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Damped pitching of a slender body partially immersed in a liquid

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Abstract

A slender cylindrical body with a high metacentre was allowed to float in a large liquid container. The body was then displaced vertically and released so that it performed damped pitching oscillations. The motion of the body can be described by a coupled system of a second order ordinary differential equation and the cylindrical heat conduction equation. If the damping is weak, a simple solution exists and the damping coefficient and the natural frequency agree well with experimental results. The damping is proportional to the square root of the kinematic viscosity of the liquid and inversely proportional to the diameter of the body.

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Abbreviations

A :

area of the wetted surface of the body

F :

total force

F v :

viscous force

g :

gravitational acceleration

l :

length of the body

m :

mass of the body

n :

integer

r :

radial coordinate

r o :

radius of the body

s :

Laplace variable

t :

time

T e :

oscillation period

x(t) :

displacement of the body

x m :

displacement at the turning points

V b :

volume of the displaced liquid

v(r, t) :

velocity of the liquid

δ:

logarithmic decrement

κ:

auxiliary parameter

μ:

dynamic viscosity of the liquid

ν:

kinematic viscosity of the liquid

ρ:

density of the liquid

ξ(t):

amplitude function

ω:

natural frequency for undamped motion

ω e :

natural frequency for damped motion

References

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Authors and Affiliations

  1. Department of Hydraulics, The Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Göran Rehbinder

Authors
  1. Göran Rehbinder
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Rehbinder, G. Damped pitching of a slender body partially immersed in a liquid. Appl. Sci. Res. 50, 69–81 (1993). https://doi.org/10.1007/BF01086453

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  • DOI: https://doi.org/10.1007/BF01086453

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