation.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q99PDE of mathematical physics and other areas
76M99Basic methods in fluid mechanics