Page 221 - Dynamic Loading and Design of Structures

Page 194

Figure 5.8 Schematic force-time history for a horizontal member or segments of a vertical member
above and below the mean water level.

inertia forces can be shown to be (Mo, 1983):

(5.34)

(5.35)

where H[ · ] is the Heaviside unit function defined by H[x] : (0 for ; 1 for
x>0). This fact will also be reflected in the probabilistic description of the complete Morison
equation.
Moreover, if a current velocity vc is added vectorially to the wave particle velocity in eqn
(5.28), the nature of the (drag) force will be affected. Consider, for simplicity, two wave
components with velocity amplitudes of v and v , respectively, together with a current v .
x1
x2
c
The dragforce during that part of the wave cycle for which the dragforce is positive may be
obtained as:

(5.36)

in which β i is ω it+ε i; and εis a (random) phase angle.
i
Clearly this (drift) expansion can be extended to comprise all frequencies ω i in the random
sea.
This expression shows that apparent wave force frequencies will have the original