Wave-induced flexural response of idealized non-uniform hull girder in random seas

Abstract

The aim is to analyze the wave-induced vertical vibration of a non-prismatic mathematical hull in a stochastic sea, by normal mode analysis. The hull has been generated mathematically, to represent two distinct Indian merchant vessels: DS (Tanker) and SCIM (Containership). The body-plan, deck waterline, bow and stern profiles, have been modeled as semi-superellipses. These render non-uniform distributions of mass and stiffness over the ship-length. The energy-based Rayleigh–Ritz method has been used to analyze the idealized hull girder natural frequencies and modeshapes. The non-uniform beam modeshape is a weighted series sum of prismatic beam-free vibration modeshapes. The 2D added mass of superelliptic sections is formulated, solving the radiation boundary value problem by the constant strength source distribution method. The hull girder is subject to the Pierson–Moskowitz sea spectrum in fully loaded condition. The diffraction force is formulated through the Khaskind’s relations. The flexural response of the girder is evaluated by the modal superposition method. The response spectra have been generated for various sea states and ship speeds. The magnitudes of the maximum flexural/shear stress for each vessel are generated. The probability of shear/tensile failure is also estimated, giving insights into the hull structural design.