Skip to main content
SpringerLink
Log in

Analysis of nonlinear vibration control for a functionally graded material plate by NiTiNOL-steel wire ropes

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

Abstract

Traditional nonlinear passive control for continuous structures often requires a non-negligible volume for installation and motion that indirectly changes the design of the original structure and degrades vibration attenuation. Functionally graded materials (FGMs) are typically used in aeronautics and astronautics and are constantly subjected to external excitations that cause significant undesirable vibration. To address this problem, the present work proposes a dynamic model of nonlinear forced vibration of a FGM rectangular plate coupled with NiTiNOL-steel wire ropes (NiTi-ST). NiTi-ST exerts on the FGM complex generalized recovery forces, which are investigated by using two methods: the Galerkin truncation method and the harmonic balanced method (HBM). The HBM coupled with arc-length continuation is used to predict the frequency response and closed detached response (CDR) of the coupling system. The results show that the NiTi-ST reduces the resonance frequency of the FGM plate. The linear damper term introduced by the NiTi-ST determines the level of vibration control. However, the appearance of a CDR could make the dynamic phenomenon more complicated. Furthermore, elimination of the CDR may improve the vibration suppression in the nonlinear system, making it more challenging and urgent to investigate the coupling system above.

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

Similar content being viewed by others

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

References

  1. Leutz, D., Wallmersperger, T.: Thermo-mechanical behavior of functionally graded materials: modeling, simulation and error estimation. Mech. Adv. Mater. Struct. 18, 32–52 (2011)

    Article  Google Scholar 

  2. Mahamood, R.M., Member, E.T.A., Shukla, M., Pityana, S.: Functionally Graded Material: An Overview, vol. III, pp. 2–6 (2012)

  3. Ibrahim, H.H., Tawfik, M.: Limit-cycle oscillations of functionally graded material plates subject to aerodynamic and thermal loads. JVC J. Vib. Control 16, 2147–2166 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hao, Y.X., Zhang, W., Yang, J., Li, S.B.: Nonlinear dynamics of a functionally graded thin simply-supported plate under a hypersonic flow. Mech. Adv. Mater. Struct. 22, 619–632 (2015)

    Article  Google Scholar 

  5. Nguyen, N.V., Nguyen, L.B., Nguyen-Xuan, H., Lee, J.: Analysis and active control of geometrically nonlinear responses of smart FG porous plates with graphene nanoplatelets reinforcement based on Bézier extraction of NURBS. Int. J. Mech. Sci. 180, 105692 (2020)

    Article  Google Scholar 

  6. Salighe, S., Mohammadi, H.: Semi-active nonlinear vibration control of a functionally graded material rotating beam with uncertainties, using a frequency estimator. Compos. Struct. 210, 367–380 (2019)

    Article  Google Scholar 

  7. Lo Feudo, 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)

    Article  Google Scholar 

  8. Ding, H., Chen, L.Q.: Designs, Analysis, and Applications of Nonlinear Energy Sinks. Springer, Dordrecht (2020)

    Book  Google Scholar 

  9. Ding, H., Ji, J., Chen, L.Q.: Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mech. Syst. Signal Process. 121, 675–688 (2019)

    Article  Google Scholar 

  10. Ye, K., Ji, J.C., Brown, T.: Design of a quasi-zero stiffness isolation system for supporting different loads. J. Sound Vib. 471, 1–21 (2020)

    Article  Google Scholar 

  11. Feng, X., Jing, X.: Human body inspired vibration isolation: Beneficial nonlinear stiffness, nonlinear damping and nonlinear inertia. Mech. Syst. Signal Process. 117, 786–812 (2019)

    Article  Google Scholar 

  12. Hu, F., Jing, X.: A 6-DOF passive vibration isolator based on Stewart structure with X-shaped legs. Nonlinear Dyn. 91, 157–185 (2018)

    Article  Google Scholar 

  13. Geng, X.F., Ding, H.: Two-modal resonance control with an encapsulated nonlinear energy sink. J. Sound Vib. 520, 116667 (2022)

    Article  Google Scholar 

  14. Wang, G.X., Ding, H.: Mass design of nonlinear energy sinks. Eng. Struct. 250, 113438 (2022)

    Article  Google Scholar 

  15. Wang, G.X., Ding, H., Chen, L.Q.: Performance evaluation and design criterion of a nonlinear energy sink. Mech. Syst. Signal Process. 169, 108770 (2022)

    Article  Google Scholar 

  16. Kani, M., Khadem, S.E., Pashaei, M.H., Dardel, M.: Vibration control of a nonlinear beam with a nonlinear energy sink. Nonlinear Dyn. 83, 1–22 (2016)

    Article  MathSciNet  Google Scholar 

  17. Huang, D., Zhou, S., Li, R., Yurchenko, D.: On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation. Mech. Syst. Signal Process. 164, 108207 (2022)

    Article  Google Scholar 

  18. Ma, X., Zhou, S.: A review of flow-induced vibration energy harvesters. Energy Convers. Manag. 254, 115223 (2022)

    Article  Google Scholar 

  19. Zhou, S., Lallart, M., Erturk, A.: Multistable vibration energy harvesters: principle, progress, and perspectives. J. Sound Vib. 528, 116886 (2022)

    Article  Google Scholar 

  20. Carboni, B., Lacarbonara, W.: A new vibration absorber based on the hysteresis of multi-configuration NiTiNOL-steel wire ropes assemblies. MATEC Web Conf. 16, 4–5 (2014)

    Article  Google Scholar 

  21. Carboni, B., Lacarbonara, W., Auricchio, F.: Hysteresis of multiconfiguration assemblies of nitinol and steel strands: experiments and phenomenological identification. J. Eng. Mech. 141, 04014135 (2015)

    Google Scholar 

  22. Carboni, B., Lacarbonara, W.: Nonlinear vibration absorber with pinched hysteresis: theory and experiments. J. Eng. Mech. 142, 04016023 (2016)

    Google Scholar 

  23. Zhang, Y., Xu, K., Zang, J., Ni, Z., Zhu, Y., Chen, L.: Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions. Appl. Math. Mech. Engl. Ed. 40, 1791–1804 (2019)

    Article  MathSciNet  Google Scholar 

  24. Zheng, L.H., Zhang, Y.W., Ding, H., Chen, L.Q.: Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes. Nonlinear Dyn. 103, 2391–2407 (2021)

    Article  Google Scholar 

  25. Yang, J.H., Sanjuán, M.A.F., Liu, H.G., Zhu, H.: Noise-induced resonance at the subharmonic frequency in bistable systems. Nonlinear Dyn. 87, 1721–1730 (2017)

    Article  Google Scholar 

  26. Emam, S.A., Abdalla, M.M.: Subharmonic parametric resonance of simply supported buckled beams. Nonlinear Dyn. 79, 1443–1456 (2015)

    Article  Google Scholar 

  27. Sojahrood, A.J., Earl, R., Haghi, H., Li, Q., Porter, T.M., Kolios, M.C., Karshafian, R.: Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactions on oversaturation and enhancement of the subharmonic (2021)

  28. Liu, C., Yu, K.: Superharmonic resonance of the quasi-zero-stiffness vibration isolator and its effect on the isolation performance. Nonlinear Dyn. 100, 95–117 (2020)

    Article  Google Scholar 

  29. Yang, J.H., Sanjuán, M.A.F., Liu, H.G.: Vibrational subharmonic and superharmonic resonances. Commun. Nonlinear Sci. Numer. Simul. 30, 362–372 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Gupta, S.K., Bukhari, M.A., Barry, O.R.: Nonlinear Mode Coupling in a Passively Isolated Mechanical System. Springer, Dordrecht (2020)

    Book  Google Scholar 

  31. Alamo Vargas, V., Gourdon, E., Ture Savadkoohi, A.: Nonlinear softening and hardening behavior in Helmholtz resonators for nonlinear regimes. Nonlinear Dyn. 91, 217–231 (2018)

    Article  Google Scholar 

  32. Jomehzadeh, E., Afshar, M.K., Galiotis, C., Shi, X., Pugno, N.M.: Nonlinear Softening and Hardening Nonlocal Bending Stiffness of an Initially Curved Monolayer Graphene. Elsevier, Amsterdam (2013)

    Book  Google Scholar 

  33. Yan, Z., Sun, W., Hajj, M.R., Zhang, W., Tan, T.: Ultra-broadband piezoelectric energy harvesting via bistable multi-hardening and multi-softening. Nonlinear Dyn. 100, 1057–1077 (2020)

    Article  Google Scholar 

  34. Gatti, G.: Uncovering inner detached resonance curves in coupled oscillators with nonlinearity. J. Sound Vib. 372, 239–254 (2016)

    Article  Google Scholar 

  35. Shen, Y., Li, H., Yang, S., Peng, M., Han, Y.: Primary and subharmonic simultaneous resonance of fractional-order Duffing oscillator. Nonlinear Dyn. 102, 1485–1497 (2020)

    Article  Google Scholar 

  36. Salvatore, A., Carboni, B.: Nonlinear dynamic response of an isolation system with superelastic hysteresis and negative stiffness. Nonlinear Dyn. 107(2), 1765–1790 (2021)

    Article  Google Scholar 

  37. Heinze, T., Panning-von Scheidt, L., Wallaschek, J.: Global detection of detached periodic solution branches of friction-damped mechanical systems. Nonlinear Dyn. 99, 1841–1870 (2020)

    Article  Google Scholar 

  38. Habib, G., Cirillo, G.I., Kerschen, G.: Uncovering detached resonance curves in single-degree-of-freedom systems. Procedia Eng. 199, 649–656 (2017)

    Article  Google Scholar 

  39. Guo, H., Yang, T., Chen, Y., Chen, L.-Q.: Singularity analysis on vibration reduction of a nonlinear energy sink system. Mech. Syst. Signal Process. 173, 109074 (2022)

    Article  Google Scholar 

  40. Liu, Y., Mojahed, A., Bergman, L.A., Vakakis, A.F.: A new way to introduce geometrically nonlinear stiffness and damping with an application to vibration suppression. Nonlinear Dyn. 96, 1819–1845 (2019)

    Article  MATH  Google Scholar 

  41. Chen, J.E., He, W., Zhang, W., Yao, M.H., Liu, J., Sun, M.: Vibration suppression and higher branch responses of beam with parallel nonlinear energy sinks. Nonlinear Dyn. 91, 885–904 (2018)

    Article  Google Scholar 

  42. 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)

    Article  Google Scholar 

  43. Zang, J., Zhang, Y.W.: Responses and bifurcations of a structure with a lever-type nonlinear energy sink. Nonlinear Dyn. 98, 889–906 (2019)

    Article  Google Scholar 

  44. Zang, J., Cao, R.Q., Zhang, Y.W., Fang, B., Chen, L.Q.: A lever-enhanced nonlinear energy sink absorber harvesting vibratory energy via giant magnetostrictive-piezoelectricity. Commun. Nonlinear Sci. Numer. Simul. 95, 105620 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zang, J., Cao, R.Q., Zhang, Y.W.: Steady-state response of a viscoelastic beam with asymmetric elastic supports coupled to a lever-type nonlinear energy sink. Nonlinear Dyn. 105, 1327–1341 (2021)

    Article  Google Scholar 

  46. Shen, Z.B., Tang, H.L., Li, D.K., Tang, G.J.: Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 61, 200–205 (2012)

    Article  Google Scholar 

  47. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: An analytical framework for rectangular FGM tapered plate resting on the elastic foundation. Mater. Today Proc. 28, 1719–1726 (2020)

    Article  Google Scholar 

  48. Zang, J., Cao, R.Q., Fang, B., Zhang, Y.W.: A vibratory energy harvesting absorber using integration of a lever-enhanced nonlinear energy sink and a levitation magnetoelectric energy harvester. J. Sound Vib. 484, 115534 (2020)

    Article  Google Scholar 

  49. Luo, A.C.J., Huang, J.: Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance. JVC J. Vib. Control 18, 1661–1674 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge that this work is supported by the National Natural Science Foundation of China (Project Nos. 12022213, 11902203 and 12272240).

Author information

Authors and Affiliations

  1. College of Aerospace Engineering, Shenyang Aerospace University, Shenyang, 110136, People’s Republic of China

    Jian Zang, Yan Wang & Ye-Wei Zhang

Authors
  1. Jian Zang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ye-Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ye-Wei Zhang.

Ethics declarations

Conflict 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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zang, J., Wang, Y. & Zhang, YW. Analysis of nonlinear vibration control for a functionally graded material plate by NiTiNOL-steel wire ropes. Nonlinear Dyn 111, 5063–5078 (2023). https://doi.org/10.1007/s11071-022-08103-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08103-0

Keywords

Search

Navigation