HYDROELASTIC COUPLED VIBRATIONS IN A CYLINDRICAL CONTAINER WITH A MEMBRANE BOTTOM, CONTAINING LIQUID WITH SURFACE TENSION

A linear free hydroelastic vibration analysis of a frictionless liquid with a free surface contained in a cylindrical tank with a flexible bottom has been performed. The side-wall has been treated as rigid and the effect of surface tension taken into consideration. The container bottom was treated as a membrane, while for the free liquid surface the effect of two contact line conditions has been investigated. One edge condition was that of a slipping contact line, while the other one treated the contact line as fixed, ie., an anchored edge. The vibration characteristics of a membrane–liquid coupled system have been investigated for various system parameters, i.e., membrane tension parameter T, liquid surface tension parameter σ, material density parameter ρ, liquid height ratio ℓ0 and vibration mode numbers m and n. The degree of coupling between a membrane and a liquid was represented with vibration mode diagrams as well as with frequency diagrams. For axisymmetric coupled vibrations with anchored edge condition, vibration mode exchanging of both a membrane and liquid free surface with membrane bottom tension parameter T has been investigated. An interesting phenomenon which is only observed for a flexible bottom container and an anchored edge free surface condition is presented.