A Rayleigh-Ritz based approach to characterize the vertical vibration of non-uniform hull girder

Previous attempts to solve for vibration of non-uniform hull girder have used Finite Element Analysis (FEA). This work utilizes the Rayleigh-Ritz (R-R) method to analyze the vertical vibration of a non-prismatic mathematical hull, with arbitrary longitudinal distribution of sectional properties. It is shown that (a) the R-R method provides reasonably accurate results for the actual natural frequency; and (b) the R-R method offers significant computational advantages over FEA. This computational supremacy can be exploited in the initial design stages when several designs are to be iteratively tested for its structural characteristics. The natural frequencies and modeshapes are obtained by the Rayleigh-Ritz method. The non-uniform beam modeshape is a weighted series sum of the (closed-form) uniform beam modeshapes. Only a few uniform beam modes are necessary to generate the non-uniform beam modeshape and a convergent hull girder frequency. Thus, the method is very effective in the low-frequency domain like ship-structure. The proposed method is compared with FEA for two illustrative structures : (a) a containership and (b) a tanker; and also with several hulls from established literature. Modal convergence studies have also been included. The distortions of the non-uniform modeshapes have been studied in the light of the loading conditions of the hull.