Book Description

The stability criteria associated with representations, of liquid layers which are in contact with flexible surfaces, are investigated theoretically by means of a linear vibration analysis. Such representations serve as mathematical models for situations involving the consideration of the stability of either a liquid stored in the elastic container of a space vehicle operating under low gravity conditions, or of the liquid phase of a material which is undergoing ablation from a flexible heat shield. The representation of the liquid layer consists of an incompressible, inviscid fluid which is subjected to a net unidirectional body force of constant intensity g and which is stored in a two-dimensional channel having a flexible floor. Irrotational flow is assumed and the cross section of the channel is restricted to the cases of a rectangle and the sector of an annulus. The equilibrium liquid-gas interface, in which the effect of surface tension is taken into account, is assumed flat for the rectangular case and to constitute a portion of a circular cylinder in the annular case. In the rectangular case the flexible floor is characterized as a uniform thin flat plate with zero in-plane edge restraint.