94
WAVE FORCES ON STRUCTURES
The most important aspects of the data in Figure 4.5 are summarized.
1. The CD and CM values apply only to smooth cylinders in deepwater for
which d/(gT2} > 0.003, where d is the water depth, T is the wave period, and
g is the accélération due to gravity.
2. No allowances were made for wave slamming or fluid interactions with
other structural members in proximity to the smooth cylinder.
3.
No allowances were made for current-wave interactions.
4. Re and Kc were not always well defined in this data survey. This may
account somewhat for the wide scatter in the reported results for these coefficients.
5. The Cd and Cm values listed in this table should be used with a wave
theory appropriate to environmental conditions, where the wave theory chosen
is used as a basis for calculating Re and Kc. Approximate values of these latter
parameters are generally adéquate for estimating the flow coefficients.
4.5
TRANSFER FUNCTIONS FOR WAVE LOADING
The basis for the formulation of the transfer functions in this section is linear
theory for a single water wave, often called a simple wave. Recall that for linear
theory, Table 3.1, the wave characteristics are defined by its height H = 2A, its
period T = 2tt/w, and its wave number k = 2%/A where A is its wave length.
Recall also that for deep water waves where the water depth d > 0.5A, then
k = J1 /g. See Problem 3.1.
The transfer function G(co) is defined as the function that relates H of the
incident wave to the load it imparts to the structural component. In general,
transfer functions are defined in the following harmonie form:
G(w) = GoeJUJt, for j =
(4-23)
Here Go is a complex number independent of time. Transfer functions for linear dynamic Systems only are defined here, Systems for which the drag and
restraining force terms are linearized. Since a simple wave is harmonie, the
loading functions q, pi(t), and Mq can also be written in the form of équation
(4.23). The connection between a loading function and its transfer function is
loading function
- -------- —. — = real{G(w)}
wave height
’
(4.24)
The transfer function for a loading q is calculated, for instance, by first finding
q/H, and then casting that resuit in the form of équation (4.23). The following
identities are useful in such a procedure:
e"1 = cos a 4- j sin a
cos(a + 0) — cos a cos 0 — sin a sin ,i'
(4.25a)
(4.25b)
WAVE FORCES ON STRUCTURES
The most important aspects of the data in Figure 4.5 are summarized.
1. The CD and CM values apply only to smooth cylinders in deepwater for
which d/(gT2} > 0.003, where d is the water depth, T is the wave period, and
g is the accélération due to gravity.
2. No allowances were made for wave slamming or fluid interactions with
other structural members in proximity to the smooth cylinder.
3.
No allowances were made for current-wave interactions.
4. Re and Kc were not always well defined in this data survey. This may
account somewhat for the wide scatter in the reported results for these coefficients.
5. The Cd and Cm values listed in this table should be used with a wave
theory appropriate to environmental conditions, where the wave theory chosen
is used as a basis for calculating Re and Kc. Approximate values of these latter
parameters are generally adéquate for estimating the flow coefficients.
4.5
TRANSFER FUNCTIONS FOR WAVE LOADING
The basis for the formulation of the transfer functions in this section is linear
theory for a single water wave, often called a simple wave. Recall that for linear
theory, Table 3.1, the wave characteristics are defined by its height H = 2A, its
period T = 2tt/w, and its wave number k = 2%/A where A is its wave length.
Recall also that for deep water waves where the water depth d > 0.5A, then
k = J1 /g. See Problem 3.1.
The transfer function G(co) is defined as the function that relates H of the
incident wave to the load it imparts to the structural component. In general,
transfer functions are defined in the following harmonie form:
G(w) = GoeJUJt, for j =
(4-23)
Here Go is a complex number independent of time. Transfer functions for linear dynamic Systems only are defined here, Systems for which the drag and
restraining force terms are linearized. Since a simple wave is harmonie, the
loading functions q, pi(t), and Mq can also be written in the form of équation
(4.23). The connection between a loading function and its transfer function is
loading function
- -------- —. — = real{G(w)}
wave height
’
(4.24)
The transfer function for a loading q is calculated, for instance, by first finding
q/H, and then casting that resuit in the form of équation (4.23). The following
identities are useful in such a procedure:
e"1 = cos a 4- j sin a
cos(a + 0) — cos a cos 0 — sin a sin ,i'
(4.25a)
(4.25b)