TABLE OF CONTENTS In time-domain simulations, the Standard spectral representation method has been widely utilized in the dynamic analysis of offshore platforms. Given the wave spectrum S ??( ?), the time history of the linear random wave elevation can be generated, that is:
| (83) |  |
and the horizontal water particle kinematics:
| (84) |  |
where ? i = k ix - ? it + ? i and the amplitude of frequency component is a i = 
; the circular frequency and wave number are related by the dispersion function ? 2 = kg tanh kd. Each harmonic component ? i( t) is assumed to be independent of the others, with the phase angle ? i being randomly and uniformly distributed between 0 and 2 ?. For accurate representation, the number of frequencies M should be large.
Once the time histories of wave kinematics are available, Morison forces and inundation force can be obtained without polynomial approximations for the modal force Q( t). The modal displacement can be computed using Newmark time-integration scheme.
For a LTI system driven by local Morison force, it has been suggested4 that an ensemble of 120 or more sample functions be simulated to obtain a reasonably stable fourth-order response moment. Each simulation, as recommended in SNAME,62 corresponds to a wave storm of 3 hours' duration. To investigate the effect of number of frequency discretizations on simulation results, Fig.
