Abstract
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• - In the present paper, a circular tank v-ith a flexible bottom under vertical periodic excitation is studied. The problem is first formulated in the form of differential equations and then in the form of a variational principle. An approximate solution is presented, which results in a pair of coupled ordinary differential equations with periodic coefficients. The stability of the solutions of these equations is discussed.
THE EFFECT OF WALL ELASTICITY AND SURFACE TENSION ON THE FORCED OSCILLATIONS OF

STATEMENT OF THE PROBLEM
A circular cylindrical container with rigid side walls and a flat, flexible, bottom contains a liquid with a free surface. The tank walls are subjected to an oscillatory axial acceleration, in addition to a constant me an-local-gravitational acceleration directed along the axis of the cylinder. Above the liquid surface is a gas with constant pressure. No external force acts underneath the tank bottom. The situation is pictured in Fig. 1 . The problem is to determine the motion of the liquid and, in particular, its stability.
STATEMENT OF THE PROBLEM
The fluid properties, including the surface tension, are assumed to be uniform, constant, incompressible, and inviscid.
STATEMENT OF THE PROBLEM
The mean free surface of the liquid is assumed to be a plane perpendicular to the cylinder axis. In low-gravity and finite surface tension, one may have to consider a curved mean free surface. The governing criterion is the Bond number defined below. In this paper, we assume that the Bond number is sufficiently large so that the free surface is approximately a plane.
STATEMENT OF THE PROBLEM
The case of low Bond number is discussed later.
STATEMENT OF THE PROBLEM
As a further simplification, we assume that the deviation from the static equilibrium condition is small, so that the deflections of the free surface and of the tank bottom, the fluid velocity, and hence the velocity potential, The pressure p is related to the pressure just outside the liquid, p r , by the relation
STATEMENT OF THE PROBLEM
where a = surface tension K = total curvature of the free surfaces ♦Here we just write out a special form of imposed axial acceleration. The method developed later can be applied to a general periodic imposed axial acceleration. If the pressure of the gas p r is a constant, then without loss of generality we may set .^..2 . P c = 0. The function c(t) can be absorbed in </ > . We can also neglect |V0| in Eq. (6) 
STATEMENT OF THE PROBLEM
Equations (18) 
STATEMENT OF THE PROBLEM
Now we can easily see that the coefficient of J ( k R) in the above series is of order o * n ' l/(.kg/2) for large n ; so the series is actually divergent after twice term-by-term introduced in order to make an infinite determinant, which will be formed below, to be convergent. 

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