Axisymmetric oscillation of a viscous liquid covered by an elastic structure

If the free liquid surface of a viscous liquid is completely covered by an elastic structure, the damped natural frequencies of such a hydroelastic system are shifted to values larger than those obtained with a free liquid surface. In addition, the sloshing of the liquid is considerably reduced and exhibits, depending on the tension or stiffness of the covering elastic structure, smaller deflection amplitudes and drastically reduced liquid forces and moments participating in the dynamic behavior of the system. The hydroelastic frequencies of a viscous liquid in a circular cylindrical tank of moderate to large liquid height aspect ratio may be covered completely by a flexible membrane or an elastic plate, and exhibit an increase with increasing liquid height ratio h/a. In addition, the damping becomes stronger with the increasing h/a and remains––as the frequency does—nearly constant from a certain height ratio onwards. This indicates that from a certain moderate liquid height ratio neither frequency nor damping does change considerably, since in the lower portion of the container the velocity distribution and its change remain quite small. he increase in the membrane tension parameter T * ≡ Ta / ρ ν 2 , the magnitude of both natural frequency and the decay of the oscillations increase. The same happens for the increase of the stiffness parameter D * ≡ D / ρ ν 2 a . In addition, higher modes show larger damping.