18
STRUCTURE-ENVIRONMENTAL FORCE INTERACTIONS
for multi-degree of freedom problems in three-dimensional physical space, the
mathematical models in this text are limited to motion in the vertical plane, a
représentation that is generally adéquate for a preliminary dynamic design of
offshore structures.
The simplest mathematical model has just one équation of motion, written
as a differential équation in terms of only one time-dependent scalar coordinate
which uniquely describes the structure’s position. Such a model defines a single
degree of freedom System. Assume that a structure or portion of a structure
is rigid, or nearly so, and has a Virtual mass m. Because of structure-fluid
interactions, discussed later in this chapter, virtual mass includes ail or part of
the structural mass, together with some water that the structure drags with it
during motion. Assume further that m is sufficiently higher than the mass of
the System restraints (guy Unes or soil foundation) that lirait its motion. Let
the motion of m be restricted to a plane on which the absolute displacement
coordinate of its mass center G is v — v(t). Let EFV dénoté the sum of the
four types of external force components on m, in line with v and positive in the
positive v direction. In these terms, Newton’s second law States
Fv = mv
(2.1)
where v is the absolute accélération of G. This équation is particularly useful in
single degree of freedom models involving rigid body translation only in which
the flexible supports restraining the motion of m are in line with v.
Figure 2.1 Free body sketch for the spread moored ship of Figure 1.6.
Example Problem 2.1. Consider the surge motion for the spread moored
ship shown in Figure 1.6. This ship is asumed to be a rigid structure for which
ihe motion is described solely by its horizontal displacement coordinate v = v(t)
of its mass center at G. Sway, pitch, heave, and yaw motions are neglected. The
ree bod\ sketch of the ship in the vertical plane, shown in Figure 2.1, depicts the
four t\pes of externally applied loads: self-weight or ship displacement W, which
is balanced by its buoyant force equal in magnitude to W-. the équivalent of ail vdirected. time-dependent environmental forces pi(t); the équivalent n-directed
moonng une nstraint force of the general form g(v); and the velocity-dependent
STRUCTURE-ENVIRONMENTAL FORCE INTERACTIONS
for multi-degree of freedom problems in three-dimensional physical space, the
mathematical models in this text are limited to motion in the vertical plane, a
représentation that is generally adéquate for a preliminary dynamic design of
offshore structures.
The simplest mathematical model has just one équation of motion, written
as a differential équation in terms of only one time-dependent scalar coordinate
which uniquely describes the structure’s position. Such a model defines a single
degree of freedom System. Assume that a structure or portion of a structure
is rigid, or nearly so, and has a Virtual mass m. Because of structure-fluid
interactions, discussed later in this chapter, virtual mass includes ail or part of
the structural mass, together with some water that the structure drags with it
during motion. Assume further that m is sufficiently higher than the mass of
the System restraints (guy Unes or soil foundation) that lirait its motion. Let
the motion of m be restricted to a plane on which the absolute displacement
coordinate of its mass center G is v — v(t). Let EFV dénoté the sum of the
four types of external force components on m, in line with v and positive in the
positive v direction. In these terms, Newton’s second law States
Fv = mv
(2.1)
where v is the absolute accélération of G. This équation is particularly useful in
single degree of freedom models involving rigid body translation only in which
the flexible supports restraining the motion of m are in line with v.
Figure 2.1 Free body sketch for the spread moored ship of Figure 1.6.
Example Problem 2.1. Consider the surge motion for the spread moored
ship shown in Figure 1.6. This ship is asumed to be a rigid structure for which
ihe motion is described solely by its horizontal displacement coordinate v = v(t)
of its mass center at G. Sway, pitch, heave, and yaw motions are neglected. The
ree bod\ sketch of the ship in the vertical plane, shown in Figure 2.1, depicts the
four t\pes of externally applied loads: self-weight or ship displacement W, which
is balanced by its buoyant force equal in magnitude to W-. the équivalent of ail vdirected. time-dependent environmental forces pi(t); the équivalent n-directed
moonng une nstraint force of the general form g(v); and the velocity-dependent