Rayleigh-Ritz method-based analysis of dry coupled horizontal-torsional-warping vibration of rectelliptic open-section containership bare-hulls

The coupled horizontal-torsional-warping vibration of a thin-walled open-section 7800 TEU container ship bare-hull, modelled as a non-uniform girder, is analysed by the efficient energy-based Rayleigh-Ritz method, in order to generate the dry asymmetric vibration frequencies. Since the centre of gravity is within the hull and the shear centre is below the keel, the horizontal and torsional modes of vibration are highly coupled. An open section is also prone to warping. In a novel attempt, the bare-hull geometry is generated mathematically, using section-wise closed-form semi super-ellipses (Lame’s curves). The main dimensions, weight distributions, and fineness ratios are preserved, and closed-form expressions of sectional properties become available in the process. The hull has arbitrarily (non-mathematically) varying mass, bending stiffness, warping stiffness, and shear stiffness distributions along the length. The non-uniform beam modeshape in horizontal/torsional vibration is assumed to be a weighted sum of the uniform beam horizontal/torsional modeshapes. Several benchmark cases of simpler geometry have been analysed first, for both torsion-warping vibration, and coupled horizontal-torsional-warping vibration. Pontoon approximation of the containership has been analysed and validated. Subsequently, the coupled dry vibration frequencies are obtained for the open deck non-uniform girder, and compared with published results.