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In a prior work, the authors proved a global bifurcation theorem forspatially periodic interfacial hydroelastic traveling waves on infinite depth,and computed such traveling waves. The formulation of the traveling waveproblem used both analytically and numerically allows for waves withmulti-valued height. The global bifurcation theorem required a one-dimensionalkernel in the linearization of the relevant mapping, but for some parametervalues, the kernel is instead two-dimensional. In the present work, we studythese cases with two-dimensional kernels, which occur in resonant andnon-resonant variants. We apply an implicit function theorem argument to proveexistence of traveling waves in both of these situations. We compute the wavesnumerically as well, in both the resonant and non-resonant cases.

Periodic traveling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples