Vibrations of a fluid containing a wide spaced net with floats under its free surface

We consider the problem of low-frequency vibrations of a heavy viscous incompressible fluid occupying a vessel. Under the free surface of the fluid, there is a wide spaced net with floats forming a nonperiodic structure. On the walls of the vessel and the surface of the floats the adhesion condition (zero Dirichlet condition) is imposed. For this problem, which is formulated in terms of a quadratic operator pencil, we construct a limit (homogenized) pencil and establish a homogenization theorem in the case of a “fairly small” number of floats. It is shown that asymptotically, this structure does not affect free vibrations of the fluid.