Statistics of Nonlinear Response to Short Crested Nonlinear Seas: The Quadratic Response.
Final rept. 1 Oct 85-30 Sep 86,
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD
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The present work is an extension of previous work on the statistics of quadratic nonlinear ship response to short-crested seas. In previous work the basic response model was a truncated functional series the short-crested exciting seaway was modeled as the superposition of linear component waves. The present work include the development of a model for the statistics of quadratic ship system response in short-crested seas which is consistent in that quadratic nonlinearities in the wave field are taken into account. If the statistical representation of the response to the nonlinear short-crested deep water wave field is carried out strictly through contributions which may be considered second order in wave excitation, the statistical estimating formulae for the quadratic response to short crested seas in which quadratic nonlinearities are included are identical to those previously developed when no wave nonlinearities were included.The difference is that the sum and difference frequency response functions required by the previous work are modified by a term which amounts to the linear ship system response to those quadratic wave field component which are produced by the wave field nonlinearities. In practice the most important statistic involving quadratic response is the expectation, or mean value. In this special case an extension is not necessary. To second order, the mean response of a linear plus quadratic ship system to a short crested wave field is not affected by wave field nonlinearities. The present development suggests that the mean value estimator may be robust through third order.
- Marine Engineering