The problem of normal oscillations of a viscous stratified fluid with an elastic membrane

Normal oscillations of a viscous stratified fluid partially filling an arbitrary vessel and bounded above by elastic horizontal membrane are studied. In this case, we consider scalar model problem that reflects the main features vector spatial problem. The characteristic equation for eigenvalues is obtained, structure spectrum asymptotics branches Assumptions made about oscillation vessel. It proved discrete, located in right complex half-plane symmetrically with respect to real axis, has single limit point $+\infty$. Moreover, localized certain way half-plane, location zone depends on dynamic viscosity fluid.