Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Numerical Analysis for Nonlinear Static and Dynamic Responses of Floating Crane with Elastic Boom

붐(Boom)의 탄성을 고려한 해상크레인의 비선형 정적/동적 거동을 위한 수치 해석

  • Cha, Ju-Hwan (Seoul Nat'l University Engineering Research Institute) ;
  • Park, Kwang-Phil (Ship & Ocean R&D Institute, Daewoo Shipbuilding & Marine Engineering) ;
  • Lee, Kyu-Yeul (Dept. of Naval Architecture and Ocean Engineering, Seoul Nat'l Univ.)
  • 차주환 (서울대학교 공학연구소) ;
  • 박광필 (대우조선해양 선박해양연구소) ;
  • 이규열 (서울대학교 조선해양공학과)
  • Published : 2010.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

A floating crane is a crane-mounted ship and is used to assemble or to transport heavy blocks in shipyards. In this paper, the static and dynamic response of a floating crane and a heavy block that are connected using elastic booms and wire ropes are described. The static and dynamic equations of surge, pitch, and heave for the system are derived on the basis of flexible multibody system dynamics. The equations of motion are fully coupled and highly nonlinear since they involve nonlinear mass matrices, elastic stiffness matrices, quadratic velocity vectors, and generalized external forces. A floating frame of reference and nodal coordinates are employed to model the boom as a flexible body. The nonlinear hydrostatic force, linear hydrodynamic force, wire-rope force, and mooring force are considered as the external forces. For numerical analysis, the Hilber-Hughes-Taylor method for implicit integration is used. The dynamic responses of the cargo are analyzed with respect to the results obtained by static and numerical analyses.

해상크레인은 크레인을 탑재한 선박으로서, 조선소에서 대형 블록이나 구조물의 탑재 및 해상 운송 작업에 사용된다. 본 논문에서는 해상크레인과 중량물의 전후 동요(Surge), 상하 동요(Heave), 종 동요(Pitch)에 대한 정적/동적거동을 분석하였다. 이 때, 유연 다물체계 동역학을 적용하여 해상크레인의 붐(boom)을 탄성으로 고려하였으며, 플로팅 프레임(floating frame)과 노드 좌표(nodal coordinates)를 사용하였다. 질량 행렬, 탄성 강성 행렬, 2 차 속도 벡터, 일반화 좌표 방향으로 작용하는 외력 등을 고려하여 모든 운동이 연성된 비선형 운동 방정식을 구성하였다. 외력으로는 비선형 유체정역학 힘, 선형화된 유체동역학 힘, wire rope 힘, 계류력이 고려되었다. 수치 해석을 위해 Hilber-Hughes-Taylor 방법을 비선형 운동방정식에 적용하였다. 정적 거동 분석을 통한 정적 평형 자세를 고려한 경우와 고려하지 않은 경우에 대해 결과를 비교하였으며, 수치 해석 방법에 대한 정적/동적 거동 분석 결과를 비교하였다.

Keywords

References

  1. Shabana, A. A., 1997, "Flexible Multibody Dynamics: Review of Past and Recent Development," Multibody System Dynamics, Vol. 1, pp. 189-222. https://doi.org/10.1023/A:1009773505418
  2. Shabana, A. A., 2005, Dynamics of Multibody Systems, Third edition, Cambridge University Press.
  3. Yoo, W. S., 2000, "Recent Trends in Multibody Dynamics," The Korean Society of Mechanical Engineering, Lectures from Spring-Autumn Annual Conference, pp. 51-65 (Korean).
  4. Yoo, W. S., 2007, "A Study on the Analysis of Real-time Multibody Dynamics," Journal of the Korean Society of Mechanical Engineers, Vol. 47, No. 11, pp. 45-49.
  5. Lee, B. H. and Yoo, W. S., 1993, "A Systematic Formulation for Dynamics of Flexible Multibody Systems," Proceeding of the Korean Society of Mechanical Engineers, pp. 2483-2490 (Korean).
  6. Lee, S. H., Bae, D. S., Han, C. S. and Suh, M. S., 1994, "A Dynamic Analysis of Constrained Multibody Systems," Proceeding of the Korean Society of Mechanical Engineers, pp. 2339-2348 (Korean).
  7. Yoon, J. W., Park, T. W., Jung, S. P., Lee, S. H. and Jun, K. J., 2007, "Systematic Analysis of Flexible Multibody System Using Object-Oriented Algorithm," Proceeding of the Korean Society of Mechanical Engineers, pp. 7-12 (Korean).
  8. Schiehlen, W., 2004, "Recent Developments in Multybody Dynamics," Proceedings of ACMD.
  9. Sohn, J. H. and Yoo, W. S., 2003, "Study of the Dynamic Analysis Method Using the Modal Coordinates and the Absolute Nodal Coordinates," Proceeding of the Korean Society of Mechanical Engineers, pp. 1730-1735 (Korean).
  10. Wasfy, T. M. and Noor, A. K., 2003, "Computational Strategies for Flexible Multibody Systems," Applied Mechanics Reviews, pp.553-613.
  11. Al-Sweiti, Y. and Sıffker, D., 2007, "Cargo Pendulation Suppression of Ship Cranes with Elastic Booms," Mathematical and Computer Modelling of Dynamical Systems, Vol. 13, No. 6, pp. 503-529. https://doi.org/10.1080/13873950701214424
  12. Ren, H., Wang, X., Hu, Y., Li, C., 2008, "Dynamic Response Analysis of a Moored Crane-Ship with a Flexible Boom," Journal of Zhejiang University Science A, Vol. 9, No. 1, pp. 29-31.
  13. Cha, J. H., Ham, S. H., Kwon, J. H., Lee, K. Y., Roh, M. I. and Park, K. P., 2008, "Simulation of Dynamic Response of a Heavy Cargo Suspended by Parallel Connected Floating Cranes," Proceeding of the SNAK(Society of Naval Architecture of Korea) Fall Conference, Changwon, Korea, pp. 921-930 (Korean).
  14. Cha, J. H., Ham, S. H. and Lee, K. Y., 2009, "Dynamic Response Analysis of a Heavy Cargo Suspended by Multi-Floating Cranes with Topological Modeling Approach of Multibody System Dynamics," Proceeding of the SNAK(Society of Naval Architecture of Korea) Spring Conference, Changwon, Korea, pp. 1752-1760 (Korean).
  15. Cha, J. H. and Lee, K. Y., 2009, "Erection Simulation Considering Interaction between a Floating Crane and a Heavy Cargo," Journal of Korean Society of CAD/CAM Engineers, Vol. 15, No. 1, pp. 654-668 (Korean).
  16. Cha, J. H., Lee, K. Y., Ham, S. H., Roh, M. I., Park, K. P. and Suh, H. W., 2009, "Discrete Event/Discrete Time Simulation of Block Erection by a Floating Crane Based on Multibody System Dynamics," 19th International Offshore and Polar Engineering Conference (ISOPE), Osaka International Convention Center, Osaka, Japan, Vol. 3, pp. 678-685.
  17. Ham, S. H., Cha, J. H. and Lee, K. Y., 2009, "Topological Modeling Approach of Multibody System Dynamics for Lifting Simulation of Floating Crane," Journal of Korean Society of CAD/CAM Engineers, Vol. 14, No. 4, pp. 261-270 (Korean).
  18. Ham, S. H., Cha, J. H., Lee, K. Y., Roh, M. I., Park, K. P., Suh, H. W., 2008. A Real-time Simulation of the Floating Object Considering Multibody Interactions and Impulse Response of the Ocean Waves and Its Application to the Shipbuilding Process Planning, Proceeding of the SNAK(Society of Naval Architecture of Korea) Spring Conference, JeJu, Korea, pp. 1669-1676 (Korean).
  19. Park, K. P., Cha, J. H. and Lee, K. Y., 2009, "Equations of Flexible Multibody System Dynamics for a Floating Crane and a Cargo with Elastic Booms," Proceeding of the SNAK(Society of Naval Architecture of Korea) Spring Conference, Changwon, Korea, pp. 1744-1751 (Korean).
  20. Cha, J. H., Ham, S. H. and Lee, K. Y., 2007, "Calculation of the Hydrostatic Force and Moment by Pressure Integration Technique," Technical report, Advanced Ship Design Automation Lab., Seoul National University (Korean).
  21. Cummins, W. E., 1962, "The Impulse Response Function and Ship Motions," Schiffstechnik, Vol. 9, pp. 101-109.
  22. Faltinsen, O. M., 1990, Sea Loads on Ships and Offshore Structures, University of Cambridge.
  23. Subbaraj, K. and Dokainish, M.A., 1989, "A Survey of Direct Time-Integration Methods in Computational Structural Dynamics - I. Explicit Methods," Computers & Structures, Vol. 32, No. 6, pp. 1371-1386. https://doi.org/10.1016/0045-7949(89)90314-3
  24. Subbaraj, K. and Dokainish, M.A., 1989, "A Survey of Direct Time-Integration Methods in Computational Structural Dynamics - II. Implicit Methods," Computers & Structures, Vol. 32, No. 6, pp. 1387-1401. https://doi.org/10.1016/0045-7949(89)90315-5
  25. Newmark, N.M., 1959, "A Method of Computation for Structural Dynamics," Journal of the Engineering Mechanics Division (Proceedings of the American Society of Civil Engineers), pp.67-94.
  26. Hilber, H.M., Hughes, T.J.R. and Taylor, R.L., 1977, "Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics," Earthquake Engineering and Structural Dynamics, Vol. 5, pp. 283-292. https://doi.org/10.1002/eqe.4290050306

Cited by

  1. A Preliminary Study on the Optimal Shape Design of the Axisymmetric Forging Component Using Equivalent Static Loads vol.35, pp.1, 2011, https://doi.org/10.3795/KSME-A.2011.35.1.001
  2. Power Control of MW Wind Turbine vol.35, pp.1, 2011, https://doi.org/10.3795/KSME-A.2011.35.1.011
  3. Modeling of Multi-Boom Floating Crane for Lifting Analysis of Offshore Wind Turbine vol.35, pp.1, 2011, https://doi.org/10.3795/KSME-A.2011.35.1.115