Skip to main content
SpringerLink
Log in

S\(^4\): simple quasi-1D model for structural health monitoring of single lap joint software

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We present a simple mathematical model in one dimension for structural health monitoring of a single lap joint. In the model, we simulate a vibrational signal which propagates throughout three subdomains: from a first aluminum panel to a second one, connected by an adhesive layer. In particular, modeling a joint area between the two layers, we easily reproduce the presence of a damage (debonding) as a simple disconnection between the first aluminum plate and the adhesive layer. To validate the mathematical model, an analytical/numerical/experimental correlation is presented. We develop (and make available) a MATLAB program (by means of finite differences discretization), with a brief user manual, which simulates the discussed problem.

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

Data Availablity Statement

This manuscript has associated data in a data repository. [Authors’ comment: Datasets generated during the current study are available from the corresponding author on reasonable request, whereas in [27] the reader can find the source code of the MATLAB program herein discussed and used.]

References

  1. L. Sun, Z. Fu, Z. Chen, A localized collocation solver based on fundamental solutions for 3d time harmonic elastic wave propagation analysis. Appl. Math. Comput. 439, 127600 (2023). https://doi.org/10.1016/j.amc.2022.127600

    Article  MathSciNet  Google Scholar 

  2. G. Noh, K.-J. Bathe, Imposing displacements in implicit direct time integration & a patch test. Adv. Eng. Softw. 175, 103286 (2023). https://doi.org/10.1016/j.advengsoft.2022.103286

    Article  Google Scholar 

  3. A. Jenabidehkordi, X. Fu, T. Rabczuk, An open source peridynamics code for dynamic fracture in homogeneous and heterogeneous materials. Adv. Eng. Softw. 168, 103124 (2022). https://doi.org/10.1016/j.advengsoft.2022.103124

    Article  Google Scholar 

  4. H.-L. Minh, T. Sang-To, S. Khatir, M.A. Wahab, T. Cuong-Le, Damage identification in high-rise concrete structures using a bio-inspired meta-heuristic optimization algorithm. Adv. Eng. Softw. 176, 103399 (2023)

    Article  Google Scholar 

  5. S. Junca, B. Lombard, Interaction between periodic elastic waves and two contact nonlinearities. Math. Models Methods Appl. Sci. 22(04), 1150022 (2012)

    Article  MathSciNet  Google Scholar 

  6. M. Viscardi, P. Napolitano, M. Arena, Simulation and experimental validation of fatigue endurance limit of copper alloy for industrial applications. Int. J. Math. Models Methods Appl. Sci. 10, 340–346 (2016)

    Google Scholar 

  7. F. Nicassio, P. Vergallo, R. Vitolo, G. Scarselli, Two dimensional finite difference model with a singularity attenuation factor for structural health monitoring of single lap joints. Struct. Control. Health Monit. 2023, 1429761 (2023). https://doi.org/10.1155/2023/1429761

    Article  Google Scholar 

  8. L. Capineri, A. Bulletti, Ultrasonic guided-waves sensors and integrated structural health monitoring systems for impact detection and localization: A review. Sensors 21(9) (2021). https://doi.org/10.3390/s21092929

  9. J. Mckenna, V. Glenis, C. Kilsby, A new riemann solver for modelling bridges in flood flows - development and experimental validation. Appl. Math. Comput. 447, 127870 (2023). https://doi.org/10.1016/j.amc.2023.127870

    Article  MathSciNet  Google Scholar 

  10. M. Arai, Y. Sato, D. Sugiura, M. Nishimura, H. Ito, H. Cho, Inverse analysis for interface fracture toughness of ti coating film by laser spallation method. Adv. Eng. Softw. 120, 62–67 (2018). https://doi.org/10.1016/j.advengsoft.2016.04.003

    Article  Google Scholar 

  11. S. Saha, A.K. Singh, A. Chattopadhyay, Rayleigh-type wave propagation in exponentially graded initially stressed composite structure resting on rigid and yielding foundations. Appl. Math. Comput. 435, 127421 (2022). https://doi.org/10.1016/j.amc.2022.127421

    Article  MathSciNet  Google Scholar 

  12. F. Ricci, E. Monaco, N.D. Boffa, L. Maio, V. Memmolo, Guided waves for structural health monitoring in composites: A review and implementation strategies. Progress in Aerospace Sciences 129, 100790 (2022). https://doi.org/10.1016/j.paerosci.2021.100790. Impact induced dynamic response and failure behavior of aircraft structures

  13. X. Zhang, S. Yuan, T. Hao, Lamb wave propagation modeling for structure health monitoring. Front. Mech. Eng. China 4(3), 326–331 (2009). https://doi.org/10.1007/s11465-009-0045-6

    Article  Google Scholar 

  14. S. Solorza-Calderón, Torsional waves of infinite fully saturated poroelastic cylinders within the framework of biot viscosity-extended theory. Appl. Math. Comput. 391, 125636 (2021). https://doi.org/10.1016/j.amc.2020.125636

    Article  MathSciNet  Google Scholar 

  15. H. Chen, G. Zhang, D. Fan, L. Fang, L. Huang, Nonlinear lamb wave analysis for microdefect identification in mechanical structural health assessment. Measurement 164, 108026 (2020). https://doi.org/10.1016/j.measurement.2020.108026

    Article  Google Scholar 

  16. O. Mesnil, A. Recoquillay, T. Druet, V. Serey, H.T. Hoang, A. Imperiale, E. Demaldent, Experimental validation of transient spectral finite element simulation tools dedicated to guided wave-based structural health monitoring. J. Nondestruct. Eval. Diagnost. Prognost. Eng. Syst. 4(4) (2021). https://doi.org/10.1115/1.4050708. 041003

  17. Products & Software. http://www.me.sc.edu/Research/lamss/html/software.html (2002)

  18. Disperse - Download Form. http://www.disperse.software/

  19. F. Dassi, C. Lovadina, M. Visinoni, Hybridization of the virtual element method for linear elasticity problems. Math. Models Methods Appl. Sci. 31(14), 2979–3008 (2021)

    Article  MathSciNet  Google Scholar 

  20. S. Wu, S. Gong, J. Xu, Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor. Math. Models Methods Appl. Sci. 27(14), 2711–2743 (2017)

    Article  MathSciNet  Google Scholar 

  21. M.E. Gurtin, The linear theory of elasticity. Linear Theories of Elasticity and Thermoelasticity, pp. 1–295. Springer (1973). https://doi.org/10.1007/978-3-662-39776-3-1

  22. V. Giurgiutiu, Structural health monitoring (SHM) of aerospace composites. Polymer Composites in the Aerospace Industry, pp. 491–558. Elsevier (2019). https://doi.org/10.1016/B978-0-08-102679-3.00017-4

  23. F. Nicassio, S. Carrino, G. Scarselli, Elastic waves interference for the analysis of disbonds in single lap joints. Mech. Syst. Signal Process. 128, 340–351 (2019). https://doi.org/10.1016/j.ymssp.2019.04.011

    Article  ADS  Google Scholar 

  24. V. Giurgiutiu, Chapter 15 - case studies of multi-method shm with pwas transducers: Damage id in experimental signals. In: Giurgiutiu, V. (ed.) Structural Health Monitoring with Piezoelectric Wafer Active Sensors (Second Edition), Second edition edn., pp. 863–905. Academic Press, Oxford (2014). https://doi.org/10.1016/B978-0-12-418691-0.00015-0

  25. G.B. Santoni, L. Yu, B. Xu, V. Giurgiutiu, Lamb wave-mode tuning of piezoelectric wafer active sensors for structural health monitoring. J. Vib. Acoust. 129(6), 752–762 (2007). https://doi.org/10.1115/1.2748469

    Article  Google Scholar 

  26. R. Courant, K. Friedrichs, H. Lewy, Über die partiellen differenzengleichungen der mathematischen physik. Math. Ann. 100(1), 32–74 (1928). https://doi.org/10.1007/BF01448839

    Article  MathSciNet  Google Scholar 

  27. Nicassio-Vergallo (S4) · GitHub. https://github.com/Nicassio-Vergallo

Download references

Acknowledgements

The authors wish to express their sincerest gratitude to Prof. G. Scarselli and Prof. R. Vitolo who provided them with a nice occasion for developing this software. PV’s research was partially supported by the research project Mathematical Methods in Non-Linear Physics (MMNLP) and by the Commissione Scientifica Nazionale – Gruppo 4 – Fisica Teorica of the Istituto Nazionale di Fisica Nucleare (INFN).

Author information

Author notes

  1. Pierandrea Vergallo and Francesco Nicassio authors contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics “Federigo Enriques”, University of Milano, Via C. Saldini, 50, Milan, 20133, Italy

    Pierandrea Vergallo

  2. Istituto Nazionale di Fisica Nucleare, Sez. di Milano, Rome, 20133, Italy

    Pierandrea Vergallo

  3. Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Italy

    Francesco Nicassio

Authors
  1. Pierandrea Vergallo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Nicassio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierandrea Vergallo.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Vergallo, P., Nicassio, F. S\(^4\): simple quasi-1D model for structural health monitoring of single lap joint software. Eur. Phys. J. Plus 138, 1135 (2023). https://doi.org/10.1140/epjp/s13360-023-04723-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04723-6

Search

Navigation