Finite-amplitude waves in a homogeneous fluid with a floating elastic plate

Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incompressible fluid covered by a thin elastic plate are obtained using the method of multiple scales and taking into account that the acceleration of vertical flexural displacements of the plate is nonlinear. Based on the obtained equations, asymptotic expansions up third-order terms are constructed for the fluid velocity potential and the perturbations of the plate-fluid interface (plate bending) caused by a traveling periodic wave of finite amplitude. The wave characteristics are analyzed as functions of the elastic modulus and thickness of the plate and the length and tilt of the initial fundamental harmonic wave.