Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Instability and vibration analyses of FG cylindrical panels under parabolic axial compressions

  • Kumar, Rajesh (Department of Civil Engineering, Birla Institute of Technology and Science) ;
  • Dey, Tanish (Department of Civil Engineering, Indian Institute of Technology (ISM)) ;
  • Panda, Sarat K. (Department of Civil Engineering, Indian Institute of Technology (ISM))
  • Received : 2018.05.14
  • Accepted : 2019.03.25
  • Published : 2019.04.25
⟨ Previous Next ⟩

Abstract

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

Keywords

References

  1. Asnafi, A. and Abedi, M. (2015), "A comparison between the dynamic stability of three types of non-linear orthotropic functionally graded plates under random lateral loads", J. Vib. Control, 23(15), 2520-2537. https://doi.org/10.1177/1077546315617857
  2. Asnafi, A. and Abedi, M. (2015), "A complete analogical study on the dynamic stability analysis of isotropic functionally graded plates subjected to lateral stochastic loads", Acta. Mech., 226(7), 2347-2363. https://doi.org/10.1007/s00707-015-1321-7
  3. Birman, V. (1995), "Buckling of functionally graded hybrid composite plates", Proc. Eng. Mech. (ASCE), 2, 1199-1202.
  4. Bolotin, V.V. (1964), The Dynamic Stability of Elastic Systems, San Francisco, Holden-Day.
  5. Chakrabarti, A. and Sheikh, A.H. (2010), "Dynamic instability of composite and sandwich laminates with interfacial slips", Int. J. Struct. Stab. Dyn., 10(2), 205-224. https://doi.org/10.1142/S0219455410003324
  6. Chen, C.-S., Chen, C.-W. and Chen, W.-R. (2013), "Dynamic stability characteristics of functionally graded plates under arbitrary periodic loads", Int. J. Struct. Stab. Dyn., 13(6), 1350026. https://doi.org/10.1142/S0219455413500260
  7. Dey, T. and Ramachandra, L.S. (2014), "Static and dynamic instability analysis of composite cylindrical shell panels subjected to partial edge loading", Int. J. Nonlin. Mech., 64, 46-56. https://doi.org/10.1016/j.ijnonlinmec.2014.03.014
  8. Dey, T., Kumar, R. and Panda, S.K. (2016), "Postbuckling and postbuckled vibration analysis of sandwich plates under nonuniform mechanical edge loadings", Int. J. Mech. Sci., 115, 226-237. https://doi.org/10.1016/j.ijmecsci.2016.06.025
  9. Feldman, F. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38(1), 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X
  10. Jiang, G., Li, F. and Zhang, C. (2018), "Postbuckling and nonlinear vibration of composite laminated trapezoidal plates", Steel Compos. Struct., Int. J., 26(1), 17-29.
  11. Kar, V.R. and Panda, S.K. (2015), "Non-linear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  12. Lanhe, W., Hongjun, W. and Daobin, W. (2007), "Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method", Compos. Struct., 77(3), 383-394. https://doi.org/10.1016/j.compstruct.2005.07.011
  13. Morimoto, T., Tanigawa, Y. and Kawamura, R. (2006), "Thermal buckling of functionally graded rectangular plates subjected to partial heating", Int. J. Mech. Sci. 48(9), 926-937. https://doi.org/10.1016/j.ijmecsci.2006.03.015
  14. Ng, T.Y., Lam, K.Y. and Liew, K.M. (2000), "Effects of FGM materials on the parametric resonance of plate structures", Comput. Methods Appl. Mech. Eng., 190(8), 953-962. https://doi.org/10.1016/S0045-7825(99)00455-7
  15. Ng, T.Y., Lam, K.Y., Liew, K.M. and Reddy, J.N. (2001), "Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading", Int. J. Solids Struct., 38(8), 1295-1309. https://doi.org/10.1016/S0020-7683(00)00090-1
  16. Noda, N., Hetnarski, R. and Tanigawa, T. (2002), "Thermal stresses", (2nd Ed.), Taylor & Francis, London, UK.
  17. Norouzi, H. and Younesian, D. (2016), "Non-linear vibration of laminated composite plates subjected to subsonic flow and external loads", Steel Compos. Struct., Int. J., 22(6), 1261-1280. https://doi.org/10.12989/scs.2016.22.6.1261
  18. Ovesy, H.R. and Fazilati, J. (2014), "Parametric instability analysis of laminated composite curved shells subjected to nonuniform in-plane load", Compos. Struct., 108, 449-455. https://doi.org/10.1016/j.compstruct.2013.09.048
  19. Park, W.-T., Han, S.-C., Jung, W.-Y. and Lee, W.-H. (2016), "Dynamic Instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., Int. J., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239
  20. Pradyumna, S. and Bandyopadhyay, J.N. (2009), "Dynamic instability of functionally graded shells using higher-order theory", J. Eng. Mech., 136(5), 551-561. https://doi.org/10.1061/(asce)em.1943-7889.0000095
  21. Ramachandra, L.S. and Panda, S.K. (2012), "Dynamic instability of composite plates subjected to non-uniform in-plane loads", J. Sound Vib., 331, 53-65. https://doi.org/10.1016/j.jsv.2011.08.010
  22. Reddy, J.N. and Liu, C.F. (1985), "A higher-order shear deformation theory of laminated elastic shells", Int. J. Eng. Sci., 23(3), 319-330. https://doi.org/10.1016/0020-7225(85)90051-5
  23. Sofiyev, A.H. (2015), "Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells", Compos. Part B Eng., 77, 349-362. https://doi.org/10.1016/j.compositesb.2015.03.040
  24. Sofiyev, A.H. and Kuruoglu, N. (2015a), "Dynamic instability of three-layered cylindrical shells containing an FGM interlayer", Thin-Wall. Struct., 93, 10-21. https://doi.org/10.1016/j.tws.2015.03.006
  25. Sofiyev, A.H. and Kuruoglu, N. (2015b), "Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads", Int. J. Mech. Sci., 101, 114-123. https://doi.org/10.1016/j.ijmecsci.2015.07.025
  26. Sofiyev, A.H., Zerin, Z., Allahverdiev, B.P., Hui, D., Turan, F. and Erdem, H. (2017), "The Dynamic Instability of FG orthotropic conical shells within the SDT", Steel Compos. Struct., Int. J., 25(5), 581-591.
  27. Soldatos, K.P. (1991), "A refined laminated plate and shell theory with applications", J. Sound Vib., 144,109-129. https://doi.org/10.1016/0022-460X(91)90736-4
  28. Sundaresan, P., Singh, G. and Rao, G.V. (1998), "Buckling of moderately thick rectangular composite plate subjected to partial edge compression", Int. J. Mech. Sci., 40, 1105-1117. https://doi.org/10.1016/S0020-7403(98)00009-5
  29. Thai, H.T. and Choi, D.H. (2012), "An efficient and simple refined theory for buckling analysis of functionally graded plates", Appl. Math. Model., 36(3), 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062
  30. Torki, M.E., Kazemi, M.T., Reddy, J.N., Haddadpoud, H. and Mahmoudkhani, S. (2014), "Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces", J. Sound Vib., 333(3), 801-817. https://doi.org/10.1016/j.jsv.2013.09.005
  31. Yang, J. and Shen, H.S. (2003), "Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels", J. Sound Vib., 261(5), 871-893. https://doi.org/10.1016/S0022-460X(02)01015-5
  32. Yang, J., Liew, K.M. and Kitipornchai, S. (2004), "Dynamic stability of laminated FGM plates based on higher-order shear deformation theory", Comput. Mech., 33(4), 305-315. https://doi.org/10.1007/s00466-003-0533-1
  33. Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mat. Sci., 44(2), 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016