A Practical Frequency-Domain Method for Random-Wave Analysis and Its Application to Jack-up Units
Authors: Chakrabarti Partha , Chakrabarti Subrata K. , Mukkamala Adinarayana 
Published: October 2008

Abstract
For dynamically sensitive systems such as jack-up rigs, a dynamic analysis is performed to assess their structural response. In order of their increasing complexity, the available analysis methods may be broadly classified as:Single degree of freedom;Frequency domain; andTime domain approach.
The random time domain approach is considered most accurate although most complex, whereas the SDOF method is the simplest but approximate. Frequency domain methods are generally applied to simple linearized models. A frequency decomposition of the wave forces on a structure indicates that even for a regular wave, higher harmonic components are present due to non-linearities. Therefore, SDOF method severely overestimates the inertia forces near the natural period, while possibly underestimating the dynamic response further away.
This paper recommends a practical frequency-domain dynamic analysis method referred here as "Wave Response Analysis" (WAVRES), which leads to comparable results on extreme values as the random time domain analysis. This method is based on mode superposition without the assumption of linearization and considers the effect of higher harmonics, which reduces the overall resonance effects predicted by the SDOF method. This method is further extended to random seas. It is computationally very efficient, applicable to reasonably large size models and amenable to simple interpretation. Therefore, this method is seen as a close alternative to the random time domain analysis, and offers significant time saving to the practicing engineer without sacrificing the accuracy and being unduly conservative. The method, however, is restricted to systems that are structurally linear.
The paper outlines the proposed technique, and discusses the various frequency domain methods, such as drag-inertia parameter and Rayleigh distribution. It analyzes a few practical examples of jack-up rig models and compares results from the above analyses with the time domain results.

Introduction
For dynamically sensitive structures such as jack-up rigs, compliant towers etc. the performance of dynamic analysis of some sort is almost inevitable to assess the safety of the unit during design storms. The dynamic analysis model becomes complicated because of several reasons. The primary ones among these are: non-linearity of the drag force, random nature of the wave, and structural or foundation non-linearity. In this paper we exclude the material and structural nonlinearity factors but include discussions on the nature of drag forces, the random process involved and the prediction of maximum expected response.
The current practice of analyzing such systems varies over a wide range. It starts with the simplest method of idealizing the structure as a single degree of freedom system (SDOF) for the evaluation of the dynamic amplification factor (DAF), to the most accurate one of nonlinear time domain method using random waves. Moreover, for the time domain simulation, since generally only one time series is realized, statistical extrapolation is absolutely necessary to extract meaningful results. In view of these limitations, the present paper discusses a frequency-domain method that is less complex and computationally less intensive than the time domain solution, but produces results much better than the SDOF method and often close to the random time domain method.