Nonlinear Wind Velocity Term and Response of Compliant Offshore Structures

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Abstract
The contribution of the nonlinear wind velocity term to the wind induced dynamic response of compliant offshore structures, e.g., a tension leg platform is evaluated. The analysis is carried out both in time and frequency domains. Analytical and numerical schemes are used to evaluate the autocorrelation and the spectrum of the nonlinear velocity term. Expectations of the product of jointly normally distributed random variables and the convolution of the spectrum of the wind fluctuations are used for autocorrelation and spectral estimates. For illustrating the procedure, the fluctuations are idealized as a sine wave, a band limited white noise, and a filtered white noise process. A general expression for the response of an offshore structure to linear and nonlinear velocity terms is formulated. The results indicate that for typical values of turbulence intensity, the contribution of the nonlinear velocity term to the structural response is negligible. Therefore, ignoring the nonlinear velocity term in the formulation of the wind loads, results in an acceptable approximation.