Finite Amplitude Waves on an Elastic Plate Horizontally Separating Two Different Fluid Streams

Nonlinear waves on a thin elastic plate horizontally separating an upper fluid stream and a lower one are analyzed theoretically. The lower stream is denser. The elastic plate is governed by the equation for large deflections including the in-plane forces due to the longitudinal deformations of the plate. Two fluid streams are assumed to be incompressible and inviscid, but on the elastic plate the balance of the normal component of force is expressed by taking the viscous stress into account. Some progressive waves of finite amplitude are found on the elastic thin plate. The nonlinear elevation of the elastic plate is obtained up to the third order approximation in the wave amplitude. The unsteady amplitude of waves tend to a finite limit after a long time under the effect of the viscosity of the fluid.