Manufacturing Technology 2024, 24(3):393-409 | DOI: 10.21062/mft.2024.040

Deformation and Velocity Wave Propagation in a Thin Isotropic Plate

Frantisek Klimenda ORCID...1, Blanka Skocilasova ORCID...1, Jan Skocilas ORCID...2, Josef Soukup ORCID...
1 Faculty of Mechanical Engineering, J. E. Purkyne University in Usti nad Labem. Pasteurova 3334/7, 400 01 Usti nad Labem. Czech Republic
2 Faculty of Mechanical Engineering, Czech Technical University in Prague, 4 Technicka, Prague 166 07, Czech Republic

The propagation and velocity of the deformation wave in the thin isotropic plate is investigated. The deformation is induced by the stroke of impact body onto the facial surface of the plate. The plate is supported perpendicularly. The excitation of the plate oscillation is initialized by a unit force (Heavi-side’s jump). The impact body has a rounded facet by radius c = 2.5 mm. Hook's material model and Kirchhoff’s and Flüegge’s geometric model have been investigated. The analytical solutions for both models are presented. The MATLAB script has been assembled to solve material and geometrical mod-els. The results were compared for two selected points on the surface of the plate. Plate deformation was recorded at two points T1 (at a distance of 20 mm from the impact location on the x axis) and T2 (at a distance of 20 mm from the impact location on the y axis).

Keywords: Thin supported isotropic plate, Impact loading, Hooke’s material model, Kirchhoff’s and Fluegge’s geometrical model

Received: January 17, 2024; Revised: April 23, 2024; Accepted: April 26, 2024; Prepublished online: April 26, 2024; Published: July 1, 2024  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Klimenda F, Skocilasova B, Skocilas J, Soukup J. Deformation and Velocity Wave Propagation in a Thin Isotropic Plate. Manufacturing Technology. 2024;24(3):393-409. doi: 10.21062/mft.2024.040.
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. ABRATE, S. (2011). Impact Engineering of Composite Structures, 1. ed. CISM: Springer - Verlag Wien, 403 p. ISBN 978-3-7091-0522-1. Go to original source...
    2. MOLNÁR, D. BLATNICKÝ, M., DIŽO, J. (2022) Comparison of Analytical and Numerical Approach in Bridge Crane Solution. In: Manufacturing Technology, Vol. 22, No. 2, pp. 192-199, ISSN 1213-2489. DOI: 10.21062/mft.2022.018 Go to original source...
    3. ZAWADA-MICHAŁOWSKA, M., PIEŚKO, P., LEGUTKO, S. (2023) Effect of the Cutting Tool on the Quality of a Machined Composite Part. In: Manufacturing Technology, Vol. 23, No. 6, pp. 870-879, ISSN 1213-2489. DOI: 10.21062/mft.2023.107 Go to original source...
    4. KHORSHIDI, K. (2011). Elasto-Plastic Response of Impacted Moderatly Thick Rectangular Plates with Different Boundary Conditions, In: Procedia Engineering Vol. 10, pp. 1742 - 1747. Go to original source...
    5. WANG, J., DONG, S., PANG, S. D., YU, X., HAN, B., OU, J. (2022). Tailoring Anti-Impact Properties of Ultra-High Performance Concrete by Incorporating Functionalized Carbon Nanotubes. In: Engineering, Vol. 18, pp. 232-245. https://doi.org/10.1016/j.eng.2021.04.030 Go to original source...
    6. VANAM, B., INALA, R. (2012). Static analysis of an isotropic rectangular plate using finite element method (FEM). In: Mech. Eng., Vol. 4, pp. 148-162. Go to original source...
    7. VOLEK, J. (2000). Nestacionární Napjatost Tenké Desky Vyvolané Příčnou Osamělou Silou; Bulletin vědeckých, výzkumných a pedagogických prací ústavu za rok 2000, Ústav techniky a řízení výroby, UJEP: Ústí nad La-bem, Czech Republic.
    8. MOHANTY, S., C., RAMU, I. (20212). Study of Free Vibration Analysis of Rectangular Plate Structures Using Finite Element Method. In: Procedia Eng., Vol. 38, pp. 2758-2766. Go to original source...
    9. KLIMENDA, F.; SOUKUP, J. (2017). Modal Analysis of Thin Aluminium Plate. In: Procedia Eng., Vol. 177, pp. 11-16. ISSN 1877-7058. Go to original source...
    10. DEUTSCH, A., EISENBERGER, M. (2022). Benchmark analytic in-plane vibration frequencies of ortho-tropic rectangular plates. In: Journal of Sound and Vibration, Vol. 541, 117248. https://doi.org/10.1016/j.jsv.2022.117248 Go to original source...
    11. DARUS, M., I., Z., TOKHI, M., O. (2010). Dynamical modelling and simulation of flexible rectangular isotropic plate structure using finite difference method, United Kingdom, p. 6.
    12. GUO, H., ZHANG, K., LIN, T. R., ZHANG, B. (2023). Effect of ribs on vibration characteristics of cantilever plate. In: Thin-Walled Structures, Vol. 182, 110205. https://doi.org/10.1016/j.tws.2022.110205 Go to original source...
    13. KLIMENDA, F.; SOUKUP, J.; RYCHLIKOVA, L.; SKOCILAS, J. (2022). Transverse Wave Propagation in a Thin Isotropic Plate Part I. In. Appl. Sci., Vol. 12, 2493. https://doi.org/10.3390/app12052493 Go to original source...
    14. WU, J., J., TING, T., C., T., BARNETT, D., M. (1991). Modern theory of anisotropic elasticity and applications, SIAM, Philadelphia,
    15. NIAZ, M., NIKKHOO, A. (2015). Inspection of a Rectangular Plate Dynamics Under a Moving Mass With Varying Velocity Utilizing BCOPs. In: Latin American Journal of Solids and Structures, Vol. 12, pp. 317-332. Go to original source...
    16. MAHABADI, R., K., SHAKERI, M., PAZHOOH, M., D. (2016). Free Vibration of Laminated Composite Plate with Shape Memory Alloy Fibers. In: Latin American Journal of Solids and Structures, Vol. 13, pp. 314-330. Go to original source...
    17. CHIKER, Y., MOURAD, B., BOUAZIZ, S., MOULOUD, G., AMAR, M., B., HADDAR, M. (2020). Free vibration analysis of hybrid laminated plates containing multilayer functionally graded carbon nanotu-be-reinforced composite plies using a layer-wise formulation. In: Arch. Appl. Mech., Vol. 91, pp. 463-485. Go to original source...
    18. KARIMIMAHABADI, R., DANESHPAZHOOH, M., SHAKERI, M. (2021) On the free vibration and design optimization of a shape memory alloy hybrid laminated composite plate. In: Acta Mech., Vol. 232, pp. 1-21. Go to original source...
    19. WANG, Z., MA, L. (2021). Effect of Thickness Stretching on Bending and Free Vibration Behaviors of Functionally Graded Graphene Reinforced Composite Plates. In: Appl. Sci., Vol. 11, 11362. https://doi.org/10.3390/app112311362. Go to original source...
    20. HSU, M. H. (2003).Vibration Analysis of Isotropic and Orthotropic Plates with Mixed Boundary Conditions. Tamkang . In: Sci. Eng., Vol. 6, pp. 217-226.
    21. WANG, Y., FAN, J., SHEN, X., LIU, X., ZHANG, J., REN, N. (2022). Free vibration analysis of stiffened rectangular plate with cutouts using Nitsche based IGA method. In: Thin-Walled Structures, Vol. 181, 109975. https://doi.org/10.1016/j.tws.2022.109975 Go to original source...
    22. VAVRO J., JR., VAVRO, J., VAVROVA, A. (2019) Experimental and Numerical Modal Analysis of the Carbon Composite Plate Damaged by Cut. In: Manufacturing Technology, Vol. 19, No. 5, pp. 892-895, ISSN 1213-2489 Go to original source...
    23. MICHNA, S., LUKAC, I., OCENASEK, V., KORENY, R., DRAPALA, J., SCHNEIDER, H., MISKUFOVA, A. and KOL. (2015). Encyklopedie hliniku, 1. vydani, Adin, s. r. o., Presov, 722 str., ISBN 80-89041-88-4
    24. MANEK, M., FUSEK, M. (2023). Comparison of measurement of aluminium alloy in high strain rate. In: Journal of Mechanical Engineering, Vol. 73, No. 99, pp. 99-106, SjF STU Bratislava, ISSN 2450-5471 Go to original source...
    25. ZHANG, L., SONG, B., LIU, R., ZHAO, A., ZHANG, J., ZHUO, L., TANG, G., SHI, Y. (2020). Effects of Structural Parameters on the Poisson's Ratio and Compressive Modulus of 2D Pentamode Structures Fabricated by Selective Laser Melting. In: Engineering, Vol. 6, No. 1, pp. 56-67. https://doi.org/10.1016/j.eng.2019.06.009 Go to original source...
    26. HRBÁČEK, P., VAŠIMA, M. (2022) Study of Light Transmission and Noise Attenuation Properties of Light Active Glass Materials. In: Manufacturing Technology, Vol. 22, No. 5, pp. 542-549, ISSN 1213-2489. DOI: 10.21062/mft.2022.062 Go to original source...
    27. VAŠIMA, M., PÖSCHL, M., ZÁDRAPA, P. (2021) Influence of Rubber Composition on Mechanical Properties. In: Manufacturing Technology, Vol. 21, No. 2, pp. 261-269, ISSN 1213-2489. DOI: 10.21062/mft.2021.021 Go to original source...

    This is an open access article distributed under the terms of the Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content