Nonlinear elastic plate fluctuations on a fluid surface

Asymptotic expansions to within the third order of smallness for flexural displacements of the floating plate and the fluid velocity potential under plate are obtained using the method of multiple scales. They are formed by a propagating periodic wave of finite-amplitude. In case of an ice plate the analysis of influence of the elastic modulus, the longitudinal compression value and nonlinearity of a plate vertical displacement acceleration on its flexural fluctuations characteristics and distribution of orbital velocity components of fluid particles movement along a flexural-gravitational wave profile under the plate is done.