Solution
The inner diameter of the pile is 0.508 2 0.01250.483 m. The mass of
entrained water per unit length is
1030
π
4
0.483^2 189 kg m^1.
The added mass per unit length is
1030
π
4
0.508^2 209 kg m^1.
The effective mass per unit length, me 195 189 209 593 kg m^1. The
apparent fixity depth is 60.5083.05 m. The effective length of the
pile 10 3.0513.05 m. The resonant frequency, fn, is
0.56
1/2
1.48 Hz.
The reduced velocity, VV/fnD0.5/(1.480.508)0.66. Assuming
that the damping factor for marine structure steel is 0.08,
Ks0.357.
From Fig. 14.23, for Ks0.357, the critical reduced velocity Vc1.33,
which is larger than V(0.66). Therefore in-line oscillations will not be
initiated.
The kinematic viscosity is 10^6 m^2 s^1 , and the Reynolds number
is 0.50.508 106 2.4 105. From Fig. 14.24, the critical value of
V/fnDVc4.7. As Vcis greater than V, cross-flow oscillations will not
occur.
References
Bai, K.J. (1975) Diffraction of oblique waves by an infinite cylinder. Journal of
Fluid Mechanics, 68 (3): 513–45.
Bearman, P.W., Graham, J.M.R. and Obasaju, E.D. (1984) A model equation for
the transverse forces on cylinders in oscillatory flows. Applied Ocean
Research, 6 (3): 166–72.
Bearman, P.W. and Hall, P.F. (1987) Dynamic response of circular cylinders in
oscillatory flow and waves, Proceedings of the International Conference on
2 593 0.08
1030 0.508^2
200 109 6.0 10 4
593 13.05^4
624 WAVES AND OFFSHORE ENGINEERING
