Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow

The interaction “viscous fluid–thin plate” is considered when the thickness of the plate, ε, tends to zero, while the density and the Youngʼs modulus of the plate are of order ε−1 and ε−3, respectively. The thickness of the fluid layer is of the order of one. An asymptotic expansion is constructed and the error estimates are proved. The leading term of the asymptotic expansion is the solution of the interaction problem “fluid-Kirchoff plate”. The method of asymptotic partial domain decomposition is discussed: the main part of the plate is described by a 1D model while a small part is simulated by the 2D elasticity equations, with appropriate junction conditions.