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Modal Parameter Estimation of a Two-Disk- Shaft System by the Unified Matrix Polynomial Approach

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Special Topics in Structural Dynamics, Volume 6

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Abstract

Modal parameters, i.e., modal frequencies, damping ratios, and mode shapes of a two disk-shaft system are estimated in Multiple Input/Multiple Output (MIMO) scheme. The response at the output degrees of freedom (dof) of the considered structure due to the excitation at the input dofs is estimated from theoretical analysis. The generated theoretical data is used to estimate the Frequency Response Function (FRF) matrix, which relates the output (vibration) at response points with the input at the excitation points in the frequency domain. The corresponding Impulse Response Function (IRF) matrix, which relates response and excitation in the time domain, is obtained by Inverse Fast Fourier Transform (IFFT) of the FRF matrix. The unified Matrix Polynomial Approach (UMPA) is employed in the frequency and time domains with the estimated FRF and IRF matrices, respectively, to estimate the desired modal parameters. The obtained results are compared with results from Theoretical Modal Analysis (TMA).

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References

  1. Shahab AS, Thomas J (1987) Coupling effect of disk flexibility on the dynamic behavior of multi disk-shaft system. J Sound Vib 114(3):435–446

    Article  Google Scholar 

  2. Wu F, Flowers GT (1992) A transfer matrix technique for evaluating the natural frequencies and critical speeds of a rotor with multiple flexible disks. J Vib Acoust 114:242–248

    Article  Google Scholar 

  3. Lee CW, Jia HS, Kim CS, Chun SB (1997) Tuning of simulated natural frequencies for a flexible shaft-multiple flexible disk system. J Sound Vib 207(4):435–451

    Article  Google Scholar 

  4. Lee C-W, Chun S-B (1998) Vibration analysis of a rotor with multiple flexible disks using assumed modes method. J Vib Acoust 120:87–94

    Article  Google Scholar 

  5. Jia HS (1999) On the bending coupled natural frequencies of a spinning, multispan Timoshenko shaft carrying elastic disks. J Sound Vib 221:623–649

    Article  Google Scholar 

  6. Jang GH et al (2002) Free vibration analysis of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft using the finite element method and substructure synthesis. J Sound Vib 251(1):59–78

    Article  Google Scholar 

  7. Shen J-Y, Tseng C-W, Chen IY (2004) Vibration of rotating disk/spindle system with flexible housing/stator assemblies. J Sound Vib 271:725–756

    Article  Google Scholar 

  8. Hili MA, Fakhfakh T, Haddar M (2007) Vibration analysis of a rotating flexible shaft-disk system. J Eng Math 57:351–363

    Article  MATH  Google Scholar 

  9. Chun SB, Lee CW (1996) Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed mode method. J Sound Vib 189(5):587–608

    Article  Google Scholar 

  10. Yang CH, Huang SC (2007) The influence of disk's flexibility on coupling vibration of shaft–disk–blades systems. J Sound Vib 301(20):1–17

    Article  Google Scholar 

  11. Khader N, Atoum A, Al-Qaisia A (2007) Theoretical and experimental modal analysis of multiple flexible disk-flexible shaft system. Paper Presented at 2007 SEM annual Conference, June 3–6, Springfield, Massachusetts, USA (2007)

    Google Scholar 

  12. Khader N (2012) “Modal parameters of a flexible disk-flexible shaft system from simulated data” Int. J Vehicle Noise Vib 8(1):60–73

    Article  Google Scholar 

  13. Allemang RJ, Brown DL (1998) A unified matrix polynomial approach to modal identification. J Sound Vib 211(3):301–322

    Article  MATH  Google Scholar 

  14. Phillips AW, Allemang RJ (2004) The unified matrix polynomial approach to understanding modal parameter estimation: an update. Proceedings, International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium

    Google Scholar 

  15. Brown DL, Phillips AW, Allemang RJ (2005) A first order extended state vector expansion approach to experimental modal parameter estimation. Proceedings, International Modal Analysis Conference (2005)

    Google Scholar 

  16. Allemang RJ (2003) The modal assurance criterion–twenty years of use and abuse. J Sound Vib 37(8):14–23

    Google Scholar 

  17. Shin CY et al (1988) A frequency domain global parameter estimation method for multiple reference frequency response measurements. Mech Syst Signal Process 2(4):349–365

    Article  Google Scholar 

  18. der Auweraer V, Leuridan J (1987) Multiple input orthogonal polynomial parameter estimation. Mech Syst Signal Process 1(3):259–272

    Article  Google Scholar 

  19. Shih CY, Tsuei YG, Allemang RJ, Brown DL (1988) Complex mode indication function and its application to spatial domain parameter estimation. J Mech Syst Signal Process 2(4):367–372, Academic Press Limited

    Article  MATH  Google Scholar 

  20. Allemang RJ, Brown DL (2006) A complete review of the complex mode indicator function (CMIF) with applications. Proceedings, International Conference on Noise and Vibration Engineering (ISMA), Katholieke Universiteit Leuven, Belgium, 38 pp

    Google Scholar 

  21. Li S, Fladung WA, Phillips AW, Brown DL (1998) Automotive applications of the enhanced mode indicator function parameter estimation method. Proceedings, International Modal Analysis Conference, pp. 36–44

    Google Scholar 

  22. Juang J-N, Pappa RS (1985) An eigensystem realization algorithm for modal parameter identification and model reduction. AIAA J Guidance Control Dyn 8(4):620–627

    Article  MATH  Google Scholar 

  23. Juang JN (1987) Mathematical correlation of modal parameter identification methods via system realization theory. J Anal Exp Modal Anal 2(1):1–18

    Google Scholar 

Download references

Acknowledgement

This work has been carried out during the author’s stay at University of Cincinnati Structural Dynamics Research Lab. (UC-SDRL) while on a sabbatical leave from Jordan University of Science & Technology (JUST) The author acknowledges the financial support provided by JUST, as well as the valuable discussions with Dr. David Brown from UC-SDRL.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jordan University of Science & Technology (JUST), 3030, Irbid, 22110, Jordan

    Naim Khader

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  1. Naim Khader
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Correspondence to Naim Khader .

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Editors and Affiliations

  1. Boeing Test & Evaluation, Seattle, Washington, USA

    Gary Foss

  2. Dept. of Mechanical Engineering, University of Massachusetts Lowell, Lowell, Massachusetts, USA

    Christopher Niezrecki

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© 2014 The Society for Experimental Mechanics, Inc.

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Khader, N. (2014). Modal Parameter Estimation of a Two-Disk- Shaft System by the Unified Matrix Polynomial Approach. In: Foss, G., Niezrecki, C. (eds) Special Topics in Structural Dynamics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04729-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-04729-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04728-7

  • Online ISBN: 978-3-319-04729-4

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