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Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes

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Abstract

NiTiNOL-steel wire rope (NiTi-ST) is a new vibration absorber with nonlinear stiffness and hysteretic damping. Although there are many studies on NiTi-ST nonlinear identification, there are few studies on vibration suppression for laminated structures with NiTi-ST. In the present work, the NiTi-ST is integrated with a composite laminated beam for structural vibration suppression for the first time. A coupling model of the composite laminated beam embedded with NiTi-ST is proposed. The nonlinear restoring force and hysteretic damping force of NiTi-ST are processed into polynomial form. The responses of the beam embedded with different NiTi-ST are investigated by the Galerkin discretization together with the harmonic balance method (HBM). The terms of the polynomial model are discussed. Two numerical methods are utilized for steady-state responses and numerical validations. Simulation results demonstrate the effectiveness of NiTi-ST. This vibration suppression method can be popularized for other laminated structures and contribute to vibration control in engineering fields.

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References

  1. Malatkar, P., Nayfeh, A.H.: Steady-state dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator. Nonlinear Dyn. 47(1), 167–179 (2007). https://doi.org/10.1007/s11071-006-9066-4

    Article  MATH  Google Scholar 

  2. Oueini, S.S., Nayfeh, A.H., Pratt, J.R.: A nonlinear vibration absorber for flexible structures. Nonlinear Dyn. 15(3), 259–282 (1998). https://doi.org/10.1023/A:1008250524547

    Article  MATH  Google Scholar 

  3. Frank Pai, P., Schulz, M.J.: A refined nonlinear vibration absorber. Int. J. Mech. Sci. 42(3), 537–560 (2000). https://doi.org/10.1016/S0020-7403(98)00135-0

    Article  MATH  Google Scholar 

  4. 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). https://doi.org/10.1016/j.jsv.2018.09.007

    Article  Google Scholar 

  5. Alujević, N., Čakmak, D., Wolf, H., Jokić, M.: Passive and active vibration isolation systems using inerter. J. Sound Vib. 418, 163–183 (2018). https://doi.org/10.1016/j.jsv.2017.12.031

    Article  Google Scholar 

  6. Afsharfard, A., Farshidianfar, A.: Design of nonlinear impact dampers based on acoustic and damping behavior. Int. J. Mech. Sci. 65(1), 125–133 (2012). https://doi.org/10.1016/j.ijmecsci.2012.09.010

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Sigalov, G., Gendelman, O.V., Al-Shudeifat, M.A., Manevitch, L.I., Vakakis, A.F., Bergman, L.A.: Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink. Nonlinear Dyn. 69(4), 1693–1704 (2012). https://doi.org/10.1007/s11071-012-0379-1

    Article  MathSciNet  Google Scholar 

  9. Motato, E., Haris, A., Theodossiades, S., Mohammadpour, M., Rahnejat, H., Kelly, P., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Targeted energy transfer and modal energy redistribution in automotive drivetrains. Nonlinear Dyn. 87(1), 169–190 (2017). https://doi.org/10.1007/s11071-016-3034-4

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  11. Zhang, Y.-W., Hou, S., Zhang, Z., Zang, J., Ni, Z.-Y., Teng, Y.-Y., Chen, L.-Q.: Nonlinear vibration absorption of laminated composite beams in complex environment. Nonlinear Dyn. (2020). https://doi.org/10.1007/s11071-019-05442-3

    Article  Google Scholar 

  12. Zhang, Y.-W., Lu, Y.-N., Zhang, W., Teng, Y.-Y., Yang, H.-X., Yang, T.-Z., Chen, L.-Q.: Nonlinear energy sink with inerter. Mech. Syst. Signal Process. 125, 52–64 (2019). https://doi.org/10.1016/j.ymssp.2018.08.026

    Article  Google Scholar 

  13. Xue, J., Zhang, Y., Ding, H., Chen, L.: Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation. Appl. Math. Mech. 41(1), 1–14 (2019). https://doi.org/10.1007/s10483-020-2560-6

    Article  Google Scholar 

  14. Zhang, Y.-W., Zhang, Z., Chen, L.-Q., Yang, T.-Z., Fang, B., Zang, J.: Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks. Nonlinear Dyn. 82(1), 61–71 (2015). https://doi.org/10.1007/s11071-015-2138-6

    Article  MathSciNet  Google Scholar 

  15. 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(2), 885–904 (2018). https://doi.org/10.1007/s11071-017-3917-z

    Article  Google Scholar 

  16. Zhang, Y.-W., Zhang, H., Hou, S., Xu, K.-F., Chen, L.-Q.: Vibration suppression of composite laminated plate with nonlinear energy sink. Acta Astronaut. 123, 109–115 (2016). https://doi.org/10.1016/j.actaastro.2016.02.021

    Article  Google Scholar 

  17. Chen, J., Zhang, W., Yao, M., Liu, J., Sun, M.: Vibration reduction in truss core sandwich plate with internal nonlinear energy sink. Compos. Struct. 193, 180–188 (2018). https://doi.org/10.1016/j.compstruct.2018.03.048

    Article  Google Scholar 

  18. 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. (2020). https://doi.org/10.1016/j.ymssp.2019.106383

    Article  Google Scholar 

  19. Tian, W., Li, Y., Li, P., Yang, Z., 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 

  20. Ozbulut, O.E., Hurlebaus, S., Desroches, R.: Seismic response control using shape memory alloys: a review. J. Intell. Mater. Syst. Struct. 22(14), 1531–1549 (2011). https://doi.org/10.1177/1045389X11411220

    Article  Google Scholar 

  21. Paiva, A., Savi, M.A.: An overview of constitutive models for shape memory alloys. Math. Probl. Eng. (2006). https://doi.org/10.1155/MPE/2006/56876

    Article  MathSciNet  MATH  Google Scholar 

  22. Machado, L.G., Savi, M.A., Pacheco, P.M.C.L.: Nonlinear dynamics and chaos in coupled shape memory oscillators. Int. J. Solids Struct. 40(19), 5139–5156 (2003). https://doi.org/10.1016/S0020-7683(03)00260-9

    Article  MATH  Google Scholar 

  23. Savi, M.A.: Nonlinear dynamics and chaos in shape memory alloy systems. Int. J. Non-linear Mech. 70, 2–19 (2015). https://doi.org/10.1016/j.ijnonlinmec.2014.06.001

    Article  Google Scholar 

  24. Ghasemi, M.R., Shabakhty, N., Enferadi, M.H.: Vibration control of offshore jacket platforms through shape memory alloy pounding tuned mass damper (SMA-PTMD). Ocean Eng. 191, 106348 (2019). https://doi.org/10.1016/j.oceaneng.2019.106348

    Article  Google Scholar 

  25. Kumbhar, S.B., Chavan, S.P., Gawade, S.S.: Adaptive tuned vibration absorber based on magnetorheological elastomer-shape memory alloy composite. Mech. Syst. Signal Process. 100, 208–223 (2018). https://doi.org/10.1016/j.ymssp.2017.07.027

    Article  Google Scholar 

  26. Huang, H., Chang, W.-S.: Application of pre-stressed SMA-based tuned mass damper to a timber floor system. Eng. Struct. 167, 143–150 (2018). https://doi.org/10.1016/j.engstruct.2018.04.011

    Article  Google Scholar 

  27. Qian, H., Li, H., Song, G.: Experimental investigations of building structure with a superelastic shape memory alloy friction damper subject to seismic loads. Smart Mater. Struct. 25(12), 125026 (2016). https://doi.org/10.1088/0964-1726/25/12/125026

    Article  Google Scholar 

  28. Lester, B.T., Baxevanis, T., Chemisky, Y., Lagoudas, D.C.: Review and perspectives: shape memory alloy composite systems. Acta Mech. 226, 3907–3960 (2015). https://doi.org/10.1007/s00707-015-1433-0

    Article  Google Scholar 

  29. Alebrahim, R., Sharifishourabi, G., Sharifi, S., Alebrahim, M., Zhang, H., Yahya, Y., Ayob, A.: Thermo-mechanical behaviour of smart composite beam under quasi-static loading. Compos. Struct. 201, 21–28 (2018). https://doi.org/10.1016/j.compstruct.2018.06.023

    Article  Google Scholar 

  30. Bayat, Y., EkhteraeiToussi, H.: A nonlinear study on structural damping of SMA hybrid composite beam. Thin-Walled Struct. 134, 18–28 (2019). https://doi.org/10.1016/j.tws.2018.09.041

    Article  Google Scholar 

  31. Bayat, Y., EkhteraeiToussi, H.: Damping capacity in pseudo-elastic and ferro-elastic shape memory alloy-reinforced hybrid composite beam. J. Reinf. Plast. Compos. 38(10), 467–477 (2019). https://doi.org/10.1177/0731684418825001

    Article  Google Scholar 

  32. Soltanieh, G., Kabir, M.Z., Shariyat, M.: A robust algorithm for behavior and effectiveness investigations of super-elastic SMA wires embedded in composite plates under impulse loading. Compos. Struct. 179, 355–367 (2017). https://doi.org/10.1016/j.compstruct.2017.07.065

    Article  Google Scholar 

  33. Tinker, M.L., Cutchins, M.A.: Damping phenomena in a wire rope vibration isolation system. J. Sound Vib. 157(1), 7–18 (1992). https://doi.org/10.1016/0022-460X(92)90564-E

    Article  Google Scholar 

  34. Gerges, R.R., Vickery, B.J.: Parametric experimental study of wire rope spring tuned mass dampers. J. Wind Eng. Ind. Aerodyn. 91(12), 1363–1385 (2003). https://doi.org/10.1016/j.jweia.2003.09.038

    Article  Google Scholar 

  35. Carboni, B., Lacarbonara, W.: A new vibration absorber based on the hysteresis of multi-configuration NiTiNOL-steel wire ropes assemblies. In: MATEC Web of Conferences vol 16 (2014). https://doi.org/https://doi.org/10.1051/matecconf/20141601004

  36. Carboni, B., Lacarbonara, W., Auricchio, F.: Hysteresis of multiconfiguration assemblies of NiTiNOL and steel strands: experiments and phenomenological identification. J. Eng. Mech. (2015). https://doi.org/10.1061/(asce)em.1943-7889.0000852

    Article  Google Scholar 

  37. Mohsenian, A., Zakerzadeh, M., Shariat Panahi, M., Fakhrzade, A.: Modeling SMA actuated systems based on Bouc–Wen hysteresis model and feed-forward neural network. J. Comput. Appl. Mech. 49(1), 9–17 (2018). https://doi.org/10.22059/JCAMECH.2017.234999.151

    Article  Google Scholar 

  38. Hassani, V., Tjahjowidodo, T., Do, T.N.: A survey on hysteresis modeling, identification and control. Mech. Syst. Signal Process. 49(1–2), 209–233 (2014). https://doi.org/10.1016/j.ymssp.2014.04.012

    Article  Google Scholar 

  39. Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis Bouc–Wen model, a survey. Arch. Comput. Methods Eng. 16(2), 161–188 (2009). https://doi.org/10.1007/s11831-009-9031-8

    Article  MATH  Google Scholar 

  40. Carboni, B., Lacarbonara, W.: Nonlinear dynamic characterization of a new hysteretic device: experiments and computations. Nonlinear Dyn. 83(1–2), 23–39 (2015). https://doi.org/10.1007/s11071-015-2305-9

    Article  Google Scholar 

  41. Carboni, B., Lacarbonara, W.: Nonlinear vibration absorber with pinched hysteresis: theory and experiments. J. Eng. Mech. (2016). https://doi.org/10.1061/(asce)em.1943-7889.0001072

    Article  Google Scholar 

  42. 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. 40(12), 1791–1804 (2019). https://doi.org/10.1007/s10483-019-2548-9

    Article  Google Scholar 

  43. Carboni, B., Lacarbonara, W., Brewick, P.T., Masri, S.F.: Dynamical response identification of a class of nonlinear hysteretic systems. J. Intell. Mater. Syst. Struct. 29(13), 2795–2810 (2018). https://doi.org/10.1177/1045389x18778792

    Article  Google Scholar 

  44. Brewick, P.T., Masri, S.F., Carboni, B., Lacarbonara, W.: Data-based nonlinear identification and constitutive modeling of hysteresis in NiTiNOL and steel strands. J. Eng. Mech. (2016). https://doi.org/10.1061/(asce)em.1943-7889.0001170

    Article  Google Scholar 

  45. Brewick, P.T., Masri, S.F., Carboni, B., Lacarbonara, W.: Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization. Int. J. Non-linear Mech. 94, 46–58 (2017). https://doi.org/10.1016/j.ijnonlinmec.2017.01.016

    Article  Google Scholar 

  46. Lacarbonara, W., Bernardini, D., Vestroni, F.: Nonlinear thermomechanical oscillations of shape-memory devices. Int. J. Solids Struct. 41(5–6), 1209–1234 (2004). https://doi.org/10.1016/j.ijsolstr.2003.10.015

    Article  MATH  Google Scholar 

  47. Bernardini, D., Rega, G.: Evaluation of different SMA models performances in the nonlinear dynamics of pseudoelastic oscillators via a comprehensive modeling framework. Int. J. Mech. Sci. 130, 458–475 (2017). https://doi.org/10.1016/j.ijmecsci.2017.06.023

    Article  Google Scholar 

  48. Luo, A.C.J., Huang, J.: Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance. J. Vib. Control 18(11), 1661–1674 (2011). https://doi.org/10.1177/1077546311421053

    Article  MathSciNet  Google Scholar 

  49. Ye, S.-Q., Mao, X.-Y., Ding, H., Ji, J.-C., Chen, L.-Q.: Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions. Int. J. Mech. Sci. (2020). https://doi.org/10.1016/j.ijmecsci.2019.105294

    Article  Google Scholar 

  50. Qu, Y., Chen, Y., Long, X., Hua, H., Meng, G.: A variational method for free vibration analysis of joined cylindrical-conical shells. J. Vib. Control 19(16), 2319–2334 (2012). https://doi.org/10.1177/1077546312456227

    Article  MathSciNet  MATH  Google Scholar 

  51. Qu, Y., Chen, Y., Long, X., Hua, H., Meng, G.: A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations. Eur. J. Mech. A/Solids 37, 200–215 (2013). https://doi.org/10.1016/j.euromechsol.2012.06.006

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Nos. 12022213, 11772205) and the Liaoning Revitalization Talents Program (XLYC1807172).

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Authors and Affiliations

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

    Li-Heng Zheng, Ye-Wei Zhang, Hu Ding & Li-Qun Chen

  2. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang, 110136, China

    Ye-Wei Zhang

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  1. Li-Heng Zheng
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All the authors conceived the project. L-HZ wrote the original draft. Y-WZ, HD, and L-QC reviewed the manuscript.

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Correspondence to Ye-Wei Zhang.

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Zheng, LH., Zhang, YW., Ding, H. et al. Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes. Nonlinear Dyn 103, 2391–2407 (2021). https://doi.org/10.1007/s11071-021-06258-w

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