상하동요하는 2차원 주상체의 고유진동수; 주파수 영역 해석
Natural Frequency of 2-Dimensional Cylinders in Heaving; Frequency-Domain Analysis
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Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), aninvestigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency isdefined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by theequation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, andnumerical results for them were obtained up to much higher frequencies than before, for which the method was known as numericallyunstable in the past. For a wide range of , the beam-draft ratio, and , the sectional area coefficient, including their practical rangesfor a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the naturalfrequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the currentresults, and for most cases it was observed that the current result is between the two values. Our numerical results showed that thevalues of the local maximum of MCFR as well as the natural frequencye increase as increases while decreases. At present,extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.
Abstract
Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), aninvestigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency isdefined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by theequation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, andnumerical results for them were obtained up to much higher frequencies than before, for which the method was known as numericallyunstable in the past. For a wide range of , the beam-draft ratio, and , the sectional area coefficient, including their practical rangesfor a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the naturalfrequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the currentresults, and for most cases it was observed that the current result is between the two values. Our numerical results showed that thevalues of the local maximum of MCFR as well as the natural frequencye increase as increases while decreases. At present,extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.
참고문헌 (8)
- 김기범, "상하동요하는 2차원 원주의 고유진동수; 시간 영역 해석", 대한조선학회 논문집, 50(4), pp.224~231 (2013), 대한조선학회
- 이동엽, "상하동요하는 2차원 원주의 고유진동수; 주파수 영역 해석", 대한조선학회 논문집, 50(2), pp.111~119 (2013), 대한조선학회
- 이승준, "상하동요하는 2차원 원주의 고유진동수", 대한조선학회 논문집, 45(4), pp.389~395 (2008), 대한조선학회
- Lee, S.J., "Natural frequency of heaving circular cylinder in the free surface", Proceedings of the Eighth International Workshop on Ship Hydrodynamics, pp.A1~A6 (2013)
- Song, J. H., "Natural Frequency of 2-Dimensional Heaving Cylinder; Frequency Domain Analysis", M.S., Dept. Naval Architecture &Ocean Engineering, pp.2014
- Tasai, F., "On the Damping Force and Added Mass of Ships Heaving and Pitching", Journal of the Society of Naval Architects of Japan, 105, pp.47~56 (1959)
- The Society of Naval Architects of Korea, "Calculations of Ship" (1999), Dongmyoung Publishers
- Ursell, F., "On the Heaving Motion of Circular Cylinder on the Surface of a Fluid", Quarterly Journal of Mechanics & Applied Mathematics, 2, pp.215~231 (1949)