Skip to main content

Shaping the Frequency Response Function (FRF) of a Multi-Degree-of-Freedom (MDOF) Structure Using Arrays of Tuned Vibration Absorbers (TVA)

  • Conference paper
  • First Online:
Topics in Modal Analysis & Testing, Volume 8

Abstract

Tuned vibration absorbers (TVA) provide passive energy dissipation from their primary structure but are limited to only having significant impact on a single frequency. Many researchers have theoretically determined optimal TVA parameters to build an array of varied sized TVAs to absorb a range of frequencies and ultimately flatten an entire peak of a structure’s frequency response function (FRF). These theoretical approaches often only considered the primary structure to have a single degree-of-freedom and did not consider material and spatial constraints that would normally arise in physical implementation. This study provides the method and results of designing and implementing multiple arrays of TVAs to flatten the FRF at and around both modal frequencies of a two-degree-of-freedom (2DOF) structure. The host 2DOF structure is comprised of two small wooden blocks supported by four thin aluminum posts in a two-story setup with base excitation. A total of 20 TVAs were attached to each primary mass—ten targeting frequencies around the low-frequency mode and ten targeting frequencies around the high-frequency mode. The TVAs were cantilever beams made of varied length dry fettuccini pasta with some including modeling-clay tip masses. The final design successfully reduced the original 2DOF structure’s first natural frequency response by more than 9 dB and second natural frequency response by more than 19 dB for both primary masses.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Davis, C.L., Lesieutre, G.A., Dosch, J.J.: Tunable electrically shunted piezoceramic vibration absorber. Proc. SPIE. 3045, 51–59 (1997)

    Article  Google Scholar 

  2. Kurdila, A.J., Lesieutre, G.A., Zhang, X., Prazenica, C., Niezrecki, C.: Averaging analysis of state-switched piezoelectric structural systems. Proc. SPIE. 5760, 413–422 (2005)

    Article  Google Scholar 

  3. Vignola, J.F., Judge, J.A., Kurdila, A.J.: Shaping of a system’s frequency response using an array of subordinate oscillators. J. Acoust. Soc. Am. 126(1), 129–139 (2009)

    Article  Google Scholar 

  4. Zuo, L., Nayfeh, S.A.: Optimization of the individual stiffness and damping parameters in multiple-tuned-mass-damper-systems. J. Vib. Acoust. 27, 77 (2005)

    Article  Google Scholar 

  5. Akay, A., Xu, Z., Carcaterra, A., Koc, I.M.: Experiments on vibration absorption using energy sinks. J. Acoust. Soc. Am. 118(5), 3043–3049 (2005)

    Article  Google Scholar 

  6. Carcaterra, A., Akay, A., Bernardini, C.: Trapping of vibration energy into a set of resonators: theory and applications to aerospace structures. Mech. Syst. Signal Process. 26, 1–14 (2012)

    Article  Google Scholar 

  7. Vignola, J., Judge, J., Sterling, J., Ryan, T., Kurdila, A., Paruchuri, S.T., Glean, A.: Structural Acoustics and Vibration (others): Paper ICA2016-798. On the use of shunted piezo actuators for mitigation of distribution errors in resonator arrays. Mitigation of Distribution Errors in Subordinate Oscillator Arrays

    Google Scholar 

  8. Paruchuri, S.T., Sterling, J., Kurdila, A., Vignola, J.: Thermodynamic variational formulations of subordinate oscillator arrays (SOA) with linear piezoelectrics, Proceedings of the ASME 2017 International Design Engineering Technical Conferences (IDETC) & Computers and Information in Engineering Conference (2017)

    Google Scholar 

  9. Paruchuri, S.T., Sterling, J., Kurdila, A., Vignola, J.: Piezoelectric composite subordinate oscillator arrays and frequency response shaping for passive vibration attenuation. In: 2017 IEEE Conference on Control Technology and Applications (CCTA), pp. 702–707. IEEE (Aug 2017)

    Google Scholar 

  10. Kitis, L., Wang, B.P., Pilkey, W.D.: Vibration reduction over a frequency range. J. Sound Vib. 84(4), 559–569 (1983)

    Article  Google Scholar 

  11. Inman, D.J.: Engineering Vibration, 4th edn. Undergraduate and Graduate Level Textbook for Vibrations of Mechanical Systems (2014)

    Google Scholar 

Download references

Acknowledgments

Tarazaga would like to acknowledge the support offered through the John R. Jones III Faculty Fellowship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. V. N. Sriram Malladi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Society for Experimental Mechanics, Inc.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Neighborgall, C.R., Kothari, K., Sriram Malladi, V.V.N., Tarazaga, P., Paruchuri, S.T., Kurdila, A. (2020). Shaping the Frequency Response Function (FRF) of a Multi-Degree-of-Freedom (MDOF) Structure Using Arrays of Tuned Vibration Absorbers (TVA). In: Mains, M.L., Dilworth, B.J. (eds) Topics in Modal Analysis & Testing, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12684-1_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-12684-1_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12683-4

  • Online ISBN: 978-3-030-12684-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics