Offshore Structure Platform Design - Offshore Structures: Design, Construction and Maintenance - page 118

Wishbone
apex joint

Wishbone
members

sp centerline

Leg joint

Pile joint-sliding release at
this end

sl centerline

FIGURE 3.23 Pile-to-leg annulus modeling.

modeling techniques. When using this modeling method, the engineer should
verify the analysis and ensure there are not compatibility problems caused by
the small stiffnesses.

3.5.4 Dynamic Structure Analysis
Dynamic analysis is becoming increasingly important for: 1) larger and more
costly structures, where dynamic analysis translates into huge construction
cost savings; 2) complex offshore structures, where ordinary static analysis
tends to result in higher risk; 3) harsh environmental conditions at many
deep water sites that cannot be adequately modeled by static analysis. Software
for dynamic analysis is now available so the process has become easier. The
equation of motion will be:

M x € + C x _ + kx = P ð _ x , € x Þ (3.4)

where

M = diagonal matrix of virtual mass;
C = matrix for structural and viscous damping;
K = square linear structure stiffness matrix;
P ð _

x , x Þ = the load vector where € x and _ x are the water velocity and accelera- €

tion, respectively;
€ x = structural acceleration;

_

x = velocity; and
x = displacement.

Natural Frequency
The first step in the dynamic analysis is to calculate the natural frequency of the
structure.