상하동요하는 2차원 원주의 고유진동수
Natural Frequency of 2-dimensional Heaving Circular Cylinder
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참고문헌
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초록
It is very well known that the natural frequency of an oscillating body on the free surface is determinable only after the added mass is given. However, it is hard to find analytical investigations in which actually the natural frequency is obtained. Difficulties arise from the fact that in order to determine the natural frequency we need to compute the added mass at least for a range of frequencies, and to solve an equation where the frequency is a variable. In this study, first, a formula is obtained for the added mass, and then an equation for finding the natural frequency is defined and solved by Newton`s iteration. It is confirmed that the formula shows a good agreement with the results given by Ursell(1949), and the value of natural frequency is reduced by 21.5% compared to the pre-natural frequency, which is obtained without considering the effect of added mass.
Abstract
It is very well known that the natural frequency of an oscillating body on the free surface is determinable only after the added mass is given. However, it is hard to find analytical investigations in which actually the natural frequency is obtained. Difficulties arise from the fact that in order to determine the natural frequency we need to compute the added mass at least for a range of frequencies, and to solve an equation where the frequency is a variable. In this study, first, a formula is obtained for the added mass, and then an equation for finding the natural frequency is defined and solved by Newton`s iteration. It is confirmed that the formula shows a good agreement with the results given by Ursell(1949), and the value of natural frequency is reduced by 21.5% compared to the pre-natural frequency, which is obtained without considering the effect of added mass.
참고문헌 (5)
- Abramowitz, M., "Handbook of Mathematical Functions" (1965), Dover Publications
- Hwang, J.H., "On the added mass and damping of chine sections in heaving oscillation", Journal of the Society of Naval Architects of Korea, 10(1), pp.33~44 (1973)
- Rhee, K.P., "On the hydrodynamic characteristics of submerged cylinders heaving in water of a finite depth", Journal of the Society of Naval Architects of Korea, 15(1), pp.1~6 (1978)
- Ursell, F., "On the heaving motion of a circular cylinder on the surface of a fluid", Quarterly Jouranl of Mechanics & Applied Mathematics, 2, pp.215~231 (1949)
- Wehausen, J. V., "Surface Waves, Encyclopedia of Physics" (1960), Springer-Verlag