Skip to main content
SpringerLink
Log in

Free and forced vibration analyses of FGP doubly curved shells based on Chebyshev polynomials

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The free and forced vibration behaviors of the functionally graded porous (FGP) doubly curved shell are investigated based on the Chebyshev polynomials. Three types of porosity distributions, including the symmetrical distribution, the uniform porosity distribution, and the non-uniform porosity distribution, are studied in this work. First, the Rayleigh–Ritz method and the multi-segments technology are employed to build the dynamic model of the doubly curved shell. Second, the third-kind Chebyshev polynomials are adopted to express the admissible displacement function of the doubly curved shell under vibration. Third, the general boundary conditions are described as a series of spring parameters via virtual spring technology. Then, the accuracy and efficiency of the proposed method are verified by comparing them with the results obtained from the finite element method and the open literature. Finally, the effect of the boundary condition, the geometrical parameter, and the porosity distribution on the free and forced vibration of the FGP doubly curved shell is investigated in details.

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

Similar content being viewed by others

References

  1. Li H, Pang F, Miao X, Du Y, Tian H (2018) A semi-analytical method for vibration analysis of stepped doubly-curved shells of revolution with arbitrary boundary conditions. Thin-Walled Struct 129:125–144

    Article  Google Scholar 

  2. Li H, Pang F, Li Y, Gao C (2019) Application of first-order shear deformation theory for the vibration analysis of functionally graded doubly-curved shells of revolution. Compos Struct 212:22–42

    Article  Google Scholar 

  3. Karami B, Shahsavari D (2020) On the forced resonant vibration analysis of functionally graded polymer composite doubly-curved nanoshells reinforced with graphene-nanoplatelets. Comput Methods Appl Mech Eng 359:112767

    Article  MathSciNet  Google Scholar 

  4. Dindarloo MH, Li L (2019) Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory. Compos B Eng 175:107170

    Article  Google Scholar 

  5. Chen D, Yang J, Kitipornchai S (2015) Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos Struct 133:54–61

    Article  Google Scholar 

  6. Sahmani S, Aghdam MM, Rabczuk T (2018) Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs. Compos Struct 198:51–62

    Article  Google Scholar 

  7. Chen D, Yang J, Kitipornchai S (2016) Free and forced vibrations of shear deformable functionally graded porous beams. Int J Mech Sci 108–109:14–22

    Article  Google Scholar 

  8. Zhao J, Xie F, Wang A, Shuai C, Tang J, Wang Q (2019) Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method. Compos B Eng 157:219–238

    Article  Google Scholar 

  9. Setoodeh AR, Shojaee M, Malekzadeh P (2019) Vibrational behavior of doubly curved smart sandwich shells with FG-CNTRC face sheets and FG porous core. Compos B Eng 165:798–822

    Article  Google Scholar 

  10. Aminipour H, Janghorban M, Civalek O (2020) Analysis of functionally graded doubly-curved shells with different materials via higher order shear deformation theory. Compos Struct 251:112645

    Article  Google Scholar 

  11. Van Dung D, Chan DQ (2017) Analytical investigation on mechanical buckling of FGM truncated conical shells reinforced by orthogonal stiffeners based on FSDT. Compos Struct 159:827–841

    Article  Google Scholar 

  12. Duc ND, Hadavinia H, Quan TQ, Khoa ND (2019) Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment. Eur J Mech A Solids 75:355–366

    Article  MathSciNet  Google Scholar 

  13. Duc ND, Cong PH (2016) Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations. J Sandwich Struct Mater 20(2):191–218

    Google Scholar 

  14. Zhang H, Shi D, Zha S, Wang Q (2018) Parameterization study on the moderately thick laminated rectangular plate-cavity coupling system with uniform or non-uniform boundary conditions. Compos Struct 194:537–554

    Article  Google Scholar 

  15. Wang Q, Choe K, Tang J, Shuai C, Wang A (2019) Vibration analyses of general thin and moderately thick laminated composite curved beams with variable curvatures and general boundary conditions. Mech Adv Mater Struct 27(12):1–15

    Google Scholar 

  16. Qin B, Zhong R, Wang T, Wang Q, Xu Y, Hu Z (2020) A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions. Compos Struct 232:111549

    Article  Google Scholar 

  17. Li H, Pang F, Gong Q, Teng Y (2019) Free vibration analysis of axisymmetric functionally graded doubly-curved shells with un-uniform thickness distribution based on Ritz method. Compos Struct 225:111145

    Article  Google Scholar 

  18. Choe K, Kim K, Wang Q (2019) Dynamic analysis of composite laminated doubly-curved revolution shell based on higher order shear deformation theory. Compos Struct 225:111155

    Article  Google Scholar 

  19. Pang F, Li H, Wang X, Miao X, Li S (2018) A semi analytical method for the free vibration of doubly-curved shells of revolution. Comput Math Appl 75(9):3249–3268

    Article  MathSciNet  Google Scholar 

  20. Wang Q, Cui X, Qin B, Liang Q, Tang J (2017) A semi-analytical method for vibration analysis of functionally graded (FG) sandwich doubly-curved panels and shells of revolution. Int J Mech Sci 134:479–499

    Article  Google Scholar 

  21. Sun S, Cao D, Han Q (2013) Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh-Ritz method. Int J Mech Sci 68:180–189

    Article  Google Scholar 

  22. Zhu C, Fang X, Nie G (2021) Nonlinear free and forced vibration of porous piezoelectric doubly-curved shells based on NUEF model. Thin-Walled Structures 163:107678

    Article  Google Scholar 

  23. Wang Q, Shao D, Qin B (2018) A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions. Compos Struct 184:211–232

    Article  Google Scholar 

  24. Jin G, Ye T, Wang X, Miao X (2016) A unified solution for the vibration analysis of FGM doubly-curved shells of revolution with arbitrary boundary conditions. Compos B Eng 89:230–252

    Article  Google Scholar 

  25. Kim J, Żur KK, Reddy JN (2019) Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos Struct 209:879–888

    Article  Google Scholar 

  26. Li Q, Wu D, Chen X, Liu L, Yu Y, Gao W (2018) Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. Int J Mech Sci 148:596–610

    Article  Google Scholar 

  27. Zhao J, Xie F, Wang A, Shuai C, Tang J, Wang Q (2019) Dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints. Compos B Eng 159:20–43

    Article  Google Scholar 

  28. Zhao J, Choe K, Shuai C, Wang A, Wang Q (2019) Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions. Compos B Eng 160:225–240

    Article  Google Scholar 

  29. Choe K, Ri K, Zhang Z, Shuai C, Wang Q (2019) A domain decomposition method for elastodynamic problems of functionally graded elliptic shells and panels with elastic constraints. Thin-Walled Struct 142:262–276

    Article  Google Scholar 

  30. Zhao J, Choe K, Xie F, Wang A, Shuai C, Wang Q (2018) Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions. Compos B Eng 155:369–381

    Article  Google Scholar 

  31. Zhao J, Wong PK, Ma X, Xie Z, Xu J, Cristino VA (2019) Simplification of finite element modeling for plates structures with constrained layer damping by using single-layer equivalent material properties. Compos B Eng 157:283–288

    Article  Google Scholar 

  32. Li H, Cong G, Li L, Pang F, Lang J (2019) A semi analytical solution for free vibration analysis of combined spherical and cylindrical shells with non-uniform thickness based on Ritz method. Thin-Walled Struct 145:106443

    Article  Google Scholar 

  33. Qin B, Zhong R, Wu Q, Wang T, Wang Q (2019) A unified formulation for free vibration of laminated plate through Jacobi-Ritz method. Thin-Walled Struct 144:106354

    Article  Google Scholar 

Download references

Funding

This study was supported by the Natural Science Foundation of Shandong Province (Grant Nos. ZR2022QE086 and ZR2023ME133).

Author information

Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang, 277160, China

    C. Yu, J. Lu, Q. Yang, K. Yang, W. Xu & C. Chiu

Authors
  1. C. Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Q. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Chiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Chiu.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Technical Editor: Santosh Kapuria.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Yu, C., Lu, J., Yang, Q. et al. Free and forced vibration analyses of FGP doubly curved shells based on Chebyshev polynomials. J Braz. Soc. Mech. Sci. Eng. 46, 241 (2024). https://doi.org/10.1007/s40430-024-04797-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-024-04797-y

Keywords

Search

Navigation