ssc-367 - Ship Structure Committee

therefore be defined uniformly along the member lengths. However,
considering the cost of modal analysis, most structural member
weights are input as lumped masses at member ends that attach to
applicable joints.
5.3.3 Motions Model and Analyses Techniques
The mass model discussedabove allowsdeterminationofa structure’s
initial responseto applied excitationalenvironmentalloads by the
use of equilibrium equation solutions. The dynamic force
equilibrium on a structure can be expressed using the following
system of six simultaneousequations:
[ [M + [Ma]} {x} + [cl {X} + [K] {x} = {FD}+ {F,} 5-3
where:
[M] =
[Ma] =
[c] =
[K] =
(FD) =
(Fl) =
{x},{x},{x} =
6 x 6 structuremass matrix
6 x 6 added mass matrix
6 x 6 structure damping matrix
6 x 6 structure stiffness matrix
6x1 wave drag force vector
6x1 wave inertia force vector
6x1 structure displacement, velocity and
acceleration
The terms on the right hand side of the dynamic equilibrium
equations represent external forces applied to the structure.
Following solution of the equilibrium equations, the structure
dynamic response can be moved to the right hand side of the equation
to define the resultant loading.
Thus, the net loading using Morison’s equation given in Section
Eqn. 5-2 can be rewritten as:
F net = : PD2[Cm~-
(Cm-l) UJ + ~f)C~Dulul
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