Geomechanics and Engineering

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Free vibration response of bio inspired helicoidal laminate plates in hygro thermal environments with nonlinear rotational layup angles

  • Ghani Gourdache (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Mohammed El Amin Bourouis (Department of Civil Engineering, Faculty of Civil Engineering and Architecture Engineering, Amar Telidji University) ;
  • Abderrahmane Menasria (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Abdelhakim Bouhadra (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Mohamed Bourada (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Abdelmoumen Anis Bousahla (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Mohammed A. Balubaid (Department of Industrial Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • A.A. Alsolami (Department of Mathematics, Faculty of Science, King Abdulaziz University) ;
  • S.R. Mahmoud (Department of GRC, Applied College, King Abdulaziz University)
  • Received : 2025.07.15
  • Accepted : 2026.01.26
  • Published : 2026.02.10
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Abstract

This study investigates the hygrothermal-thermodynamic free-vibration response of bio-inspired helicoidal laminated composite plates. A simplified integral Higher-Order Shear Deformation Theory (HSDT) is used to model a range of nonlinear rotation-angle layups, including Helicoidal-Recursive (HR), Helicoidal-Exponential (HE), Helicoidal-Semicircular (HS), Fibonacci Helicoidal (FH), and Linear Helicoid (LH) configurations. An analytical 2D formulation with four unknowns was developed using integral expressions. The motion equations were derived using Hamilton's principle and solved using the Navier method. Our findings clarify how hygrothermal environments affect laminated composite structures, revealing distinct performance differences between conventional and bio-inspired helicoidal designs under these conditions. Both temperature and moisture, individually and in combination, consistently lowered the fundamental vibration frequencies, indicating reduced structural stiffness under environmental loading. We examined the effects of key factors, including layer count (up to 50), helicoidal layup schemes, and geometric properties, on the free-vibration behaviour. This comprehensive analysis advances the understanding of vibrational performance under varying conditions and offers valuable guidance for designing composites with improved environmental resilience, particularly in aerospace and marine applications. The novelty of this study lies in its detailed examination of the hygrothermodynamic behaviour of bio-inspired helicoidal composites, offering valuable insights for optimising structural integrity in fluctuating environmental settings.

Keywords

Acknowledgement

This Project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (IPP: 1084-130-2025). The authors, therefore, acknowledge with thanks DSR for technical and financial support.

References

  1. Panchal, B. (2021). Classical Laminate Theory (CLT) and its use for designing and manufacturing of FRP plates. DJ Sanghvi College of Engineering: Mumbai, India. https://doi.org/10.13140/RG.2.2.26515.55845.
  2. Nguyen, H.N., Hong, T.T., Vinh, P.V., Quang, N.D., Thom, D.V. (2019). A refined simple first-order shear deformation theory for static bending and free vibration analysis of advanced composite plates. Materials, 12(15), 2385. https://doi.org/10.3390/ma12152385.
  3. Swain, P., Adhikari, B., Dash, P. (2019). A higher-order polynomial shear deformation theory for geometrically nonlinear free vibration response of laminated composite plate. Mechanics of Advanced Materials Structures, 26(2), 129-138. https://doi.org/10.1080/15376494.2017.1365981.
  4. Loredo, A., d'Ottavio, M., Vidal, P., Polit, O. (2019). A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates. Composite Structures, 225, 111146. https://doi.org/10.1016/j.compstruct.2019.111146.
  5. Adim, B., Daouadji, T.H., Rabahi, A. (2016). A simple higher order shear deformation theory for mechanical behavior of laminated composite plates. International Journal of Advanced Structural Engineering, 8(2), 103-117. https://doi.org/10.1007/s40091-016-0109-x.
  6. Tamrabet, A., Mourad, C., Ali Alselami, N., Menasria, A., Mamen, B., Bouhadra, A. (2024). Efficient kinematic model for stability analysis of imperfect functionally graded sandwich plates with ceramic middle layer and varied boundary edges. Journal of Computational Applied Mechanics, 55(2), 184-200. https://doi.org/10.22059/jcamech.2024.371464.947.
  7. Slimani, R., Menasria, A., Ali Rachedi, M., Mourad, C., Refrafi, S., Nimer, A.A., Bouhadra, A., Mamen, B. (2024). A novel quasi-3D refined HSDT for static bending analysis of porous functionally graded plates. Journal of Computational Applied Mechanics, 55(3), 519-537. https://doi.org/10.22059/jcamech.2024.372417.968.
  8. Messaoudi, A., Bouhadra, A., Menasria, A., Mamen, B., Boucham, B., Benguediab, M., Tounsi, A., AlOsta, M. (2023). Impact of the shear and thickness stretching effects on the free vibrations of advanced composite plates. Mechanics of Composite Materials, 59(5), 1001-1018. https://doi.org/10.1007/s11029-023-10148-0.
  9. Mohamed, N., Mohamed, S.A., Abdelrhmaan, A.A., Eltaher, M.A. (2023). Nonlinear stability of bioinspired composite beams with higher order shear theory. Steel and Composite Structures, 46(6), 759-772. https://doi.org/10.12989/scs.2023.46.6.759.
  10. Baakeel, F.K., Eltaher, M.A., Muhammad, A., Abdelwahed, M.S. (2025). Impact response of bioinspired laminated composite plates: a numerical simulation model using 2D shell element. Steel and Composite Structures, 54(1), 33-52. https://doi.org/10.12989/scs.2025.54.1.033.
  11. Zhang, Y.W., She, G.L. (2023). Nonlinear harmonic resonances of spinning graphene platelets reinforced metal foams cylindrical shell with initial geometric imperfections in thermal environment. Structural Engineering and Mechanics, 88(5), 405-417. https://doi.org/10.12989/sem.2023.88.5.405.
  12. He, Y., She, G. (2024). Nonlinear forced vibration of imperfect FG beams with hygro-thermal factor. Structural Engineering and Mechanics, 92(2), 163-172. https://doi.org/10.12989/sem.2024.92.2.163.
  13. Chen, W.R., Chiu, L.H., Lin, C.H. (2024). Vibration of elastically supported bidirectional functionally graded sandwich Timoshenko beams on an elastic foundation. Structural Engineering and Mechanics, 91(2), 197-209. https://doi.org/10.12989/sem.2024.91.2.197.
  14. Frih, A., Bourada, F., Kaci, A., Bouremana, M., Tounsi, A., Al-Osta, M.A., Khedher, K.M., Salem, M. A. (2023). A novel hyperbolic integral-Quasi-3D theory for flexural response of laminated composite plates. Geomechanics and Engineering, 34(3), 233-250. https://doi.org/10.12989/gae.2023.34.3.233.
  15. Alimoradzadeh, M., Akbas, S. (2023). Nonlinear vibration analysis of carbon nanotube-reinforced composite beams resting on nonlinear viscoelastic foundation. Geomechanics and Engineering, 32(2), 125-135. https://doi.org/10.12989/gae.2023.32.2.125.
  16. Avcar, M., Hadji, L., Akan, R. (2022). The influence of Winkler-Pasternak elastic foundations on the natural frequencies of imperfect functionally graded sandwich beams. Geomechanics and Engineering, 31(1), 99-112. https://doi.org/10.12989/gae.2022.31.1.099.
  17. She, G.L., Gan, L.L., Xu, J.Q. (2025). Nonlinear snap-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection. Geomechanics and Engineering, 40(3), 183-191. https://doi.org/10.12989/gae.2025.40.3.183.
  18. Xu, J., She, G.L. (2023). The effects of temperature and porosity on resonance behavior of graphene platelet reinforced metal foams doubly-curved shells with geometric imperfection. Geomechanics and Engineering, 35(1), 81-93. https://doi.org/10.12989/gae.2023.35.1.081.
  19. Benachi, H., Menasria, A., Bouhadra, A., Chitour, M., Rachedi, M.A., Mamen, B., Tounsi, A. (2025). Elastic instability analysis of functionally graded nanoplates under nonlinear coupling loads on a shear elastic foundation via non-local theory. Geomechanics and Engineering, 41(5), 507-525. https://doi.org/10.12989/gae.2025.41.5.507.
  20. Reddy, J.N. (2003). Mechanics of laminated composite plates and shells: theory and analysis. CRC press. https://doi.org/10.1201/b12409.
  21. Sharma, N., Nishad, M., Maiti, D.K., Sunny, M.R., Singh, B.N. (2021). Uncertainty quantification in buckling strength of variable stiffness laminated composite plate under thermal loading. Composite Structures, 275, 114486. https://doi.org/10.1016/j.compstruct.2021.114486.
  22. Huang, J., Nguyen-Thanh, N., Gao, J., Fan, Z., Zhou, K. (2022). Static, free vibration, and buckling analyses of laminated composite plates via an isogeometric meshfree collocation approach. Composite Structures, 285, 115011. https://doi.org/10.1016/j.compstruct.2021.115011.
  23. Trinh, M.C., Jun, H. (2023). Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling. Engineering with Computers, 39(2), 1459-1497. https://doi.org/10.1007/s00366-021-01544-y.
  24. Das, S., Jana, P. (2024). Buckling analysis of nonuniformly compressed rectangular FG-CNT reinforced laminated composite plate resting on elastic foundation: an analytical solution. Mechanics of Advanced Materials Structures, 31(30), 12699-12720. https://doi.org/10.1080/15376494.2024.2327645.
  25. Parida, S.P., Jena, P.C., Das, S.R., Basem, A., Khatua, A.K., Elsheikh, A.H. (2024). Transverse vibration of laminated-composite-plates with fillers under moving mass rested on elastic foundation using higher order shear deformation theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 238(20), 9878-9888. https://doi.org/10.1177/09544062241256589.
  26. Jiang, H., Ren, Y., Liu, Z., Zhang, S., Lin, Z. (2019). Low-velocity impact resistance behaviors of bioinspired helicoidal composite laminates with non-linear rotation angle based layups. Composite Structures, 214, 463-475. https://doi.org/10.1016/j.compstruct.2019.02.034.
  27. Ginzburg, D., Pinto, F., Iervolino, O., Meo, M. (2017). Damage tolerance of bio-inspired helicoidal composites under low velocity impact. Composite Structures, 161, 187-203. https://doi.org/10.1016/j.compstruct.2016.10.097.
  28. Grunenfelder, L., Suksangpanya, N., Salinas, C., Milliron, G., Yaraghi, N., Herrera, S., Evans-Lutterodt, K., Nutt, S., Zavattieri, P., Kisailus, D. (2014). Bio-inspired impact-resistant composites. Acta Biomaterialia, 10(9), 3997-4008. https://doi.org/10.1016/j.actbio.2014.03.022.
  29. Cheng, L., Thomas, A., Glancey, J.L., Karlsson, A.M. (2011). Mechanical behavior of bio-inspired laminated composites. Composites Part A: Applied Science Applied Science Manufacturing, 42(2), 211-220. https://doi.org/10.1016/j.compositesa.2010.11.009.
  30. Apichattrabrut, T., Ravi-Chandar, K. (2006). Helicoidal composites. Mechanics of Advanced Materials, 13(1), 61-76. https://doi.org/10.1080/15376490500343808.
  31. Shang, J., Ngern, N.H., Tan, V.B.J. (2016). Crustacean-inspired helicoidal laminates. Composites Science Technology, 128, 222-232. https://doi.org/10.1016/j.compscitech.2016.04.007.
  32. Malekinejad, H., Carbas, R.J., Akhavan-Safar, A., Marques, E.A., Ferreira, M., da Silva, L.F. (2024). Bio-inspired helicoidal composite structure featuring graded variable ply pitch under transverse tensile loading. Journal of Composites Science, 8(6), 228. https://doi.org/10.3390/jcs8060228.
  33. Lu, T., Shen, H.S., Wang, H., Chen, X., Feng, M. (2024). Linear and nonlinear free vibration and optimal design of bio-inspired helicoidal CFRPC laminated plates. International Journal of Structural Stability Dynamics, 24(9), 2450098. https://doi.org/10.1142/S0219455424500986.
  34. Saurabh, S., Kiran, R., Singh, D., Vaish, R., Chauhan, V.J. (2025). A comprehensive investigation on nonlinear vibration and bending characteristics of bio-inspired helicoidal laminated composite structures. Applied Mathematics Mechanics of Advanced Materials, 46(1), 81-100. https://doi.org/10.1007/s10483-025-3200-7.
  35. Meski, K., Boutrid, A., Menasria, A., Bouhadra, A., Mamen, B., Tounsi, A., Cuong-Le, T. (2024). Analytical modeling of flexural behavior of advanced composite sandwich beams under nonlinear hygro-thermo-mechanical loads. Multiscale Multidisciplinary Modeling, Experiments Design, 7(5), 4701-4719. https://doi.org/10.1007/s41939-024-00414-6.
  36. Masmoudi, F., Tamrabet, A., Refrafi, S., Alselami, N., Menasria, A., Bouhadra, A., Benyoucef, S. (2024). Coupled loading hygro-thermo-mechanical effect on the stability of imperfect functionally graded sandwich plates. Journal of Computational Applied Mechanics, 55(4), 617-635. https://doi.org/10.22059/jcamech.2024.374122.1007.
  37. Yao, L., Wang, J., He, Y., Zhao, X., Chen, X., Liu, J., Guo, L., Alderliesten, R. (2024). Hygrothermal effects on fatigue delamination behavior in composite laminates. Composite Structures, 330, 117830. https://doi.org/10.1016/j.compstruct.2023.117830.
  38. Song, X.Y., Zhao, W.R., Zang, J., Zhang, Z., Zhang, Y.W. (2024). Theoretical modeling and vibration analysis of composite laminated wing-box structures of hydrogen-electric aircraft under hygrothermal environment. Thin-Walled Structures, 199, 111854. https://doi.org/10.1016/j.tws.2024.111854.
  39. Zang, J., Chen, B., Song, X.Y., Zhang, Z., Zhang, Y.W., Chen, L.Q. (2025). Vibration of composite laminated airfoil-beam-structures of electric aircraft in hygrothermal environment: theory formulation and experimental investigation. Composite Structures, 354, 118781. https://doi.org/10.1016/j.compstruct.2024.118781.
  40. Menasria, A., Slimani, R., Bouhadra, A., Refrafi, S., Chitour, M., Rachedi, M.A., Himeur, N., Zerari, K. (2025). A simple quasi-3D theory for static stability analysis of imperfect FG beam. Archives of Mechanics, 77(3), 263-287. https://doi.org/10.24423/aom.4642.
  41. Garg, A., Li, L., Belarbi, M.O., Zheng, W., Raman, R. (2025). Stochastic free vibration behavior of multi-layered helicoidal laminated composite shells under thermal conditions. Journal of Composites Science, 9(3), 106. https://doi.org/10.1177/03093247231160414.
  42. Doan, T.S., Tran, T.T., Thao, P.H., Luong, H.G., Do, N.T. (2025). Free vibration and buckling analysis of bio-inspired helicoid laminated composite plates resting on Pasternak foundation using the first-order meshfree. Latin American Journal of Solids Structures, 22(1), e8346. https://doi.org/10.1590/1679-7825/e8346.
  43. Gulia, R., Garg, A., Sahu, V., Li, L.J. (2025). Free vibration and buckling analysis of functionally graded hybrid reinforced laminated composite plates under thermal conditions. Journal of Composites Science, 9(3), 94. https://doi.org/10.3390/jcs9030094.
  44. Garg, A., Belarbi, M.O., Li, L., Sharma, N., Gupta, A., Chalak, H.D. (2023). Free vibration analysis of bio-inspired helicoid laminated composite plates. The Journal of Strain Analysis for Engineering Design, 58(7), 538-548. https://doi.org/10.3390/ jcs9030106.
  45. Patnaik, S.S., Roy, T. (2021). Vibration characteristics and damping properties of functionally graded carbon nanotubes reinforced hybrid composite skewed shell structures under hygrothermal conditions. Journal of Vibration Control, 27(21-22), 2494-2512. https://doi.org/10.1016/j.oceaneng.2022.111851.
  46. Karamanli, A., Vo, T.P., Eltaher, M.A. (2024). Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models. Thin-Walled Structures, 198, 111735. https://doi.org/10.1016/j.tws.2024.111735.
  47. Whitney, J.M., Pagano, N. (1970). Shear deformation in heterogeneous anisotropic plates. Journal of Applied Mechanics. https://doi.org/10.1115/1.3408654.
  48. Noor, A.K. (1973). Free vibrations of multilayered composite plates. AIAA Journal, 11(7), 1038-1039. https://doi.org/10.2514/3.6868.
  49. Sehoul, M., Benguediab, M., Bakora, A., Tounsi, A. (2017). Free vibrations of laminated composite plates using a novel four variable refined plate theory. Steel and Composite Structures, 24(5), 603-613. https://doi.org/10.12989/scs.2017.24.5.603.
  50. Noor, A.K., Burton, W.S. (1990). Three-dimensional solutions for antisymmetrically laminated anisotropic plates. The American Society of Mechanical Engineers. 57(1), https://doi.org/10.1115/1.2888300.
  51. Mohamed, S.A., Mohamed, N., Eltaher, M.A.J.O.E. (2022). Bending, buckling and linear vibration of bio-inspired composite plates. Ocean Engineering, 259, 111851. https://doi.org/10.1016/j.oceaneng.2022.111851.