Hydraulic Structures: Fourth Edition

OSCILLATIONS OF CYLINDERS IN WAVES 617

If the above non-linear term for the damping force is used, it is impossible
to solve equation (14.73) in closed form. Hence the drag term is linearized
as

FD cw x ̇D (14.80)

wherecwis the value of CD|x ̇ |, averaged over a whole cycle.

14.12.4 Onset of instability

In order to determine whether a vertical pile will be subjected to flow-
induced vibrations in a steady current, the pile equivalent to the structure
under investigation is first established. For the equivalent pile, the stability
parameterKs, the reduced velocity and the Reynolds number for the
current are found. It is shown in Figs 14.23 and 14.24 whether onset of
instability in the in-line or cross-flow can occur. The amplitude of oscilla-
tions is then given as a function of Ksin Hallam, Heaf and Wootton
(1978).
Vortex-induced oscillations may be prevented at the design stage by
a suitable choice of the values of reduced velocity and the stability para-
meter. Devices that modify the flow and reduce excitation may be fitted to
the circular structure in the field. The ones that are commonly used are
strakes (fins wound around the cylinder) and a shroud (a tube with a
number of small holes placed over the cylinder and separated from it by a
small gap).

14.13 Oscillations of cylinders in waves

In time-dependent flows, the vibratory behaviour of a cylinder is different
from that in steady flow. For such a cylinder, dimensional considerations
show that the amplitude of motion may be expressed as:



D



≈ ,Ks,Kc,Re,.

For a smooth cylinder without Reynolds number dependence the above
expression becomes



D



≈

f

u

nD

m

,Ks,Kc. (14.81)

k



D

um



fnD

1



2