Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Coupled hydroelastic vibrations of a liquid on flexible space structures under zero-gravity - Part I. Mechanical model

  • Received : 2013.12.10
  • Accepted : 2014.02.14
  • Published : 2013.12.25
⟨ Previous Next ⟩

Abstract

The coupled free vibration of flexible structures and on-board liquid in zero gravity space was analyzed, considering the spacecraft main body as a rigid mass, the flexible appendages as two elastic beams, and the on-board liquid as a "spring-mass" system. Using the Lagrangians of a rigid mass (spacecraft main body), "spring-mass" (liquid), and two beams (flexible appendages), as well as assuming symmetric motion of the system, we obtained the frequency equations of the coupled system by applying Rayleigh-Ritz method. Solving these frequency equations, which are governed by three system parameters, as an eigenvalue problem, we obtained the coupled natural frequencies and vibration modes. We define the parameter for evaluating the magnitudes of coupled motions of the added mass (liquid) and beam (appendages). It was found that when varying one system parameter, the frequency curves veer, vibration modes exchange, and the significant coupling occurs not in the region closest to the two frequency curves but in the two regions separate from that region.

Keywords

References

  1. Abramson, H.N. (1966), The dynamic behavior of liquids in moving containers, Chapter 11, NASA SP-106.
  2. Agrawal, B.N. (1993), "Dynamic characteristics of liquid motion in partially filled tanks of a spinning spacecraft", J. Guid. Control. Dynam., 16(4), 636-640. https://doi.org/10.2514/3.21061
  3. Bauer, H.F. and Eidel, W. (1990a), "Linear liquid oscillations in cylindrical container under zero gravity", Appl. Microgravity Tech., II, 212-220.
  4. Bauer, H.F. and Eidel,W. (1990b), "Small amplitude liquid oscillations in a rectangular container under zero gravity", Zeitsschrift fur Flugwissenschaften und Weltraumforschung, 14(1-2), 1-8.
  5. Berglund, M.D., Bassett, C.E., Kelso, J.M., Mishic, J. and Schrange, D. (2007), "The Boeing Delta IV launch vehicle-Pulse-settling approach for second-stage hydrogen propellant management", Acta Astronaut., 61, 416-424. https://doi.org/10.1016/j.actaastro.2007.01.048
  6. Buzhinskii, V.A. (2009), "The equations of the perturbed motion of a rocket as a thin-walled structure with a liquid", J. Appl. Math. Mech., 73, 692-695. https://doi.org/10.1016/j.jappmathmech.2010.01.009
  7. Chiba, M., Watanabe, H. and Bauer, H.F. (2002), "Hydroelastic coupled vibrations in a cylindrical container with a membrane bottom, containing liquid with surface tension", J. Sound. Vib., 251(4), 717-740. https://doi.org/10.1006/jsvi.2001.3986
  8. Farhat, C., Chiu, E.K. and Amsallem, D. (2013), "Modeling of fuel sloshing and its physical effects on flutter", AIAA J., 51(9), 2252-2265. https://doi.org/10.2514/1.J052299
  9. He, Y.J., Ma, X.R., Wang, P.P. and Wang, B.L. (2007), "Low-gravity liquid nonlinear sloshing analysis in a tank under pitching excitation", J. Sound. Vib., 299, 164-177. https://doi.org/10.1016/j.jsv.2006.07.003
  10. Komatsu, K. (1999), "Modeling of the dynamic behavior of liquids in spacecraft", Int. J. Microgravity Sci. Appl., 16(3), 182-190.
  11. Komatsu, K. and Shimizu, J. (1989), Dynamic behavior of liquid in spacecraft (in Japanese), NAL-NASDA Report.
  12. Lu, J., Li, J.F. and Wang, T.S. (2005), "Dynamic response of liquid filled rectangular tank with elastic appendages under pitching excitation", Appl. Math. Mech-Engl., 28(3), 351-359.
  13. McIntyre, J.E. and McIntyre, J.M. (1982), "Some effects of propellant motion on the performance of spinning satellites", Acta Astronaut., 9(11), 645-661. https://doi.org/10.1016/0094-5765(82)90044-3
  14. Santini, P. and Barboni, R. (1978), "Motion of orbiting spacecrafts with a sloshing fluid", Acta Astronaut., 5(7-8), 467-490. https://doi.org/10.1016/0094-5765(78)90078-4
  15. Santini, P. and Barboni, R. (1983), "A minicomputer finite elements program for microgravity hydroelastic analysis", Acta Astronat., 10(2), 81-90. https://doi.org/10.1016/0094-5765(83)90004-8
  16. Utsumi, M. (2004), "A mechanical model for low-gravity sloshing in an axisymmetric tank", Trans. ASME, J. Appl. Mech., 71, 724-730. https://doi.org/10.1115/1.1794700
  17. Vreeburg, J.P.B. (2008), "Sloshsat spacecraft calibration at stationary spin rates", J. Spacecraft. Rockets, 45(1), 65-75. https://doi.org/10.2514/1.30975

Cited by

  1. Influence of liquid sloshing on dynamics of flexible space structures vol.401, 2017, https://doi.org/10.1016/j.jsv.2017.04.029
  2. Strongly coupling partitioned scheme for enhanced added mass computation in 2D fluid-structure interaction vol.5, pp.3, 2013, https://doi.org/10.12989/csm.2016.5.3.235
  3. Influence of torsional rigidity of flexible appendages on the dynamics of spacecrafts vol.8, pp.1, 2013, https://doi.org/10.12989/csm.2019.8.1.019