Abstract
Analytical method using Rayleigh–Ritz method has not been widely used recently due to intensive use of finite element analysis (FEA). However as long as suitable mode functions together with component mode synthesis (CMS) can be provided, Rayleigh–Ritz method is still useful for the vibration analysis of many local structures in a ship such as tanks and supports for an equipment. In this study, polynomials which combines a simple and a fixed support have been proposed for the satisfaction of boundary conditions at a junction. Higher order polynomials have been generated using those suggested by Bhat. Since higher order polynomials used only satisfy geometrical boundary conditions, two ways are tried. One neglects moment continuity and the other satisfies moment continuity by sum of mode polynomials. Numerical analysis have been performed for typical shapes, which can generate easily more complicated structures. Comparison with FEA result shows good agreements enough to be used for practical purpose. Frequently dynamic behavior of one specific subcomponent is more concerned. In this case suitable way to estimate dynamic and static coupling of subcomponents connected to this specific subcomponent should be provided, which is not easy task. Elimination of generalized coordinates for subcomponents by mode by mode satisfaction of boundary conditions has been proposed. These results are still very useful for initial guidance.
Highlights
IntroductionEach tank installed on the ship is arranged in the stern and engine room of the ship considering the cargo loading space, and there is a possibility that excessive vibration may occur due to the main excitation forces (main engine and propeller) that causes the ship vibration
Each tank installed on the ship is arranged in the stern and engine room of the ship considering the cargo loading space, and there is a possibility that excessive vibration may occur due to the main excitation forces that causes the ship vibration
It is not strictly a fixed condition because deflection occurs at the middle point, but it is suitable as a simplification method as it satisfies the allowable range of analysis when calculated considering the fixed boundary condition
Summary
Each tank installed on the ship is arranged in the stern and engine room of the ship considering the cargo loading space, and there is a possibility that excessive vibration may occur due to the main excitation forces (main engine and propeller) that causes the ship vibration. CMS (component mode synthesis) method was applied to calculate the connection structure [8,9]. In order to calculate the normal mode analysis of the connected structure using the CMS method, it is important to define the constraint at the connection part, and various studies on the constraint conditions at the junction were performed by Hurty et al [12,13,14,15,16,17,18]. We have proposed polynomials combining fixed and simple supports to satisfy boundary condition at junctions between each subsystem. We know that this approach has never been tried. It is a reasonable guTehses fboerammoids esefpuanrcattieodnsintotobtewroepsreecsteionntesdObAy acnodmObiBn,ewd hsuosme ocof ofurdnicntiaotenss aforer fishxoewd nand as sswihmATo;hwpxelneapnsirnudoppFwpiegoBrutr;itrxe.es.T1oofirssetuprsureecdsteu.nrVteistbhrueastbeiodansiinconitdhlyeeainsnuotmfhteehrpeiclmaanleeathnooafdlpyaosipfsemarroiesdsachloosnywsnindtheinreesdTis.a, balne example 1
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