Skip to main content
SpringerLink
Log in

Wide Band-gaps in Finite Timoshenko Locally Resonant Beams Carrying Periodic Separated Force and Moment Resonators: Forced Vibration Analysis Based on an Exact Wave-Based Approach

  • Original Paper
  • Published:
Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Introduction

Artificial materials, known as phononic crystals (PCs) and acoustics/elastic metamaterials (AMs/EMs), have been proved to have band-gaps within which no flexural wave can propagate through, which have received great attentions. Among AMs/EMs, locally resonant (LR) beams are frequently encountered in the field of mechanical, civil and aeronautical engineering. However, the analysis of finite LR beams lacks of an efficient and exact approach.

Objectives

The primary objective of this study is to employ and develop an exact and efficient wave-based vibration analysis approach to study a finite Timoshenko LR beam carrying periodic separated force and moment type resonators.

Methods

The proposed wave-based analysis approach is a powerful method that provides the exact solution in vibration analysis for structural waves that propagate along uniform structural elements and reflect and transmit at structural discontinuities. With the approach, the modeling and analysis process can be well simplified, which improves the efficiency in the design and analysis of finite LR beams.

Results

The frequency response results with three sets of resonators obtained through wave-based analysis approach show great agreements with both simulation and experimental results. Moreover, the measured results of the resonator with higher natural frequency show the promising advantage in achieving broader band-gap in low-frequency range, because the propagation attenuation in the experiment causes the absence of the narrow pass-bands which exists in the theoretical results.

Conclusion

This paper proves that the wave-based vibration analysis approach was an exact and efficient method in solving complex vibration problem in finite periodic LR structures. In addition, the rich dispersion relation and wide band-gap property of the separated force and moment type resonators are demonstrated with the theoretical, simulation, and experimental results.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Liu Z, Chan CT, Sheng P (2005) Analytic model of phononic crystals with local resonances. Phys Rev B 71:014103

    Article  Google Scholar 

  2. Yu D, Liu Y, Wang G, Zhao H, Qiu J (2006) Flexural vibration band gaps in Timoshenko beams with locally resonant structures. J Appl Phys 100(12):124901

    Article  Google Scholar 

  3. Qiao H, Li QS, Li GQ (2002) Vibratory characteristics of flexural non-uniform Euler-Bernoulli beams carrying an arbitrary number of spring–mass systems. Int J Mech Sci 44(4):725–743

    Article  Google Scholar 

  4. Zhou J, Dou L, Wang K, Xu D, Ouyang H (2019) A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dyn 96:647–665

    Article  Google Scholar 

  5. Hajhosseini M, Rafeeyan M, Ebrahimi S (2017) Vibration band gap analysis of a new periodic beam model using GDQR method. Mech Res Commun 79:43–50

    Article  Google Scholar 

  6. Liang X, Wang T, Jiang X, Liu Z, Ruan Y, Deng Y (2019) A numerical method for flexural vibration band gaps in a phononic crystal beam with locally resonant oscillators. Crystals 9:293

    Article  Google Scholar 

  7. Sugino C, Xia Y, Leadenham S, Ruzzene M, Erturk A (2017) A general theory for bandgap estimation in locally resonant metastructures. J Sound Vib 406:104–123

    Article  Google Scholar 

  8. El-Borgi S, Fernandes R, Rajendran P, Yazbeck R, Boyd JG, Lagoudas DC (2020) Multiple bandgap formation in a locally resonant linear metamaterial beam: Theory and experiments. J Sound Vibr 488:115647

    Article  Google Scholar 

  9. Chen S, Song Y, Zhang H (2019) Wave propagation in l-shape beams with piezoelectric shunting arrays. Shock Vibr 2019:6264251

    Google Scholar 

  10. Wu X, Li Y, Zuo S (2020) The study of a locally resonant beam with aperiodic mass distribution. Appl Acoust 165:107306

    Article  Google Scholar 

  11. Sangiuliano L, Claeys C, Deckers E, Desmet W (2020) Influence of boundary conditions on the stop band effect in finite locally resonant metamaterial beams. J Sound Vib 473:115225

    Article  Google Scholar 

  12. Pires FA, Claeys C, Deckers E, Desmet W (2021) The impact of resonant additions’ footprint on the stop band behavior of 1D locally resonant metamaterial realizations. J Sound Vib 491:115705

    Article  Google Scholar 

  13. Ba’ba’a HBA, Nouh M (2017) Mechanics of longitudinal and flexural locally resonant elastic metamaterials using a structural power flow approach. Int J Mech Sci 122:341–354

    Article  Google Scholar 

  14. Wen S, Xiong Y, Hao S, Li F, Zhang C (2020) Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections. Int J Mech Sci 166:105229

    Article  Google Scholar 

  15. Mei C (2018) A wave-based analytical solution to free vibrations in a combined euler-bernoulli beam/frame and a two-degree-of-freedom spring-mass system. J Vib Acoust 140:061001

    Article  Google Scholar 

  16. Leamy MJ (2012) Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices. J Sound Vib 331:1580–1596

    Article  Google Scholar 

  17. Lv H, Zhang Y (2020) A wave-based vibration analysis of a finite timoshenko locally resonant beam suspended with periodic uncoupled force-moment type resonators. Crystals 10:1132

    Article  Google Scholar 

  18. Lv H, Leamy MJ (2021) Damping frame vibrations using anechoic stubs: analysis using an exact wave-based approach. J Vibr Acoust 143(5):051012

    Article  Google Scholar 

  19. Graff KF (1975) Wave Motion in Elastic Soilds. Ohio State University Press, Columbus

    Google Scholar 

  20. Wang MY, Wang X (2013) Frequency band structure of locally resonant periodic flexural beams suspended with force–moment resonators. J Phys D Appl Phys 46:255502

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the China Scholarship Council under grant number 201906085003.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China

    Hangyuan Lv

  2. Equipment Reliability Institute, Shenyang University of Chemical Technology, Shenyang, China

    Yimin Zhang

Authors
  1. Hangyuan Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yimin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hangyuan Lv.

Ethics declarations

Conflict of interests

The authors declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lv, H., Zhang, Y. Wide Band-gaps in Finite Timoshenko Locally Resonant Beams Carrying Periodic Separated Force and Moment Resonators: Forced Vibration Analysis Based on an Exact Wave-Based Approach. J. Vib. Eng. Technol. 9, 1109–1121 (2021). https://doi.org/10.1007/s42417-021-00285-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42417-021-00285-y

Keywords

Search

Navigation