Oscillations of a floating elastic plate under nonlinear interaction of bending-gravitational waves

Asymptotic decomposition to small quantities of the third order for the velocity potential of a fluid of finite depth and the bending deformations of a floating elastic plate arising from the interaction of harmonics of finite-amplitude progressive surface waves were constructed using the method of many scales. An expression for the second-harmonic amplitude was obtained, and critical values of the wavenumber were determined. Oscillations of the plate for different values of its thickness and elastic modulus were analyzed. Vertical displacements of the plate under bending deformation were studied.