Skip to main content
SpringerLink
Log in

Some features of the acceleration impulse response function

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Impulse response functions (IRFs) and frequency response functions (FRFs) are fundamental quantities that describe the dynamic behaviour of a linear vibrating system in the time and frequency domains respectively. The acceleration IRF is of particular concern in this paper, because unlike the displacement and velocity IRFs it contains a Delta function as well as a decaying oscillation. The origin of this Delta function is shown to be due to the causality constraint rather than the system. To illustrate the characteristics of the IRFs and FRFs, simulations are presented for a single-degree-of-freedom system, and are supported by some laboratory experimental work. The acceleration IRF is partitioned into the impulse component (Delta function for the simulations) and the oscillatory component. They are separately transformed to the frequency domain to illustrate their effects in the accelerance FRFs for both simulated and measured data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Shin K, Hammond JK (2008) Fundamentals of signal processing for sound and vibration engineers. Wiley, Chichester

    Google Scholar 

  2. Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Wiley, Chichester

    Google Scholar 

  3. Davies P (1983) A recursive approach to Prony parameter estimation. J Sound Vib 89(4):571–583. https://doi.org/10.1016/0022-460X(83)90358-9

    Article  Google Scholar 

  4. Liu JM, Zhu WD, Lu QH, Ren GX (2011) An efficient iterative algorithm for accurately calculating impulse response functions in modal testing. J Vib Acoust 133(6):1–9. https://doi.org/10.1115/1.4005221

    Article  Google Scholar 

  5. Newland DE (2009) An introduction to random vibrations, spectral & wavelet analysis, 3rd edn. Dover Publications Inc, New York

    Google Scholar 

  6. Rice SO (1944) Mathematical analysis of random noise. Bell Syst Tech J 23(3):282–332. https://doi.org/10.1002/j.1538-7305.1944.tb00874.x

    Article  MathSciNet  MATH  Google Scholar 

  7. Roberts JB (1965) The response of linear vibratory systems to random impulses. J Sound Vib 2(4):375–390. https://doi.org/10.1016/0022-460X(65)90116-1

    Article  Google Scholar 

  8. Roberts JB (1966) On the response of a simple oscillator to random impulses. J Sound Vib 4(1):51–61. https://doi.org/10.1016/0022-460X(66)90153-2

    Article  Google Scholar 

  9. Roberts JB (1972) System response to random impulses. J Sound Vib 24(1):23–34. https://doi.org/10.1016/0022-460X(72)90119-8

    Article  MATH  Google Scholar 

  10. Di Paola M, Pirrotta A, Valenza A (2011) Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech Mater 43(12):799–806. https://doi.org/10.1016/j.mechmat.2011.08.016

    Article  Google Scholar 

  11. Pinnola FP (2016) Statistical correlation of fractional oscillator response by complex spectral moments and state variable expansion. Commun Nonlinear Sci Numer Simul 39:343–359. https://doi.org/10.1016/j.cnsns.2016.03.013

    Article  MathSciNet  MATH  Google Scholar 

  12. Fuller CR, Elliott SJ, Nelson PA (1996) Active control of vibration. Elsevier, Amsterdam. https://doi.org/10.1016/B978-0-12-269440-0.X5000-6

    Book  Google Scholar 

  13. Brennan MJ, Kim S-M (2001) Feedforward and feedback control of sound and vibration—a Wiener filter approach. J Sound Vib 246(2):281–296. https://doi.org/10.1006/jsvi.2001.3635

    Article  MathSciNet  MATH  Google Scholar 

  14. Da Silva S, Dias Júnior M, Lopes Junior V (2009) Identification of mechanical systems through Kautz filter. J Vib Control 15(6):849–865. https://doi.org/10.1177/1077546308091458

    Article  MathSciNet  MATH  Google Scholar 

  15. Li J, Hao J, Fan X (2015) Structural damage identification with extracted impulse response functions and optimal sensor locations. Electron J Struct Eng 14(1):123–132

    Article  Google Scholar 

  16. Antoni J, Randall RB (2003) A stochastic model for simulation and diagnostics of rolling element bearings with localized faults. J Vib Acoust 125(3):282–289. https://doi.org/10.1115/1.1569940

    Article  Google Scholar 

  17. D’Elia G, Cocconcelli M, Mucchi E (2018) An algorithm for the simulation of faulted bearings in non-stationary conditions. Meccanica 53:1147–1166. https://doi.org/10.1007/s11012-017-0767-1

    Article  MathSciNet  Google Scholar 

  18. McConnell MG, Varoto PS (2008) Vibration testing: theory and practice, 2nd edn. Wiley, New York

    Google Scholar 

  19. Anthony DK, Simón F (2009) Generating ‘‘idealised” impulse response functions to improve or repair single degree of freedom system measurements. Appl Acoust 70(4):531–539. https://doi.org/10.1016/j.apacoust.2008.07.008

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the financial support provided by São Paulo Research Foundation (FAPESP) under Grant Nos. 2013/50412-3, 2017/16953-8 and 2017/14432-0, the National Natural Science Foundation of China (NSFC) under Grant No. 11672058, and the Coordination for the Improvement of Higher Education Personnel (CAPES) under Grant No. 88887.374001/2019-00.

Funding

This research was supported by São Paulo Research Foundation (FAPESP) under Grant Nos. 2013/50412-3, 2017/16953-8 and 2017/14432-0, the National Natural Science Foundation of China (NSFC) under Grant No. 11672058, and the Coordination for the Improvement of Higher Education Personnel (CAPES) under Grant No. 88887.374001/2019-00.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, UNESP-FEIS, Ilha Solteira, São Paulo, 15385-000, Brazil

    M. K. Iwanaga, M. J. Brennan & O. Scussel

  2. Institute of Internal Combustion Engine, Dalian University of Technology, Dalian, 116023, Liaoning, China

    B. Tang

  3. Faculty of Science and Engineering, UNESP-FCE, Tupã, São Paulo, 17602-496, Brazil

    F. C. L. Almeida

  4. Department of Mechanical Engineering, UNESP-FEB, Bauru, São Paulo, 17033-360, Brazil

    F. C. L. Almeida

Authors
  1. M. K. Iwanaga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. J. Brennan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. Scussel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. F. C. L. Almeida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. K. Iwanaga.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 2914 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iwanaga, M.K., Brennan, M.J., Tang, B. et al. Some features of the acceleration impulse response function. Meccanica 56, 169–177 (2021). https://doi.org/10.1007/s11012-020-01265-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-020-01265-4

Keywords

Search

Navigation