This paper briefly reviews historical development of spectral analysis, and derives a concise linear theory for spectral wave forces .and resulting hot spot stresses, including directionality and spreading.
After calibration, this is used in dynamic analysis and spectral fatigue damage calculations for a proposed thousand-foot platform in the Gulf of Mexico.
The traditional design approach for fixed offshore structures involves the use of a higher order, regular wave theory, such as Stokes' Fifth. Where the design is governed ay applied force from a single largest wave which completely envelops the structure, and nonlinear drag or shallow water effects are important, this approach is appropriate, with reasonable ease of computation and order-of magnitude accuracy.
However, for deep water structures in which dynamic response and fatigue are important, this approach no longer suffices. It is particularly unrealistic to consider that all the wave energy is concentrated at one frequency. Beginning in the early 1950's, Pierson et al pioneered the application of spectral energy theory to the analysis of ship motions (see Michel, ref. 1).
Using leads by Borgman (ref. 2) and Nath (ref. 3) similar spectral techniques have been applied since 1967 in the design of Shell's caissons, deepwater templates and rough sea designs. An early fatigue analysis can be found in Reference 4. A more rigorous formulation by Penzein (ref. 7) has recently been implemented as program TOWER. In both these approaches, drag forces are retained in a variable linearization, along with hydrodynamic damping; however, this is done at the expense of a grossly simplified representation of the structure. Calibration is based on spectral analysis of forces on instrumented cylinders (refs. 2, 9), and by comparisons of predicted extremes with the traditional deterministic approach. Fatigue criteria for use in random loading in the offshore environment have been developed (see fig. 1), and results have been calibrated by hindcasting existing structures (ref. 10).
However, this was not to be the final answer. Reviews of recent in-house fatigue analyses for fixed and floating structures in North Sea service indicated that using directional spectra might yield a substantial reduction in computed forces. One, a twin torpedo semi submersible, was particularly sensitive to perfectly broadside prying waves, so that fatigue life calculations based on unidirectional waves might be considered unreasonably pessimistic.
It has long been recognized that real waves are not infinitely long crested and that directional spectra, which account for the spreading of wave energy by direction as well as by frequency, are required for a complete statistical distribution of the real sea. In the late 1960 l s work at Shell1s Bellaire Research Center by Gibbs and Brown showed that considering directional spectra can qualitatively explain a number of anomalies in existing wave force measurements and analyses, including the CD shotgun plot which typically results from deterministic attempts at wave force calibration.
