Analysis of the global bending modes of a floating structure using the proper orthogonal decomposition

In this paper a time-domain procedure to identify the vibration modes of floating structures, based on the analysis of both displacements and accelerations, is presented. The implemented time-domain technique is the proper orthogonal decomposition (POD), known also as Karhunen–Loeve decomposition, that provides the functional basis that accounts for more captured energy than any other orthogonal one. The POD has been applied in its straightforward formulation and in a slightly different version as well, named band-pass POD, that exploits preliminary filtering around the resonant peaks of the analyzed signals to enhance the convergence of the proper orthogonal modes (POMs) to the linear normal modes (LNMs) in the case of poor information about the mass distribution. The presented procedure has been employed to analyze the experimental data provided by accelerometers and strain-gages applied to the flexible backbone of an elastically scaled segmented-hull model tested in both irregular sea and regular waves in the towing-tank. Among several aspects of the identification of wet-modes, it is discussed in particular how the excitation mechanism provided by the sea meets the requirements of the ambient load typically exploited in output-only modal analysis. The comparisons between the mode shapes identified with the two different procedures (classical POD on the displacements and band-pass POD on the accelerations) show the effectiveness of the POD and the possibilities and limitations related to the use of each procedure. Some results related to the present application, like energy ordering of the wet-modes and its dependence on the encountered sea pattern, as well as the modal damping variation with ship forward speed, are discussed in the paper, showing the POD capability to provide new insights in the analysis of hydroelastic phenomena.