222 M. Richmond et al. Fig. 22.1 Diagram of damage process used to map damages implemented in a structural model with structural response caused by a change in the structure information about the structure, and numerically solving the eigenvalue problem can provide information on how the structure responds to damage cases. The aim of this research is to investigate how the use of a numerical model can improve understanding of the impact of damage on the structure and aid those conducting OMA to detect, identify and quantify damage as it occurs. The approach used is shown in Fig. 22.1. 22.2 Background The structure being is a the four-legged jacket from the Wikinger wind farm. These jackets are at a water depth of between 39–42 meters. At their base they are 23 m square, they are 62 meters tall and support 5 MW turbines [6]. Each leg is fixed with 40 m piles [7]. The rotor diameter is 135 m. Dynamic analysis is conducted using Ramboll’s proprietary, in-house software, Ramboll Offshore Structural Analysis (ROSA). In this case, version 53, the latest at the time, is used [8]. ROSA, the main part of the ROSAP package, is a beam element-based design software. The ROSAP package, and the module ROSA, has been used for the design of the majority of offshore wind turbine foundations worldwide [9]. The first five mode shapes are investigated. The first two are first order modes, one where the tower sways fore-aft and the other side-side, these have natural frequencies around 0.3 Hz. The third is a torsional mode where the tower oscillates about the verticle axis, its natural frequency is calculated to be around 1.3 Hz. The 4th and 5th modes are 2nd order, tower swaying modes, fore-aft and side-side, both with frequencies around 1.4 Hz. A damage metric used in this study is the modal assurance criterion (MAC). MAC calculates indicates the level of consistency between two vectors {ϕA} and {ϕX}. The equation is as follows [10]: MAC(r,q) = {ϕA}r T{ϕX}q 2 {ϕA}r T{ϕA}r {ϕX}q T{ϕX}q (22.1) Some environmental factors which are expected to occur are included at an average value expected over the life of the structure, such as marine growth, scour, corrosion and some others [11, 12]. Scour is investigated as a process which impacts the system’s modes and is different from element damage. Scour is varied from 0 to 5.5 m, which in this case is removing the top layers, exposing some length of the piles. Researchers who have developed damage detectability models by implementing some damage into an FEA structure have typically limited their investigation to joint damage [1]. The way that joint damage has typically been implemented is through the reduction of either joint or element stiffness. Within many equations used to derive the equations of motion for the beam members, the effect from a change in stiffness and from area are proportional, as is seen in the Lagrange equation. The assumption that a change in stiffness is proportional to a change in area due to the growth of a crack is not always strictly realistic, but for investigating the first five natural frequencies this assumption has been made by other authors [3, 13].
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