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Identification of nonlinear bolted lap joint parameters using instantaneous power flow balance-based substructure approach

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Abstract

This paper presents a novel nonlinear lap joint parameter identification method based on the instantaneous power flow balance approach, which includes structural nonlinear parameters for realistic modelling. In the present approach, substructure instantaneous power flow balance, whereby the algebraic sum of input power, dissipated power, transmitted power, and time rate of kinetic and strain energy is equated to zero, is used as an objective criterion to formulate an inverse problem for nonlinear joint parameter identification. The correct values of the nonlinear coefficients are estimated by minimizing the objective function using the particle swarm optimization algorithm. The substructure-based identification strategy reduces the number of sensor requirements and also improves the identification performance than the global identification technique. The method was applied to experiments involving a steel beam assembly connected by a single bolted lap joint with various tightening torques. Furthermore, validation studies were also conducted to predict the effectiveness of the proposed method in nonlinear parameter identification. The experimental structure applications have shown that the proposed method is effective for the nonlinear parameter identification of joints.

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References

  1. Ibrahim RA, Pettit CL (2005) Uncertainties and dynamic problems of bolted joints and other fasteners. J Sound Vib 279:857–936. https://doi.org/10.1016/j.jsv.2003.11.064

    Article  Google Scholar 

  2. Jalali H, Khodaparast HH, Friswell MI (2019) The effect of preload and surface roughness quality on linear joint model parameters. J Sound Vib 447:186–204. https://doi.org/10.1016/j.jsv.2019.01.050

    Article  Google Scholar 

  3. Gaul L, Nitsche R (2001) The role of friction in mechanical joints. ASME Appl Mech Rev 54:93–106. https://doi.org/10.1115/1.3097294

    Article  Google Scholar 

  4. Iwan WD (1966) A distributed-element model for hysteresis and its steady-state dynamic response. ASME J Appl Mech 33:893–900

    Article  Google Scholar 

  5. Bograd S, Reuss P, Schmidt A, Gaul L, Mayer M (2011) Modeling the dynamics of mechanical joints. Mech Syst Signal Process 25:2801–2826. https://doi.org/10.1016/j.ymssp.2011.01.010

    Article  Google Scholar 

  6. Segalman DJ (2006) Modelling joint friction in structural dynamics. Struct Control Health Monit 13:430–453. https://doi.org/10.1002/stc.119

    Article  Google Scholar 

  7. Juhn G, Manolis GD (1990) A substructuring technique for time-domain analyses. Comput Struct 36:1097–1102. https://doi.org/10.1016/0045-7949(90)90217-P

    Article  Google Scholar 

  8. Koh CG, See LM, Balendra T (1991) Estimation of structural parameters in time domain: a substructure approach. Earthq Eng Struct Dyn 20:787–801. https://doi.org/10.1002/eqe.4290200806

    Article  Google Scholar 

  9. Koh CG, Hong B, Liaw CY (2003) Substructural and progressive structural identification methods. Eng Struct 25:1551–1563. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:8(957)

    Article  Google Scholar 

  10. Koh CG, Shankar K (2003) Substructural identification method without interface measurement. J Eng Mech 129:769–776. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:7(769)

    Article  Google Scholar 

  11. Lee DH, Hwang WS (2007) An identification method for joint structural parameters using an FRF-based substructuring method and an optimization technique. J Mech Sci Technol 21:2011–2022. https://doi.org/10.1007/BF03177459

    Article  Google Scholar 

  12. Kishore Kumar R, Sandesh S, Shankar K (2007) Parametric identification of nonlinear dynamic systems using combined Levenberg–Marquardt and genetic algorithm. Int J Struct Stab Dyn 7:715–725. https://doi.org/10.1142/S0219455407002484

    Article  MathSciNet  MATH  Google Scholar 

  13. Tee KF, Koh CG, Quek ST (2009) Numerical and experimental studies of a substructural identification strategy. Struct Health Monit 8:397–410. https://doi.org/10.1177/1475921709102089

    Article  Google Scholar 

  14. Mehrjoo M, Khaji N, Moharrami H, Bahreininejad A (2008) Damage detection of truss bridge joints using artificial neural networks. Expert Syst Appl 35:1122–1131. https://doi.org/10.1016/j.eswa.2007.08.008

    Article  Google Scholar 

  15. Law SS, Yong D (2011) Substructure methods for structural condition assessment. J Sound Vib 330:3606–3619. https://doi.org/10.1016/j.jsv.2011.03.003

    Article  Google Scholar 

  16. Varghese CK, Shankar KK (2014) Damage identification using combined transient power flow balance and acceleration matching technique. Struct Control Health Monit 21:135–155. https://doi.org/10.1002/stc.1551

    Article  Google Scholar 

  17. Liu K, Law SS, Zhu XQ (2015) Substructural condition assessment based on force identification and interface force sensitivity. Int J Struct Stab Dyn 15:1450046. https://doi.org/10.1142/S0219455414500461

    Article  MathSciNet  MATH  Google Scholar 

  18. Lyon RH, Maidanik G (1962) Power flow between linearly coupled oscillators. J Acoust Soc Am 34:623–639. https://doi.org/10.1121/1.1918177

    Article  Google Scholar 

  19. Fahy FJ (1994) Statistical energy analysis: a critical overview. Philos Trans R Soc Lond Ser A Phys Eng Sci 346:431–447. https://doi.org/10.1098/rsta.1994.0027

    Article  Google Scholar 

  20. Langley RS (1997) Can an undamped oscillator dissipate energy. J Sound Vib 206:624–626. https://doi.org/10.1006/jsvi.1997.1066

    Article  Google Scholar 

  21. Stephen NG (2006) On energy harvesting from ambient vibration. J Sound Vib 293:409–425. https://doi.org/10.1016/j.jsv.2005.10.003

    Article  Google Scholar 

  22. Li WL, Bonilha MW, Xiao J (2007) Vibrations and power flows in a coupled beam system. J Vib Acoust 129:616–622. https://doi.org/10.1115/1.2775518

    Article  Google Scholar 

  23. Shankar K, Keane AJ (1995) Energy flow predictions in a structure of rigidly joined beams using receptance theory. J Sound Vib 185:867–890. https://doi.org/10.1006/jsvi.1995.0422

    Article  MATH  Google Scholar 

  24. George SK, Shankar K (2006) Vibrational energies of members in structural networks fitted with tuned vibration absorbers. Int J Struct Stab Dyn 6:269–284. https://doi.org/10.1142/S0219455406001952

    Article  Google Scholar 

  25. Mandal NK, Biswas S (2005) Vibration power flow: a critical review. Shock Vib Dig 37:3. https://doi.org/10.1177/0583102404049168

    Article  Google Scholar 

  26. Varghese CK, Shankar K (2011) Identification of structural parameters using combined power flow and acceleration approach in a substructure. Int J Eng Technol Innov 1:65

    Google Scholar 

  27. Xiong YP, Cao QJ (2011) Power flow characteristics of coupled linear and nonlinear oscillators with irrational nonlinear stiffness system. In: Proceedings of the 7th European nonlinear dynamics conference ENOC 2011, Rome, Italy

  28. Yang J, Xiong YP, Xing JT (2014) Nonlinear power flow analysis of the Duffing oscillator. Mech Syst Signal Process 45:563–578. https://doi.org/10.1016/j.ymssp.2013.11.004

    Article  Google Scholar 

  29. Anish R, Shankar K (2021) Non-linear structural parameter identification using instantaneous power flow balance approach. Inverse Probl Sci Eng 29:636–662. https://doi.org/10.1080/17415977.2020.1800685

    Article  MathSciNet  MATH  Google Scholar 

  30. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS'95, Proceedings of the sixth international symposium on micro machine and human science. IEEE, pp 39–43. https://doi.org/10.1109/MHS.1995.494215

  31. Poli R (2008) Analysis of the publications on the applications of particle swarm optimisation. J Artif Evol Appl. https://doi.org/10.1155/2008/685175

    Article  Google Scholar 

  32. Nandakumar P, Shankar K (2013) Structural parameter identification using damped transfer matrix and state vectors. Int J Struct Stab Dyn 13:1250076. https://doi.org/10.1142/S0219455412500769

    Article  Google Scholar 

  33. Khaniki HB, Zohoor H, Sohrabpour S (2017) Performance analysis and geometry optimization of metal belt-based continuously variable transmission systems using multi-objective particle swarm optimization. J Braz Soc Mech Sci Eng 39:4289–4303. https://doi.org/10.1007/s40430-017-0816-7

    Article  Google Scholar 

  34. Weiel M, Götz M, Klein A, Coquelin D, Floca R, Schug A (2021) Dynamic particle swarm optimization of biomolecular simulation parameters with flexible objective functions. Nat Mach Intell 3:727–734. https://doi.org/10.1038/s42256-021-00366-3

    Article  Google Scholar 

  35. Dhanachandra N, Chanu YJ (2020) An image segmentation approach based on fuzzy c-means and dynamic particle swarm optimization algorithm. Multimed Tools Appl 79:18839–18858. https://doi.org/10.1007/s11042-020-08699-8

    Article  Google Scholar 

  36. Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 congress on evolutionary computation, CEC00 (Cat. No. 00TH8512), IEEE, pp 84–88. https://doi.org/10.1109/CEC.2000.870279

  37. Xue S, Tang H, Zhou J (2009) Identification of structural systems using particle swarm optimization. J Asian Archit Build Eng 8:517–524. https://doi.org/10.3130/jaabe.8.517

    Article  Google Scholar 

  38. Quaranta G, Monti G, Marano GC (2010) Parameters identification of Van der Pol-Duffing oscillators via particle swarm optimization and differential evolution. Mech Syst Signal Process 24:2076–2095. https://doi.org/10.1016/j.ymssp.2010.04.006

    Article  Google Scholar 

  39. Ibanez P (1973) Identification of dynamic parameters of linear and non-linear structural models from experimental data. Nucl Eng Des 25:30–41. https://doi.org/10.1016/0029-5493(73)90059-9

    Article  Google Scholar 

  40. Wang J, Sas P (1990) A method for identifying parameters of mechanical joints. ASME J Appl Mech 57:337–342. https://doi.org/10.1115/1.2891994

    Article  Google Scholar 

  41. Liu W, Ewins DJ (2000) Substructure synthesis via elastic media Part I: Joint identification. In: Proceedings of the 18th international modal analysis conference, pp 1153–1159

  42. Kerschen G, Worden K, Vakakis AF, Golinval JC (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process 20:505–592. https://doi.org/10.1016/j.ymssp.2005.04.008

    Article  Google Scholar 

  43. Noël JP, Kerschen G (2017) Nonlinear system identification in structural dynamics: 10 more years of progress. Mech Syst Signal Process 83:2–35. https://doi.org/10.1016/j.ymssp.2016.07.020

    Article  Google Scholar 

  44. Khaniki HB, Ghayesh MH, Chin R, Amabili M (2021) Large amplitude vibrations of imperfect porous-hyperelastic beams via a modified strain energy. J Sound Vib 513:116416. https://doi.org/10.1016/j.jsv.2021.116416

    Article  Google Scholar 

  45. Khaniki HB, Ghayesh MH, Chin R, Chen LQ (2022) Experimental characteristics and coupled nonlinear forced vibrations of axially travelling hyperelastic beams. Thin-Walled Struct 170:108526. https://doi.org/10.1016/j.tws.2021.108526

    Article  Google Scholar 

  46. Khaniki HB, Ghayesh MH, Hussain S, Amabili M (2021) Effects of geometric nonlinearities on the coupled dynamics of CNT strengthened composite beams with porosity, mass and geometric imperfections. Eng Comput. https://doi.org/10.1007/s00366-021-01474-9

    Article  Google Scholar 

  47. Ahmadian H, Jalali H (2007) Generic element formulation for modelling bolted lap joints. Mech Syst Signal Process 21:2318–2334. https://doi.org/10.1016/j.ymssp.2006.10.006

    Article  Google Scholar 

  48. Pirdayr A, Mohammadi M, Kazemzadeh-Parsi MJ, Rajabi M (2021) Self-loosening effects on vibration characteristics of plates with bolted joints: an experimental and finite element analysis. Measurement 185:109922. https://doi.org/10.1016/j.measurement.2021.109922

    Article  Google Scholar 

  49. Jalali H, Ahmadian H, Mottershead JE (2007) Identification of nonlinear bolted lap-joint parameters by force-state mapping. Int J Solids Struct 44:8087–8105. https://doi.org/10.1016/j.ijsolstr.2007.06.003

    Article  MATH  Google Scholar 

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  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India

    R. Anish & K. Shankar

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Anish, R., Shankar, K. Identification of nonlinear bolted lap joint parameters using instantaneous power flow balance-based substructure approach. Int. J. Dynam. Control 11, 1690–1703 (2023). https://doi.org/10.1007/s40435-022-01086-1

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