The higher-harmonic response of a vertical cantilever beam to fully nonlinear wave loads is investigated. Such responses are also known as ‘ringing’ and is of practical interest in the context of offshore wind turbine foundations which, in contrast to the classical incidents of ringing at deep water, are placed at intermediate or shallow water.

The purpose of the study is to provide generic results which can be of later use for the interpretation of more complex cases of irregular wave forcing. To this end, the problem parameters are defined and reduced by dimensional analysis. A simple numerical model is proposed, based on linear beam theory and fully nonlinear regular stream function waves. The hydrodynamic forces are determined from the extended Morison equation.

Parametric studies of the response dependence to relative forcing period, wave height and depth are presented and discussed. A central finding of the paper is that for waves of 85% maximum height, the third-harmonic response increases substantially when the depth is reduced from deep-water conditions into intermediate depth.

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