Hydroelastic Viscous Oscillations in a Circular Cylindrical Container With an Elastic Cover

Viscous oscillations in a circular cylinder with an elastic cover on the free surface

“…The results from the current method for the case of no elastic cover are in excellent agreement with extensive experimental results of Howell et al [8]. However, there is a large discrepancy between the present results and those in [1] and [3].…”

“…We now explore the variation of the frequency and damping rate of the lowest slosh modes with h, τ and ζ. Figure 9(a,b) show the variation of the damping rate and frequency of the (1, 0), (2, 0), (3, 0) and (1, 1) modes with liquid depth h. ζ = 0.01 and τ = 0.1, being the parameters in [1] and [3], have been used for these calculations with a view to comparing the results. The latter employ different non-dimensional parameters from ours; Table 3 gives the relationship between the two.…”

“…For instance, the recent paper [1] presents a method that works only for large liquid depths, ignoring as it does the no-slip condition on the bottom wall. Bauer and Chiba [3] present another method for the same problem; however, the applicability in this case is only to small liquid depths. Analogous studies for axisymmetric oscillations have been published in [4].…”

“…Section 3 presents an eigenvalue formulation and solution of the problem where the natural viscous complex eigenfunctions of the problem are used. Section 4 presents results for a range of Reynolds number, liquid depth and mass and tension parameters; these include comparisons with published analytical [9], experimental [8] and numerical results of [1] and [3]. The variations of the frequency and damping rate with the mass parameter ζ, the tension parameter τ , liquid depth h and the Reynolds number Re are also explored for the lowest slosh modes.…”

Viscous Hydroelastic Vibrations in a Cylindrical Container With an Elastic Bottom

“…For large aspect ratios h/a'1, the side wall conditions are predominant and have been treated in references [33,34] for rigid container bottom. The hydroelastic behavior of a rigid circular cylinder with a complete coverage of the liquid surface in the form of a #exible membrane or an elastic plate has been treated for viscous liquid recently [35].…”