Vibrations of a Floating Elastic Plate Upon Nonlinear Interaction of Flexural-Gravity Waves

The method of many scales was used to construct an asymptotic expansion up to thirdorder terms for the velocity potential of a fluid of finite depth and the flexural deformations of a floating elastic plate arising from the interaction of harmonics of finite-amplitude progressive surface waves. An expression for the second-harmonic amplitude was obtained, and critical values of the wavenumber were determined. Vibrations of plates with different thicknesses and elastic modulus were analyzed. Vertical displacements of the plate under flexural deformation were studied.