Skip to main content

Advertisement

SpringerLink
Log in

Theoretical and experimental study of an enhanced nonlinear energy sink

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Based on theoretical and experimental investigations, this paper proposes a nonlinear energy sink (NES) with piecewise linear springs to enhance vibration suppression effects. A cubic nonlinear oscillator is coupled with a piecewise linear spring to form an enhanced NES (E-NES). Without adding a new resonance region and changing the resonance frequency of the primary system, the enhanced NES can achieve better vibration suppression effects. Based on the free vibration and the forced vibration, the effect of piecewise linear stiffness and gap displacement on the vibration suppression is profoundly investigated. Moreover, the parameters of the piecewise spring are optimized through the differential evolution algorithm to obtain the best damping effect of the E-NES. Furthermore, the experiments are conducted to verify the theoretical results. The results show that the E-NES has a better suppression effect on the vibration of the primary structure than that of the cubic NES in most cases. However, it also happens that the vibration suppression effect of the E-NES is weaker than that of the conventional NES. The design parameters can be optimized efficiently by the differential evolution algorithm. Experiments show that vibration elimination efficiency of the E-NES can exceed 90%. Therefore, it is believed that research on using piecewise springs to enhance the vibration suppression efficiency will attract attention.

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36

Similar content being viewed by others

Data availability statements

The data that support the findings of this study are available from the corresponding author [H. Ding], upon reasonable request.

References

  1. Wang, G.X., Ding, H., Chen, L.Q.: Dynamic effect of internal resonance caused by gravity on the nonlinear vibration of vertical cantilever beams. J. Sound Vib. 474, 115265 (2020). https://doi.org/10.1016/j.jsv.2020.115265

    Article  Google Scholar 

  2. Zhang, B.L., Han, Q.L., Zhang, X.M.: Recent advances in vibration control of offshore platforms. Nonlinear Dyn. 89, 755–771 (2017). https://doi.org/10.1007/s11071-017-3503-4

    Article  Google Scholar 

  3. Domenico, D.D., Ricciardi, G., Takewaki, I.: Design strategies of viscous dampers for seismic protection of building structures: a review. Soil. Dyn. Earthq. Eng. 118, 144–165 (2019). https://doi.org/10.1016/j.soildyn.2018.12.024

    Article  Google Scholar 

  4. Lu, Z., Wang, Z., Zhou, Y., Lu, X : Nonlinear dissipative devices in structural vibration control: a review. J. Sound Vib. 423, 18–49 (2018). https://doi.org/10.1016/j.jsv.2018.02.052

    Article  Google Scholar 

  5. Zhou, S.Y., Claire, J.-M., Chesne, S.: Influence of inerters on the vibration control effect of series double tuned mass dampers: two layouts and analytical study. Struct. Control. Hlth. 26, 2414 (2019). https://doi.org/10.1002/stc.2414

    Article  Google Scholar 

  6. Riascos, C., Marulanda, J., Thomson, P.: Structural control of a grandstand using a semi-active pressurized tuned liquid column damper considering effects of passive crowds. Struct. Control. Hlth. 26, e2426 (2019). https://doi.org/10.1002/stc.2426

    Article  Google Scholar 

  7. Ding, H., Chen, L.Q.: Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dyn. 100, 3061–6107 (2020). https://doi.org/10.1007/s11071-020-05724-1

    Article  Google Scholar 

  8. Jiang, X.A., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dyn. 33(1), 87–102 (2003). https://doi.org/10.1023/A:1025599211712

    Article  MATH  Google Scholar 

  9. Viguie, R., Kerschen, G., Golinval, J.C., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Wouw, N.V.D.: Using passive nonlinear targeted energy transfer to stabilize drill-string systems. Mech. Syst. Signal Process 23, 148–169 (2009). https://doi.org/10.1016/j.ymssp.2007.07.001

    Article  Google Scholar 

  10. Qiu, D.H., Seguy, S., Paredes, M.: Tuned nonlinear energy sink with conical spring: design theory and sensitivity analysis. J. Mech. Design 140(1), 011404 (2018). https://doi.org/10.1115/1.4038304

    Article  Google Scholar 

  11. McFarland, D., Kerschen, M.G., Kowtko, J.J., Lee, Y.S., Bergman, L.A., Vakakis, A.F.: Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J. Acoust. Soc. Am. 118(2), 791–799 (2005). https://doi.org/10.1121/1.1944649

    Article  Google Scholar 

  12. Snoun, C., Bergeot, B., Berger, S.: Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach. Eur. J. Mech. A-Solid. 80, 103917 (2020). https://doi.org/10.1016/j.euromechsol.2019.103917

    Article  MathSciNet  MATH  Google Scholar 

  13. Tsiata, G.C., Karatzia, D.A.: Reliability analysis of the hysteretic nonlinear energy sink in shock mitigation considering uncertainties. J. Vib. Control 26(23–24), 2261–2273 (2020). https://doi.org/10.1177/1077546320919304

    Article  MathSciNet  Google Scholar 

  14. Bitar, D., Ture, S.A., Lamarque, C.H., Gourdon, E., Collet, M.: Extended complexification method to study nonlinear passive control. Nonlinear Dynam. 99(2), 1433–1450 (2019). https://doi.org/10.1007/s11071-019-05365-z

    Article  MATH  Google Scholar 

  15. Bellizzi, S., Chung, K.W., Sampaio, R.: Response regimes of a linear oscillator with a nonlinear energy sink involving an active damper with delay. Nonlinear Dynam. 97(2), 1667–1684 (2019). https://doi.org/10.1007/s11071-019-05089-0

    Article  MATH  Google Scholar 

  16. Gourc, E., Michon, G., Seguy, S., Berlioz, A.: Experimental investigation and design optimization of targeted energy transfer under periodic forcing. J. Vib. Acoust 136(2), 021021 (2014). https://doi.org/10.1115/1.4026432

    Article  Google Scholar 

  17. Dekemele, K., Torre, P.V., Loccufier, M.: Design, construction and experimental performance of a nonlinear energy sink in mitigating multi-modal vibrations. J. Sound Vib. 473, 115243 (2020). https://doi.org/10.1016/j.jsv.2020.115243

    Article  Google Scholar 

  18. Li, Z.Y., Xiong, L.Y., Tang, L.H., Liu, K.F., Mace, B.: Vibration energy harvesting based on a piezoelectric nonlinear energy sink with synchronized charge extraction interface circuit. J. Phys. D: Appl. Phys. 53, 505502 (2020). https://doi.org/10.1016/j.engstruct.2020.111020

    Article  Google Scholar 

  19. Xue, J.R., Zhang, Y.W., Ding, H.: Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation. Appl. Math. Mech.-Engl. Ed. 41(1), 1–14 (2020). https://doi.org/10.1007/s10483-020-2560-6

    Article  MATH  Google Scholar 

  20. Ahmadabadi, Z.N., Khadem, S.E.: Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech. Mach. Theory 50, 134–149 (2012). https://doi.org/10.1016/j.mechmachtheory.2011.11.007

    Article  Google Scholar 

  21. Zang, J., Zhang, Y.W., Ding, H., Yang, T.Z., Chen, L.Q.: The evaluation of a nonlinear energy sink absorber based on the transmissibility. Mech. Syst. Signal Process 125, 99–122 (2019). https://doi.org/10.1016/j.ymssp.2018.05.061

    Article  Google Scholar 

  22. Wei, Y.M., Wei, S., Zhang, Q.L., Dong, X.J., Peng, Z.K., Zhang, W.M.: Targeted energy transfer of a parallel nonlinear energy sink. Appl. Math. Mech. 40(5), 621–630 (2019). https://doi.org/10.1007/s10483-019-2477-6

    Article  MathSciNet  Google Scholar 

  23. Yang, K., Zhang, Y.W., Ding, H., Yang, T.Z., Li, Y., Chen, L.Q.: Nonlinear Energy sink for whole-spacecraft vibration reduction. J. Vib. Acoust 139(2), 021011 (2017). https://doi.org/10.1115/1.4035377

    Article  Google Scholar 

  24. Lo, F.S., Touzé, C., Boisson, J., Cumunel, G.: Nonlinear magnetic vibration absorber for passive control of a multi-storey structure. J. Sound Vib. 438, 33–53 (2019). https://doi.org/10.1016/j.jsv.2018.09.007

    Article  Google Scholar 

  25. Ahmadabadi, Z.N.: Nonlinear energy transfer from an engine crankshaft to an essentially nonlinear attachment. J. Sound Vib. 443, 139–154 (2019). https://doi.org/10.1016/j.jsv.2018.11.040

    Article  Google Scholar 

  26. Yao, H.L., Wang, Y.W., Xie, L.Q., Wen, B.C.: Bi-stable buckled beam nonlinear energy sink applied to rotor system. Mech. Syst. Signal Process 138, 106546 (2020). https://doi.org/10.1016/j.ymssp.2019.106546

    Article  Google Scholar 

  27. Zhang, W.X., Chen, J.E.: Influence of geometric nonlinearity of rectangular plate on vibration reduction performance of nonlinear energy sink. J. Mech. Sci. Technol. 34(8), 3127–3135 (2020). https://doi.org/10.1007/s12206-020-0704-4

    Article  Google Scholar 

  28. Tian, W., Li, Y.M., Li, P., Yang, Z.C., Zhao, T.: Passive control of nonlinear aeroelasticity in hypersonic 3-D wing with a nonlinear energy sink. J. Sound Vib. 462, 114942 (2019). https://doi.org/10.1016/j.jsv.2019.114942

    Article  Google Scholar 

  29. Zang, J., Yuan, T.C., Lu, Z.Q., Zhang, Y.W., Ding, H., Chen, L.Q.: A lever-type nonlinear energy sink. J. Sound Vib. 437, 119–134 (2018). https://doi.org/10.1016/j.jsv.2018.08.058

    Article  Google Scholar 

  30. Zhang, Z., Ding, H., Zhang, Y.W., Chen, L.Q.: Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks. Acta Mech. Sinica-Prc. 37(3), 387–401 (2021). https://doi.org/10.1007/s10409-021-01062-6

    Article  MathSciNet  Google Scholar 

  31. Chen, H.Y., Mao, X.Y., Ding, H., Chen, L.Q.: Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mech. Syst. Signal Process 135, 106383 (2020). https://doi.org/10.1016/j.ymssp.2019.106383

    Article  Google Scholar 

  32. Lu, X.L., Liu, Z.P., Lu, Z.: Optimization design and experimental verification of track nonlinear energy sink for vibration control under seismic excitation. Struct. Control Health Monit. 24, e2033 (2017). https://doi.org/10.1002/stc.2033

    Article  Google Scholar 

  33. Foroutan, K., Jalali, A., Ahmadi, H.: Investigations of energy absorption using tuned bistable nonlinear energy sink with local and global potentials. J. Sound Vib. 447, 155–169 (2019). https://doi.org/10.1016/j.jsv.2019.01.030

    Article  Google Scholar 

  34. Geng, X.F., Ding, H., Mao, X.Y., Chen, L.Q.: Nonlinear energy sink with limited vibration amplitude. Mech. Syst. Signal Process 156, 107625 (2021). https://doi.org/10.1016/j.ymssp.2021.107625

    Article  Google Scholar 

  35. Li, T., Gourc, E., Seguy, S., Berlioz, A.: Dynamics of two vibro-impact nonlinear energy sinks in parallel under periodic and transient excitations. Int. J. Nonlin. Mech. 90, 100–110 (2017). https://doi.org/10.1016/j.ijnonlinmec.2017.01.010

    Article  Google Scholar 

  36. AL-Shudeifat, M. A.: Nonlinear energy sinks with piecewise-Linear nonlinearities. J. Comput. Nonlinear Dyn. 14(12), 124501 (2019). https://doi.org/10.1115/1.4045052

    Article  Google Scholar 

  37. Mao, X.Y., Ding, H., Chen, L.Q.: Nonlinear torsional vibration absorber for flexible structures. J. Appl. Mech. T-Asme. 139, 379–406 (2019). https://doi.org/10.1115/1.4042045

    Article  Google Scholar 

  38. Geng, X.F., Ding, H., Wei, K.X., Chen, L.Q.: Suppression of multiple modal resonances of a cantilever beam by an impact damper. Appl. Math. Mech-Engl. Ed. 41(3), 383–400 (2020). https://doi.org/10.1007/s10483-020-2588-9

    Article  Google Scholar 

  39. Lu, Z., Wang, Z.X., Masri, S.F., Lu, X.L.: Particle impact dampers: Past, present, and future. Struct. Control Health Monit. 25, e2058 (2018). https://doi.org/10.1002/stc.2058

    Article  Google Scholar 

  40. Jiang, J.W., Zhang, P., Patil, D., Li, H.N., Song, G.B.: Experimental studies on the effectiveness and robustness of a pounding tuned mass damper for vibration suppression of a submerged cylindrical pipe. Struct. Control Health Monit. 24, e2027 (2017). https://doi.org/10.1002/stc.2027

    Article  Google Scholar 

  41. Li, K., Darby, A.P.: An approach to the design of buffer for a buffered impact damper. Struct. Control Health Monit. 17, 68–82 (2010). https://doi.org/10.1002/stc.294

    Article  Google Scholar 

  42. Lee, Y.S., Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Physica D-Nonlin. Phenom. 238(18), 1868–1896 (2009). https://doi.org/10.1016/j.physd.2009.06.013

    Article  MATH  Google Scholar 

  43. Nucera, F., Iacono, F.L., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: experimental results. J. Sound Vib. 313(1–2), 57–76 (2008). https://doi.org/10.1016/j.jsv.2007.11.018

    Article  Google Scholar 

  44. Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Kerschen, G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50(3), 651–677 (2007). https://doi.org/10.1007/s11071-006-9189-7

    Article  MATH  Google Scholar 

  45. Wang, D., Lee, Y.S., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Mitigating the effect of impact loading on a vehicle using an essentially nonlinear absorber. Veh. Syst. Dyn. 47(10), 1183–1204 (2009). https://doi.org/10.1080/00423110802531083

    Article  Google Scholar 

  46. Wei, Y.M., Dong, X.J., Guo, P.F., Peng, Z.K., Zhang, W.M.: Enhanced targeted energy transfer by vibro impact cubic nonlinear energy sink. Int. J. Appl. Mech. 10(6), 850061 (2018). https://doi.org/10.1142/S1758825118500618

    Article  Google Scholar 

  47. Yao, H.L., Cao, Y.B., Ding, Z.Y., Wen, B.C.: Using grounded nonlinear energy sinks to suppress lateral vibration in rotor systems. Mech. Syst. Signal Process 124, 237–253 (2019). https://doi.org/10.1016/j.ymssp.2019.01.054

    Article  Google Scholar 

  48. Savadkoohi, A.T., Lamarque, C.H. Dimitrijevic., Z. : Vibratory energy exchange between a linear and a non-smooth system in the presence of the gravity. Nonlinear Dyn. 70(2), 1473–1483 (2012). https://doi.org/10.1007/s11071-012-0548-2

    Article  Google Scholar 

  49. Dimatteo, A., Vannucci, M., Colla, V.: Prediction of mean flow stress during hot strip rolling using genetic algorithms. ISIJ Int. 54(1), 171–178 (2014). https://doi.org/10.2355/isijinternational.54.171

    Article  Google Scholar 

  50. Qu, F.Z., Jiang, Q.G., Jin, Z.: Mud pulse signal demodulation based on support vector machines and particle swarm optimization. J Petrol. Sci. Eng. 192, 107432 (2020). https://doi.org/10.1016/j.petrol.2020.107432

    Article  Google Scholar 

  51. Mehdizadeh, S., Mohammadi, B., Pham, Q.B.: Implementing novel hybrid models to improve indirect measurement of the daily soil temperature: Elman neural network coupled with gravitational search algorithm and ant colony optimization. Measurement 165, 108127 (2020). https://doi.org/10.1016/j.measurement.2020.108127

    Article  Google Scholar 

  52. Zou, W.Q., Pan, Q.K., Meng, T.: An effective discrete artificial bee colony algorithm for multi-AGVs dispatching problem in a matrix manufacturing workshop. Expert. Syst. Appl. 161, 113675 (2020). https://doi.org/10.1016/j.eswa.2020.113675

    Article  Google Scholar 

  53. Chen, C.H.: Compensatory neural fuzzy networks with rule-based cooperative differential evolution for nonlinear system control. Nonlinear Dyn. 75, 355–366 (2014). https://doi.org/10.1007/s11071-013-1071-9

    Article  Google Scholar 

  54. Fister, I., Suganthan, P.N., Fister, I., Kamal, S.M., Al-Marzouki, F.M., Perc, M., Strnad, D.: Artificial neural network regression as a local search heuristic for ensemble strategies in differential evolution. Nonlinear Dyn. 84, 895–914 (2016). https://doi.org/10.1007/s11071-015-2537-8

    Article  MathSciNet  Google Scholar 

  55. Formica, G., Milicchio, F.: Kinship-based differential evolution algorithm for unconstrained numerical optimization. Nonlinear Dyn. 99, 1341–1361 (2020). https://doi.org/10.1007/s11071-019-05358-y

    Article  Google Scholar 

  56. Ali, I.M., Essam, D., Kasmarik, K.: Novel binary differential evolution algorithm for knapsack problems. Inform. Sciences 542, 177–194 (2021). https://doi.org/10.1016/j.ins.2020.07.013

    Article  MathSciNet  Google Scholar 

  57. AL-Shudeifat M.A. : Highly efficient nonlinear energy sink. Nonlinear Dyn. 76(4), 1905–1920 (2014). https://doi.org/10.1007/s11071-014-1256-x

    Article  MathSciNet  MATH  Google Scholar 

  58. Gourdon, E., Alexander, N.A., Taylor, C.A., Lamarque, C.H., Pernot, S.: Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J. Sound Vib. 300, 522–551 (2007). https://doi.org/10.1016/j.jsv.2006.06.074

    Article  Google Scholar 

  59. Vaurigaud, B., Savadkoohi, A.T., Lamarque, C.H.: Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments. Nonlinear Dyn. 67, 37–46 (2012). https://doi.org/10.1007/s11071-011-9955-z

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the National Science Fund for Distinguished Young Scholars (No. 12025204) and the Program of Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-09-E00018).

Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Xiao-Feng Geng & Hu Ding

Authors
  1. Xiao-Feng Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hu Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hu Ding.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

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

Geng, XF., Ding, H. Theoretical and experimental study of an enhanced nonlinear energy sink. Nonlinear Dyn 104, 3269–3291 (2021). https://doi.org/10.1007/s11071-021-06553-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06553-6

Keywords

Search

Navigation