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Fundamental frequency optimization of variable stiffness composite skew plates

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Abstract

In this study, natural frequencies and vibrational mode shapes of variable stiffness composite skewed plates are optimized applying a genetic algorithm. The variable stiffness behavior is obtained by altering the fiber angles continuously according to two selected curvilinear fıber path functions in the composite laminates. Fundamental frequency and related mode shapes of the plates are optimized for two different fiber path functions using the structural model obtained based on the virtual work principle. A three-layer composite skewed plate with four types of boundary conditions and different plate geometries is considered as case study in this research. Diverse sweptback angles as well as different aspect ratios are considered as various plate geometries. The present study aims to calculate the best fiber path with maximized fundamental frequency or in-plane strengths for a composite skewed plate. The generalized differential quadrature method of solution is employed to solve the governing equations of motion. Moreover, the linear kinematic strain assumptions are used, and the first-order shear deformation theory is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. Numerical results demonstrate the effect of the fiber angles, boundary conditions, and diverse geometries on the natural frequencies of the composite plate. The optimal fiber angles of each layer are presented for the above cases in free vibration analysis. It is verified that the application of optimized curvilinear fibers instead of the traditional straight fibers introduces a higher degree of flexibility, which can be used to adjust frequencies and mode shapes.

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References

  1. Javanshir, J., Farsadi, T., Yuceoglu, U.: Free vibrations of composite base plates stiffened by two adhesively bonded plate strips. J. Aircraft 49(4), 1135–1152 (2012)

    Article  Google Scholar 

  2. Javanshir, J., Farsadi, T., Yuceoglu, U.: Free flexural vibration response of integrally stiffened and/or stepped-thickness composite plates or panels. Int. J. Acoust. Vib. 19(2), 114–126 (2014)

    Google Scholar 

  3. Kaveh, A., Dadras Eslamlou, A., Geran Malek, N., Ansari, R.: An open-source computational framework for optimization of laminated composite plates. Acta Mech. 1–22 (2020)

  4. Attaran, A., Majid, D.L., Basri, S., Rafie, A.M., Abdullah, E.J.: Structural optimization of an aeroelastically tailored composite flat plate made of woven fiberglass/epoxy. Acta Mech. 196(3–4), 161–173 (2008)

    Article  Google Scholar 

  5. Gurdal, Z., Olmedo, R.: In-plane response of laminates with spatially varying fiber orientations-variable stiffness concept. AIAA J. 31(4), 751–758 (1993)

    Article  Google Scholar 

  6. Gürdal, Z., Tatting, B.F., Wu, C.K.: Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response. Compos. A Appl. Sci. Manuf. 39(5), 911–922 (2008)

    Article  Google Scholar 

  7. Farsadi, T., Asadi, D., Kurtaran, H.: Flutter improvement of a thin walled wing-engine system by applying curvilinear fiber path. Aerosp. Sci. Technol. 93, 105353 (2019)

    Article  Google Scholar 

  8. Zamani, Z., Haddadpour, H., Ghazavi, M.R.: Curvilinear fiber optimization tools for design thin walled beams. Thin-Walled Struct. 49(3), 448–454 (2011)

    Article  Google Scholar 

  9. Günay, M.G., Timarcı, T.: Stresses in thin-walled composite laminated box-beams with curvilinear fibers: Antisymmetric and symmetric fiber paths. Thin-Walled Struct. 138, 170–182 (2019)

    Article  Google Scholar 

  10. Antunes, A.M., Ribeiro, P., Rodrigues, J.D., Akhavan, H.: Modal analysis of a variable stiffness composite laminated plate with diverse boundary conditions: experiments and modelling. Compos. Struct. 239, 111974 (2020)

    Article  Google Scholar 

  11. Akhavan, H., Ribeiro, P.: Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers. Compos. Struct. 93(11), 3040–3047 (2011)

    Article  Google Scholar 

  12. Asadi, D., Farsadi, T.: Active flutter control of thin walled wing-engine system using piezoelectric actuators. Aerosp. Sci. Technol. (2020). https://doi.org/10.1016/j.ast.2020.105853

  13. Ribeiro, P., Akhavan, H., Teter, A., Warmiński, J.: A review on the mechanical behavior of curvilinear fibre composite laminated panels. J. Compos. Mater. 48(22), 2761–2777 (2014)

    Article  Google Scholar 

  14. Lozano, G.G., Tiwari, A., Turner, C., Astwood, S.: A review on design for manufacture of variable stiffness composite laminates. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 230(6), 981–992 (2016)

    Article  Google Scholar 

  15. Honda, S., Igarashi, T., Narita, Y.: Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II. Compos. B Eng. 45(1), 1071–1078 (2013)

    Article  Google Scholar 

  16. Tornabene, F., Fantuzzi, N., Bacciocchi, M., Viola, E.: Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method. Compos. B Eng. 81, 196–230 (2015)

    Article  Google Scholar 

  17. Zhao, W., Kapania, R.K.: Pre-stressed vibration of stiffened variable-angle tow laminated plates. AIAA J. 57(6), 2575–2593 (2019)

    Article  Google Scholar 

  18. Wu, C.P., Lee, C.Y.: Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness. Int. J. Mech. Sci. 43(8), 1853–1869 (2001)

    Article  Google Scholar 

  19. Abdalla, M.M., Setoodeh, S., Gürdal, Z.: Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Compos. Struct. 81(2), 283–291 (2007)

    Article  Google Scholar 

  20. Blom, A.W., Setoodeh, S., Hol, J.M., Gürdal, Z.: Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Comput. Struct. 86(9), 870–878 (2008)

    Article  Google Scholar 

  21. Houmat, A.: Three-dimensional free vibration analysis of variable stiffness laminated composite rectangular plates. Compos. Struct. 194, 398–412 (2018)

    Article  Google Scholar 

  22. An, H., Chen, S., Huang, H.: Multi-objective optimal design of hybrid composite laminates for minimum cost and maximum fundamental frequency and frequency gaps. Compos. Struct. 209, 268–276 (2019)

    Article  Google Scholar 

  23. Kaveh, A., Dadras, A., Malek, N.G.: Buckling load of laminated composite plates using three variants of the biogeography-based optimization algorithm. Acta Mech. 229(4), 1551–1566 (2018)

    Article  MathSciNet  Google Scholar 

  24. Das Neves Carneiro, G., António, C.C.: Reliability-based Robust Design Optimization with the Reliability Index Approach applied to composite laminate structures. Compos. Struct. 209, 844–855 (2019)

    Article  Google Scholar 

  25. Kaveh, A., Dadras, A., Malek, N.G.: Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms. Eng. Comput. 35(3), 813–832 (2019)

    Article  Google Scholar 

  26. Jafari, R., Yousefi, P., Hosseini-Hashemi, S.: Stacking sequence optimization of laminated composite plate’s free vibration using genetic algorithm and neural networks, In: International Conference on Advances in Mechanical Engineering, ICAME’15, Istanbul, Turkey, 13–15 May 2015 (2015)

  27. Jafari, R., Yousefi, P., Hosseini-Hashemi, S.: Vibration optimization of skew composite plates using the Rayleigh-Ritz & response surface methods, In: Proceedings of STME-2013 International Conference on Smart Technologies for Mechanical Engineering, Istanbul, Turkey, 25–26 October 2013 (2013)

  28. Apalak, M.K., Karaboga, D., Akay, B.: The artificial bee colony algorithm in layer optimization for the maximum fundamental frequency of symmetrical laminated composite plates. Eng. Optim. 46(3), 420–437 (2014)

    Article  MathSciNet  Google Scholar 

  29. Iyengar, N.G.R., Prasad, A.B.: Optimal design of composite laminates with and without cutout undergoing free vibration. IES J. Part A Civil Struct. Eng. 3(3), 161–167 (2010)

    Article  Google Scholar 

  30. Apalak, M.K., Yildirim, M., Ekici, R.: Layer optimization for maximum fundamental frequency of laminated composite plates for different edge conditions. Compos. Sci. Technol. 68(2), 537–550 (2008)

    Article  Google Scholar 

  31. Bargh, H.G., Sadr, M.H.: Stacking sequence optimization of composite plates for maximum fundamental frequency using particle swarm optimization algorithm. Meccanica 47(3), 719–730 (2012)

    Article  MathSciNet  Google Scholar 

  32. Ghashochi-Bargh, H., Sadr, M.H.: PSO algorithm for fundamental frequency optimization of fiber metal laminated panels. Struct. Eng. Mech. 47(5), 713–727 (2013)

    Article  Google Scholar 

  33. Kalita, K., Dey, P., Haldar, S., Gao, X.Z.: Optimizing frequencies of skew composite laminates with metaheuristic algorithms. Eng. Comput. 36(2), 741–761 (2020)

    Article  Google Scholar 

  34. Civan, F.: Application of differential quadrature to solution of pool boiling cavities. In: Proceedings of the Oklahoma Academy of Science vol. 65, pp. 73–78 (1985)

  35. Lam, S.S.E.: Application of the differential quadrature method to two-dimensional problems with arbitrary geometry. Comput. Struct. 47(3), 459–464 (1993)

    Article  Google Scholar 

  36. Wang, S.: Vibration of thin skew fiber reinforced composite laminates. J. Sound Vib. 201(3), 335–352 (1997)

    Article  Google Scholar 

  37. Kurtaran, H.: Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Compos. Struct. 131, 821–831 (2015)

    Article  Google Scholar 

  38. Kurtaran, H.: Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method. Compos. Struct. 128, 241–250 (2015)

    Article  Google Scholar 

  39. Farsadi, T., Asadi, D., Kurtaran, H.: Nonlinear flutter response of a composite plate applying curvilinear fiber paths. Acta Mech. 231(2), 715–731 (2020)

    Article  MathSciNet  Google Scholar 

  40. Farsadi, T.: Enhancement of static and dynamic performance of composite tapered pretwisted rotating blade with variable stiffness. J. Vib. Acoust. 143(2) (2020)

  41. Song, Z.G., Li, F.M.: Optimal locations of piezoelectric actuators and sensors for supersonic flutter control of composite laminated panels. J. Vib. Control 20(14), 2118–2132 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. Adana Alparslan Türkeş Science and Technology University, Adana, Turkey

    Touraj Farsadi, Davood Asadi & Hasan Kurtaran

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  1. Touraj Farsadi
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  2. Davood Asadi
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  3. Hasan Kurtaran
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Correspondence to Touraj Farsadi.

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Farsadi, T., Asadi, D. & Kurtaran, H. Fundamental frequency optimization of variable stiffness composite skew plates. Acta Mech 232, 555–573 (2021). https://doi.org/10.1007/s00707-020-02871-9

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  • DOI: https://doi.org/10.1007/s00707-020-02871-9

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