Digital cross-inspectoral analysis techniques are used to determine quadratic transfer functions (QTF'?s) which model the nonlinear -relationship between the high frequency sea wave input and the low frequency response of a vessel-mooring system. Procedures for determining the QTF directly from the raw sea wave input data and the moored-vessel response data are described.
Ships and barges moored in random seas have been observed to undergo large-amplitude oscillations at or near the undraped natural frequency of the vesse1mooring system. This phenomenon is frequently termed low-frequency drift oscillation since the frequencies of such motions are well below those of individual waves. The observed oscillation frequencies are those associated with dynamic systems having large masses and small restoring-stiffness. Unlike stationary regular waves which exert only a steady force on a moored vessel (in addition to high-frequency excitation), stationary random waves exert both a steady and a low frequency component of force. Large oscillations can occur if the low frequency component of force has significant energy content at or near the natural frequency of the-vessel-mooring system. Work by several investigators (see for examples, refs. 1-3) has indicated that the mean and low frequency drift forces exerted on a floating structure are proportional to the square of the wave height. Thus, the low frequency drift force problem is a nonlinear one. Classical spectral analysis techniques are inherently linear and, consequently, are of limited value when analyzing input-output relations for such a nonlinear system. It is the purpose of this paper to point out how input-output relations for a quadratic ally nonlinear system can be modeled with the aid of linear and quadratic transfer functions. We also point out from a practical and computational point of view that cross-inspectoral analysis techniques can be utilized to determine quadratic transfer functions. The cross-bispectrum can be computed directly from the Fourier transforms of the sea wave input and moored-vessel response. Data from a scaled (1:48) model wave basin tests of a moored barge in an irregular sea are analyzed to demonstrate the application of digital time series analysis to determine the spectral domain character of nonlinear drift forces. Examples of computed quadratic transfer functions for drift wave oscillations are presented.
In order to assess the extent to which low-frequency drift oscillations of installation barges might complicate critical operations, scaled (1:48) model tests were conducted in a wave basin. Tests of a single barge were conducted in unidirectional and directionally spread random waves. Among parameters varied were significant wave height, spectrum frequency content, barge heading, and mooring stiffness.
The directionally spread random seas were generated by fans directed obliquely to the water surface and no precise evaluation of the degree of spreading was possible. Barge motions were observed as functions of the control parameters. The data reported here are for the barge in beam seas. The mooring configuration is shown in Fig. 1, along with the time records of the irregular sea wave amplitude and sway response of the barge. This particular data set was chosen to illustrate an extreme situation when strong drift motions are excited by the incident unidirectional wave field.
