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Force limited vibration testing: an evaluation of the computation of C2 for real load and probabilistic source

  • Wijker, J.J. (Faculty Engineering Technology, Department Applied Mechanics, University Twente) ;
  • de Boer, A. (Faculty Engineering Technology, Department Applied Mechanics, University Twente) ;
  • Ellenbroek, M.H.M. (Faculty Engineering Technology, Department Applied Mechanics, University Twente)
  • Received : 2014.09.30
  • Accepted : 2015.01.10
  • Published : 2015.04.25
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Abstract

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the load (test item), $C^2$ is a very important parameter for FLVT. A number of computational methods to estimate $C^2$ are described in the literature, i.e., the simple and the complex two degrees of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of $C^2$ to perform a representative random vibration test based on force limitation, when the adjacent structure (source) description is more or less unknown. Marchand discussed the formal description of getting $C^2$, using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between load and source. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected, consisting of modal effective masses and the spring stiffness's associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter $C^2$. When no mathematical model of the source can be made available, estimations of the value $C^2$ can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value $C^2$ can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature have been analyzed and discussed to get more knowledge about the applicability of the probabilistic method.

Keywords

References

  1. Ayyub, B.M. and McCuen, R.H. (1997), Probability, Statistics, & Reliability for Engineers, CRC Press, ISBN 0-8493-2690-7.
  2. Blevins, R.D. (1995), Formulas for Natural Frequency and Mode Shape, Krieger Publishing Company, ISBN 0-89464-894-2.
  3. Ceresetti, A. (2000), "Vibration overtesting on space H/W due to shaker mechanical impedance", Proceedings of the European Conference on Spacecraft Structures, Materials and Mechanical Testing(ESA-SP-468), ESA.
  4. Chang, K.Y. (2002), "Structural loads prediction in force-limited vibration testing", Spacecraft & Launch Vehicle Dynamic Environment Workshop, El Segundo, CA, June.
  5. Cote, A., Sedagliati, R. and Soucy, Y. (2004), "Force-limited vibration complex two-degree-of-system method", AlAA J., 42(6), 1208-1218.
  6. Davis, G.L. (1998), "An Analysis of Nonlinear Damping and Stiffness Effects in Force-Limited Random Vibration Testing", PhD Thesis, Rice University, Houston Texas.
  7. Destefanis, S., Ullio, R., Tritoni, L. and Newerla, A. (2009), "Outcomes from the ESA study IFLV-Improvement of Force Limites Vibration Testing Methods for Equipment Instrument Unit Mechanical Verification", Proceedings of the European Conference on Spacecraft Structures, Materials & Environmental Testing, Toulouse, France, September.
  8. Dharanipathi, V.R. (2003), "Investigation of the semi-empirical method for force limited vibration testing", Master's Thesis, Concordia University, Montreal, Quebec, Canada.
  9. Ewins, D.J. (1986), Modal testing: Theory and Practice, Bruel & Kjaer, ISBN 0 86380 036 X.
  10. Fitzpatrick, K. and McNeill, S.I. (2007), "Methods to specify random vibration acceleration environments that comply with force limit specifications", Proceedings of the lMAC-XXV: Conference & Exposition on Structural Dynamics-Smart Structures and Transducers.
  11. Fullekrug, U. (1996), "Determination of effective masses and modal masses from base-driven test", Proceedings of the lMAC XIV - 14th International Modal Analysis Conference, 671-681.
  12. Girard, A. and Roy, N.A. (1997), "Modal effective parameters in structural dynamics", Eur. J. Finite Elem., 6(2), 233-254.
  13. Gordon, A. (2013), "Analytical force limiting and application to testing", SCLV 2013, Spacecraft and Launch Vehicle Dynamics Environments Workskshop, El Segundo, CA, June.
  14. Kolaini, A.R. and Kern, D.L. (2012), "New approaches in force limited vibration testing of flight hardware", Proceedings of the Aerospace Conference, Mechanical Systems Division/Dynamics Environment, June.
  15. Machard, P. (2007), "Investigation of $C^2$ parameter of force limited vibration testing for multiple degrees of freedom systems", Master's Thesis, Ottawa-Carleton Institute for Mechanical and Aerospace Engineering, University of Ottawa, Ottawa, Canada.
  16. Nowak, A.S. and Collins, K.R. (2000), Reliability of Structures, McGraw-Hill International Editions, ISBN 0-07-116364-9.
  17. Plesseria, P., Rochus, J.Y. and Defise, J.M. (2000), "Effective modal mass", Proceedings of the 5th Conges national de Mecanique Theorique at Appliquee, Louvian-la-Neuve, Belgium, May.
  18. Rosenblueth, E. (1975), "Point estimates for probability moments", Proc. Nat. Acad Sci. USA, 72(10), 3812-3814. https://doi.org/10.1073/pnas.72.10.3812
  19. Scharton, T., Kern, D. and Koliani, A. (2001), "Force limiting practices revisited", Proceedings of the JPL/Aerospace Conference, JPL, California Institute of Technology. Mechanical Systems Division/Dynamics Environment, June.
  20. Scharton, T.D. (1995), "Vibration-test force limits derived from frequency-shift method", AIAA J. Spacecraft Rocket., 32(2), 312-316. https://doi.org/10.2514/3.26611
  21. Scharton, T.D. (1997), Force Limited Vibration Testing Monograph, NASA RP-1403.
  22. Scharton, T.D. (2012), NASA Handbook, Force Limited Vibration Testing, NASA HDBK-7004C
  23. Sedaghati, R., Soucy, Y.Y. and Etienne, N.N. (2003), "Experimental estimation of effective mass for structural dynamics and vibration applications", Proceedings of the Conference: 2003 IMAC-XXI: Conference & Exposition on Structural Dynamics.
  24. Soucy, Y. (2001), "Force limited vibration for testing space hardware", Advanced Aerospace Applications, Proceedings 29th IMAC, Springer.
  25. Soucy, Y., Dharanipathi, V. and Sedaghati, R. (2005), "Comparison of methods for force limited vibration testing", Proceedings of the IMAC-XXIII Conference, Orlando, 31/1-3/2.
  26. Stevens, R.R. (1996), "Development of a force specification for a force-limited random vibration test", Proceedings of the 16th Aerospace Testing Seminar, Manhattan Beach, CA, USA, March 12-4.
  27. Wijker, J.J. (2004), Mechanical Vibrations in Spacecraft Design, Springer, ISBN 3-540-40530-5.
  28. Wijker, J.J. (2014), "Force limited vibration testing: Computation $C^2$ for real load and probabilistic source", Proceedings of the 13th European Conference on Spacecraft Structures, Materials & Environmental Testing (SP-727), Braunschweig Germany, April.

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