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http://dx.doi.org/10.5762/KAIS.2018.19.12.32

Eigen-Frequency of a Cantilever Beam Restrained with Added Mass and Spring at Free End or a Node Point  

Sim, Woo-Gun (Department of Mechanical Engineering, Hannam University)
Publication Information
Journal of the Korea Academia-Industrial cooperation Society / v.19, no.12, 2018 , pp. 32-40 More about this Journal
Abstract
In order to avoid excessive vibration, it is required to carry out a vibration analysis of heat-exchanger/nuclear-reactor at the design stage. Information of eigen-frequency in the vibration problem is required to evaluate safety of heat-exchange/nuclear reactor. This paper describes a numerical method, Galerkin's method, to solve the eigenvalue problem occurred in a cantilever beam. The beam is restrained with added mass and spring at the free end or a node point of a mode shape. The numerical results of eigen-frequency were compared with simple analytical and experimental results given by simple approach and simple test, respectively. It is found that Galerkin's method is applicable to estimate the eigen-frequency of the cantilever beam. The frequencies become lower with increasing the added mass and the frequencies increase with the spring force. It is shown the heavy added mass has a role of support on the flexible tube. The eigen-frequency of the first mode, for the system with the added mass mounted at the free end, can be calculated by the approximate analytical method existing with more or less accuracy.
Keywords
Added Mass; Cantilever Beam; Eigen-frequency; Flow-induced-Vibration; Galerkin's Method;
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