Skip to main content
SpringerLink
Log in

Model Order Reduction and Nonlinear Dynamic Analysis of the Folding Fin with Freeplay Nonlinearity

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

Abstract

Purpose

To reduce the model size and improve the efficiency of the dynamic analysis of folding fins, a novel condensation modeling method is proposed in this paper.

Methods

The linear degree-of-freedoms (DOFs) of the components of folding fins are truncated via finite element model reduction by using the fixed-interface component mode synthesis method, and the DOFs at the connection interface between the adjacent components are reduced via coordinate condensation. The linear and nonlinear case studies of a folding fin with adjustable connection conditions are conducted to validate the proposed condensation modeling method.

Results

The results obtained by the finite element calculation and experiment measurement of a folding fin with different connection conditions are in good agreement with their counterpart of the condensation model, and the computation time of the condensation model is significantly less than that of the finite element model.

Conclusion

The proposed condensation modeling method can significantly improve the computational efficiency and simultaneously guarantee the accuracy compared to the traditional finite element modeling method for folding fins.

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

Data availability

Data will be made available on request.

References

  1. Liu S-S, Zhao R, Yu K-P, Zheng B-W (2022) Nonlinear system identification framework of folding fins with freeplay using backbone curves. Chin J Aeronaut 35(10):183–194

    Article  Google Scholar 

  2. Yang N, Wang N, Zhang X, Liu W (2016) Nonlinear flutter wind tunnel test and numerical analysis of folding fins with freeplay nonlinearities. Chin J Aeronaut 29(1):144–159

    Article  Google Scholar 

  3. Ma Z-S, Wang B, Zhang X, Ding Q (2019) Nonlinear system identification of folding fins with freeplay using direct parameter estimation. Int J Aerosp Eng 2019:3978260

    Article  Google Scholar 

  4. He H-N, Yu K-P, Tang H, Li J-Z, Zhou Q-K, Zhang X-L (2019) Vibration experiment and nonlinear modelling research on the folding fin with freeplay. Chin J Theor Appl Mech 51(5):1476–1488

    Google Scholar 

  5. Al-Mashhadani WJ, Dowell EH, Wasmi HR, Al-Asadi AA (2017) Aeroelastic response and limit cycle oscillations for wing-flap-tab section with freeplay in tab. J Fluid Struct 68:403–422

    Article  Google Scholar 

  6. Noël JP, Renson L, Kerschen G (2014) Complex dynamics of a nonlinear aerospace structure: experimental identification and modal interactions. J Sound Vib 333(12):2588–2607

    Article  Google Scholar 

  7. Bae JS, Yang SM, Lee I (2002) Linear and nonlinear aeroelastic analysis of fighter-type wing with control surface. J Aircr 39(4):697–708

    Article  Google Scholar 

  8. Abdelkefi A, Vasconcellos R, Marques FD, Hajj MR (2012) Modeling and identification of freeplay nonlinearity. J Sound Vib 331(8):1898–1907

    Article  Google Scholar 

  9. Noël JP, Kerschen G (2017) Nonlinear system identification in structural dynamics: 10 more years of progress. Mech Syst Signal Process 83:2–35

    Article  Google Scholar 

  10. Lee D-M, Kim J-Y (2008) Nonlinear aeroelastic analysis in time domain for folded fins using zaero. J Korea Inst Mil Sci Technol 11(4):159–165

    MathSciNet  Google Scholar 

  11. Tang D, Dowell EH (2010) Aeroelastic airfoil with free play at angle of attack with gust excitation. AIAA J 48(2):427–442

    Article  Google Scholar 

  12. Chung KW, Chan CL, Lee BHK (2007) Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method. J Sound Vib 299(3):520–539

    Article  Google Scholar 

  13. Guo X-Y, Zhang Y, Zhang W, Sun L, Chen S-P (2017) Nonlinear dynamics of z-shaped folding wings with 1:1 inner resonance. Int J Bifurc Chaos 27(8):1750124

    Article  MathSciNet  Google Scholar 

  14. Kim DH, Lee IN (2000) Transonic and low-supersonic aeroelastic analysis of a two-degree-of-freedom airfoil with a freeplay non-linearity. J Sound Vib 234(5):859–880

    Article  Google Scholar 

  15. Vasconcellos R, Abdelkefi A, Marques FD, Hajj MR (2012) Representation and analysis of control surface freeplay nonlinearity. J Fluid Struct 31:79–91

    Article  Google Scholar 

  16. Sazesh S, Shams S (2017) Nonlinear aeroelastic analysis of an airfoil with control surface free-play using stochastic approach. J Fluid Struct 72:114–126

    Article  Google Scholar 

  17. Qi W-C, Zhao C-X, Liu B-H, Tian S-M (2022) Flutter and discrete gust load alleviation characteristics of multi-segment folding wings with constant cross section. J Sound Vib 540:117312

    Article  Google Scholar 

  18. He H-N, Tang H, Yu K-P, Li J-Z, Yang N, Zhang X-L (2020) Nonlinear aeroelastic analysis of the folding fin with freeplay under thermal environment. Chin J Aeronaut 33(9):2357–2371

    Article  Google Scholar 

  19. Palomba I, Richiedei D, Trevisani A (2016) Mode selection for reduced order modeling of mechanical systems excited at resonance. Int J Mech Sci 114:268–276

    Article  Google Scholar 

  20. Sinha K, Singh NK, Abdalla MM, De Breuker R, Alijani F (2020) A momentum subspace method for the model-order reduction in nonlinear structural dynamics: theory and experiments. Int J Non-Linear Mech 119:103314

    Article  Google Scholar 

  21. Kumar R, Ali SF, Jeyaraman S, Gupta S (2021) Uncertainty quantification of bladed disc systems using data driven stochastic reduced order models. Int J Mech Sci 190:106011

    Article  Google Scholar 

  22. Jiang Z, Li W, Chai Y, Gui Q (2023) Application of overlapping finite element for free and forced vibration analysis of 2d linear elastic solids. J Vib Eng Technol. https://doi.org/10.1007/s42417-023-01098-x

    Article  Google Scholar 

  23. Zhai Y-J, Ma Z-S, Wang B, Ding Q (2023) Dynamic characteristic analysis of beam structures with nonlinear elastic foundations and boundaries. Int J Non-Linear Mech 153:104409

    Article  Google Scholar 

  24. Wang D (2023) Theoretical dynamic reduction for steady-state nonlinear vibration responses of complex jointed structures having hysteretic contact behavior. Int J Non-Linear Mech 157:104556

    Article  Google Scholar 

  25. Mazzilli CEN, Gonçalves PB, Franzini GR (2022) Reduced-order modelling based on non-linear modes. Int J Mech Sci 214:106915

    Article  Google Scholar 

  26. Ma Z-S, Ding Q, Zhai Y-J (2021) Hybrid modeling of nonlinear-jointed structures via finite-element model reduction and deep learning techniques. J Vib Eng Technol 9(4):575–585

    Article  Google Scholar 

  27. Wang S, Li J-H, Sun L (2023) Reduced-order modeling for the coupling vibration analysis of bladed rotors supported by journal bearings. J Vib Eng Technol. https://doi.org/10.1007/s42417-023-01088-z

    Article  Google Scholar 

  28. Bae JS, Kim DK, Shin WH, Lee I, Kim SH (2004) Nonlinear aeroelastic analysis of a deployable missile control fin. J Spacecr Rocket 41(2):264–271

    Article  Google Scholar 

  29. Kim DK, Bae JS, Lee I, Han JH (2005) Dynamic model establishment of a deployable missile control fin with nonlinear hinge. J Spacecr Rocket 42(1):66–77

    Article  Google Scholar 

  30. Shin WH, Lee I, Shin YS, Bae JS (2007) Nonlinear aeroelastic analysis for a control fin with an actuator. J Aircr 44(2):597–605

    Article  Google Scholar 

  31. Liu C-Y, An C, Xie C-C, Zhang X, Yang L (2024) Experimental and numerical flutter analysis of a folding fin with multiple asymmetric free-plays. Chin J Aeronaut. https://doi.org/10.1016/j.cja.2023.10.030

    Article  Google Scholar 

  32. Ren H-Y, Wang Y, Wang L, Zhou J-B, Chang H-J, Cai Y-P, Lei B (2024) Design-oriented dynamic model of deployable fin under time-varying elevated temperature environment. Aeronaut J 128(1322):631–654

    Article  Google Scholar 

  33. Yoon KH, Heo SP, Song KN, Jung YH (2004) Dynamic impact analysis of the grid structure using multi-point constraint (MPC) equation under the lateral impact load. Comput Struct 82(23–26):2221–2228

    Article  Google Scholar 

  34. Jendele L, Červenka J (2009) On the solution of multi-point constraints – application to FE analysis of reinforced concrete structures. Comput Struct 87(15–16):970–980

    Article  Google Scholar 

  35. Gonzalez Perez I, Fuentes Aznar A (2017) Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints. Mech Mach Theory 117:35–47

    Article  Google Scholar 

  36. Kong L-F, Jiang H-L, Amir HG, Li Y (2019) Condensation modeling of the bolted joint structure with the effect of nonlinear dynamics. J Sound Vib 442:657–676

    Article  Google Scholar 

  37. Ma Z-S, Chang H-Z, Ding Q, Wang W (2021) Condensation modeling of the linear structure with nonlinear boundary conditions. Arch Appl Mech 91(6):2747–2759

    Article  Google Scholar 

  38. Zhai Y-J, Ma Z-S, Chang H-Z, Ding Q (2021) Model order reduction and dynamic characteristic analysis of the bolted flange structure with free-free boundaries. Struct 34:149–157

    Article  Google Scholar 

  39. Craig RR, Bampton MCC (1968) Coupling of substructures for dynamic analyses. AIAA J 6(7):1313–1319

    Article  Google Scholar 

  40. Hurty WC (1965) Dynamic analysis of structural systems using component modes. AIAA J 3(4):678–685

    Article  Google Scholar 

  41. Hurty WC (1960) Vibrations of structural systems by component mode synthesis. J Eng Mech Div 86(4):51–69

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 12272258), the Aeronautical Science Foundation of China (Grant no. 2020Z009048001), and the Young Elite Scientists Sponsorship Program by Tianjin (Grant no. TJSQNTJ-2020-01).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Tianjin, 300350, China

    Jie Fu, Zhi-Sai Ma & Qian Ding

  2. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, 300350, China

    Jie Fu, Zhi-Sai Ma & Qian Ding

  3. China Academy of Launch Vehicle Technology, Beijing, 100076, China

    Zhixin Ma, Xin Sui & Bo Liu

Authors
  1. Jie Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Sai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhixin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin Sui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Qian Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Sai Ma.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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

Fu, J., Ma, ZS., Ma, Z. et al. Model Order Reduction and Nonlinear Dynamic Analysis of the Folding Fin with Freeplay Nonlinearity. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01396-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42417-024-01396-y

Keywords

Search

Navigation