We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this article. Although the literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by
$We < n^2 + k^2 -1$
, is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here,
$We = \rho \varOmega ^2 a^3 / \gamma$
is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with
being the angular velocity of the rigidly rotating column,
the column radius,
the density of the fluid and
the surface tension coefficient;
denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the
plane. For all
$n > 1$
, the viscously unstable region, corresponding to
$We > n^2 + k^2-1$
, contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the
axis, persists for
. This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.
This paper reports the theoretical findings of the new modified type of tuned liquid column ball damper (TLCBD), called a tuned liquid column ball spring damper (TLCBSD). In this new modified form, the ball inside the horizontal section of the damper is attached to the spring. Furthermore, two types of this modified version are proposed, known as a tuned liquid column ball spring sliding damper (TLCBSSD) and a tuned liquid column ball spring rolling damper (TLCBSRD). In the former, the rotational motion of the ball attached to the spring is restricted, whereas in the latter, the ball attached to the spring can translate as well as rotate. Mathematical models and optimum design parameters are formulated for both types. The performance of these new modified damper versions is assessed numerically and subjected to harmonic, seismic, and impulse loadings. The results show that the performance of the newly proposed dampers is relatively better than traditional TLCBDs in harmonic and seismic excitations. The peak response reduction soon after the impact load becomes zero is comparatively better in TLCBSDs over TLCBDs. Overall, the newly proposed passive vibration control devices performed excellently in structure response reduction over TLCBDs.
Liquid column dampers are adjusted based on the characteristics of the host structure and the type of external forces. It is assumed in most studies that the structure is rigidly connected to the ground, and the characteristics of the structure are invariant during external excitations. The performance of passive dampers may lose, or structural displacements may be increased by changing these conditions. This study presented a new method to find the optimal control forces for structures equipped with smart tuned liquid column gas damper (TLCGDs), considering variable characteristics of the structure and the soil–structure interaction. The proposed method calculates the gas pressure inside the columns by regularly adjusting and updating the frequency and damping of the TLCGD. The unknown or changed soil–structure characteristics are estimated by a system identification method, and damper parameters are determined through an optimization algorithm. The method was tested on 3- 9- and 10-story shear buildings under harmonic and earthquake excitation. According to the results, the smart damper more effectively reduced the structural displacement.