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Free in-plane vibration analysis of elastically restrained functionally graded porous plates with porosity distributions in the thickness and in-plane directions

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Abstract

A unified solution for free in-plane vibration analysis of elastically functionally graded restrained porous plates (FGPP) with porosity distributions in the thickness and in-plane directions in the framework of a semi-analytical solution is proposed for the first time. The segment technique, penalty function and energy principle are used to establish the motion equation of porous plates. The boundary conditions are simulated by setting of penalty function. The displacement tolerance function of porous plates is expressed by Jacobian series, which is introduced into the energy expression. Then a set of simple linear equations can be obtained by partial differential operation of unknown expansion coefficients. By compared results obtained by the current method, FEM and experiment, the correctness and accuracy of this model are validated. On the above basis, comprehensive parametric investigations are carried out to analyze the behavior of vibration of FGPP with respect to a several factors. The numerical results presented in this paper can lay a foundation for future research in this field.

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References

  1. Y. Xue et al., Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach. Int. J. Mech. Sci. 152, 346–362 (2019)

    Article  Google Scholar 

  2. E. Arshid, A.R. Khorshidvand, Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method. Thin-Walled Struct. 125, 220–233 (2018)

    Article  Google Scholar 

  3. A.S. Rezaei, A.R. Saidi, Buckling response of moderately thick fluid-infiltrated porous annular sector plates. Acta Mech. 228(11), 3929–3945 (2017)

    Article  MathSciNet  Google Scholar 

  4. A.S. Rezaei, A.R. Saidi, An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates. J. Vib. Control 24(18), 4130–4144 (2017)

    Article  MathSciNet  Google Scholar 

  5. A.S. Rezaei, A.R. Saidi, Exact solution for free vibration of thick rectangular plates made of porous materials. Compos. Struct. 134, 1051–1060 (2015)

    Article  Google Scholar 

  6. A.S. Rezaei, A.R. Saidi, Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous–cellular plates. Compos. B Eng. 91, 361–370 (2016)

    Article  Google Scholar 

  7. P.T. Thang et al., Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions. Aerosp. Sci. Technol. 79, 278–287 (2018)

    Article  Google Scholar 

  8. E. Magnucka-Blandzi, Axi-symmetrical deflection and buckling of circular porous-cellular plate. Thin-Walled Struct. 46(3), 333–337 (2008)

    Article  Google Scholar 

  9. M. Heshmati, F. Daneshmand, A study on the vibrational properties of weight-efficient plates made of material with functionally graded porosity. Compos. Struct. 200, 229–238 (2018)

    Article  Google Scholar 

  10. Y.Q. Wang, Y.H. Wan, Y.F. Zhang, Vibrations of longitudinally traveling functionally graded material plates with porosities. Eur. J. Mech. A. Solids 66, 55–68 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  11. A.S. Rezaei et al., Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach. Thin-Walled Struct. 120, 366–377 (2017)

    Article  Google Scholar 

  12. A.M. Zenkour, A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities. Compos. Struct. 201, 38–48 (2018)

    Article  Google Scholar 

  13. D. Shahsavari et al., A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp. Sci. Technol. 72, 134–149 (2018)

    Article  Google Scholar 

  14. H. Shahverdi, M.R. Barati, Vibration analysis of porous functionally graded nanoplates. Int. J. Eng. Sci. 120, 82–99 (2017)

    Article  MathSciNet  Google Scholar 

  15. M.H. Shojaeefard et al., Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT. Appl. Math. Model. 50, 633–655 (2017)

    Article  MathSciNet  Google Scholar 

  16. Y.Q. Wang, J.W. Zu, Large-amplitude vibration of sigmoid functionally graded thin plates with porosities. Thin-Walled Struct. 119, 911–924 (2017)

    Article  Google Scholar 

  17. J. Zhao et al., Free vibration analysis of laminated composite elliptic cylinders with general boundary conditions. Compos. B Eng. 158, 55–66 (2019)

    Article  Google Scholar 

  18. J. Zhao et al., Dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints. Compos. B Eng. 159, 20–43 (2019)

    Article  Google Scholar 

  19. P. Lyu et al., Free in-plane vibration analysis of elastically restrained annular panels made of functionally graded material. Compos. Struct. 178, 246–259 (2017)

    Article  Google Scholar 

  20. T. Liu et al., A unified formulation for free in-plane vibrations of arbitrarily-shaped straight-sided quadrilateral and triangular thin plates. Appl. Acoust. 155, 407–422 (2019)

    Article  Google Scholar 

  21. P. Lyu et al., Free in-plane vibration analysis of rotating annular panels with elastic boundary restraints. J. Sound Vib. 439, 434–456 (2019)

    Article  ADS  Google Scholar 

  22. Y. Yuan et al., An exact analytical solution for free in-plane vibration of sector plates with simply supported radial edges. J. Sound Vib. 466, 115024 (2020)

    Article  Google Scholar 

  23. Z. Wang, Y. Xing, Q. Sun, Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions. J. Sound Vib. 470, 115166 (2020)

    Article  Google Scholar 

  24. A. Arreola-Lucas et al., In-plane vibrations of a rectangular plate: plane wave expansion modelling and experiment. J. Sound Vib. 342, 168–176 (2015)

    Article  ADS  Google Scholar 

  25. Y. Narita, M. Innami, Identifying all combinations of boundary conditions for in-plane vibration of isotropic and anisotropic rectangular plates. Thin-Walled Struct. 164, 107320 (2021)

    Article  Google Scholar 

  26. Y. Zhou et al., Exact solutions for the free in-plane vibrations of rectangular plates with arbitrary boundary conditions. Int. J. Mech. Sci. 130, 1–10 (2017)

    Article  Google Scholar 

  27. T. Liu et al., Modeling and experimental study on free vibration of plates with curved edges. J. Sound Vib. 513, 116417 (2021)

    Article  Google Scholar 

  28. R. Zhong et al., Investigation on flutter instability of magnetic-electric-thermo-elastic functionally graded plates in the supersonic airflow with any yawed angle. Int. J. Mech. Sci. 198, 106356 (2021)

    Article  Google Scholar 

  29. N.K. HS, S. Kattimani, T. Nguyen-Thoi, Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates. Def. Technol. (2021)

  30. H.S. Naveen Kumar, S. Kattimani, Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: a finite element study. Def. Technol. (2021)

  31. L.S. Esayas, S. Kattimani, Effect of porosity on active damping of geometrically nonlinear vibrations of a functionally graded magneto-electro-elastic plate. Def. Technol. (2021)

  32. Z. Li et al., Vibration and acoustic radiation of magneto-electro-thermo-elastic functionally graded porous plates in the multi-physics fields. Int. J. Mech. Sci. 185, 105850 (2020)

    Article  Google Scholar 

  33. R. Zhong, et al., Prediction of the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions. Mech. Adv. Mater. Struct. 1–25 (2021)

  34. D. Chen, S. Kitipornchai, J. Yang, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Struct. 107, 39–48 (2016)

    Article  Google Scholar 

  35. H. Li et al., A unified vibration modeling and dynamic analysis of FRP-FGPGP cylindrical shells under arbitrary boundary conditions. Appl. Math. Model. 97, 69–80 (2021)

    Article  MathSciNet  Google Scholar 

  36. C. Gao et al., An approximate solution for vibrations of uniform and stepped functionally graded spherical cap based on Ritz method. Compos. Struct. 233, 111640 (2020)

    Article  Google Scholar 

  37. Y. Du et al., A unified formulation for dynamic behavior analysis of spherical cap with uniform and stepped thickness distribution under different edge constraints. Thin-Walled Struct. 146, 106445 (2020)

    Article  Google Scholar 

  38. B. Qin et al., A unified formulation for free vibration of laminated plate through Jacobi-Ritz method. Thin-Walled Struct. 144, 106354 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 11902368).

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Authors and Affiliations

  1. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, People’s Republic of China

    Zhengxiong Chen, Rui Zhong & Qingshan Wang

  2. Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha, 410075, People’s Republic of China

    Bin Qin

  3. Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha, 410075, People’s Republic of China

    Bin Qin

  4. National and Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, Changsha, 410075, People’s Republic of China

    Bin Qin

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  1. Zhengxiong Chen
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  2. Bin Qin
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  3. Rui Zhong
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  4. Qingshan Wang
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Correspondence to Bin Qin.

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Chen, Z., Qin, B., Zhong, R. et al. Free in-plane vibration analysis of elastically restrained functionally graded porous plates with porosity distributions in the thickness and in-plane directions. Eur. Phys. J. Plus 137, 158 (2022). https://doi.org/10.1140/epjp/s13360-021-02153-w

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-02153-w

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