Pelvic vibration

Harmonics of a prismatic body of liquid

Under Beck vibrations all periodic fluid movements to be construed in an open-topped container whose side walls can be fixed, be construed as movable or deformable in any way. The vibration of the body of liquid in the vessel can be caused by periodic or pulse-like movement of the vessel as a whole, by the periodic or pulse-like movement of the walls of the vessel or by other types of action on the surface of the liquid or on the bottom of the vessel.

Depending on the type of action, the direction of action and the shape of the pool edges, the reflection from the pool walls leads to more or less complex water level deflections . When a prismatic body of water is excited only in the longitudinal direction, its natural frequencies f are only dependent on the length D of the basin and the possible phase velocity c in it :

${\displaystyle f=(n+1)\,{\frac {c}{2D}}}$

With n = 0 is the intrinsic shape of the fundamental frequency in and n = 1, 2, 3, ... are designated as first, second, third, ... harmonics ( harmonic named). The corresponding first 4 theoretical eigenmodes, which can be taken from the figure, represent perfectly standing waves ( Clapotis waves).

Harmonics of a wedge-shaped body of liquid

In the same way, the natural frequencies can also be specified for wedge-shaped bodies of liquid, see the adjacent figure. With regard to the formation of the eigenmodes on the surface of the liquid body

• for the inclined pool wall ( embankment ) from a vibration node (corresponding to a phase jump ) and
• for the vertical pool wall of an antinode

be assumed:

${\displaystyle f=(2n+1)\,{\frac {c}{4D}}}$

In the case of oscillation states occurring in nature (with several degrees of freedom) in lakes, bays, harbors and other basin formations, a distinction must be made depending on the type of stimulation:

• Free oscillations of the pool contents, in which atmospheric or seismic impulse forces have disturbed the equilibrium and then the pool water mass swings out in a pronounced natural shape as a seiche until the movement has subsided due to frictional effects, see also tsunami , damped oscillation and
• Forced vibrations of the body of water, in which periodic excitation forces (including those of a wave spectrum) maintain different natural forms over a longer period of time, see wave resonance , tidal resonance .

Resonant pelvic vibrations (with the formation of partially standing waves) appear all the more prominent the longer they are. This also applies to partially open basins and those with irregular and / or gently sloping edges (bank embankments).

literature

• Fritz Büsching: Storm wave resonance on the west coast of the island of Sylt , In: The coast , issue 67, 2003, pp. 51–82
  • Storm Wave Resonance Controlled by Hollow Block Structures , In: COPEDEC VI, Colombo, Sri Lanka, 2003; Book of Abstracts: “Hollow Blocks for the Protection of a Ridge Coast” pp. 179-180, CD Proceedings: Paper No. 90 pp. 1-20
  • Phase jump in the partial reflection of irregular water waves on steep bank slopes , 1. HANSA - International Maritime Journal - C 3503 E, 147, issue 5 pp. 87–98, 2010; 2. INLAND NAVIGATION - C 4397 D, 65, Issue 9 pp. 73–77, Issue 10 pp. 64–69, 2010
  • Phase Jump due to Partial Reflection of Irregular Water Waves at Steep Slopes , Coastlab 10, Barcelona, ​​September 28 to October 1, 2010, Paper No. 67, pp. 1-9