Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2015, Article ID 896204, 29 pages
http://dx.doi.org/10.1155/2015/896204
Research Article

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China

Received 23 December 2014; Accepted 15 April 2015

Academic Editor: Tai Thai

Copyright © 2015 Guoyong Jin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Selmane and A. A. Lakis, “Dynamic analysis of anisotropic open cylindrical shells,” Computers and Structures, vol. 62, no. 1, pp. 1–12, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. E. Bahmyari, M. M. Banatehrani, M. Ahmadi, and M. Bahmyari, “Vibration analysis of thin plates resting on Pasternak foundations by element free Galerkin method,” Shock and Vibration, vol. 20, no. 2, pp. 309–326, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. T. Ye, G. Jin, Y. Chen, and S. Shi, “A unified formulation for vibration analysis of open shells with arbitrary boundary conditions,” International Journal of Mechanical Sciences, vol. 81, pp. 42–59, 2014. View at Publisher · View at Google Scholar · View at Scopus
  4. Ö. Civalek, “Vibration analysis of conical panels using the method of discrete singular convolution,” Communications in Numerical Methods in Engineering, vol. 24, no. 3, pp. 169–181, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. L. Zhang and Y. Xiang, “Vibration of open circular cylindrical shells with intermediate ring supports,” International Journal of Solids and Structures, vol. 43, no. 13, pp. 3705–3722, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. Y. Qu, S. Wu, Y. Chen, and H. Hua, “Vibration analysis of ring-stiffened conical-cylindrical-spherical shells based on a modified variational approach,” International Journal of Mechanical Sciences, vol. 69, pp. 72–84, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. M. S. Qatu and E. Asadi, “Vibration of doubly curved shallow shells with arbitrary boundaries,” Applied Acoustics, vol. 73, no. 1, pp. 21–27, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Bashmal, R. Bhat, and S. Rakheja, “In-plane free vibration analysis of an annular disk with point elastic support,” Shock and Vibration, vol. 18, no. 4, pp. 627–640, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. X. Zhao, T. Y. Ng, and K. M. Liew, “Free vibration of two-side simply-supported laminated cylindrical panels via the mesh-free kp-Ritz method,” International Journal of Mechanical Sciences, vol. 46, no. 1, pp. 123–142, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. B. Liu, Y. F. Xing, M. S. Qatu, and A. J. M. Ferreira, “Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells,” Composite Structures, vol. 94, no. 2, pp. 484–493, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. A. W. Leissa, “Vibration of shells,” NASA SP-288, Government Printing Office, Washington, DC, USA, 1973. View at Google Scholar
  12. J. N. Reddy, “Exact solutions of moderately thick laminated shells,” Journal of Engineering Mechanics, vol. 110, no. 5, pp. 794–809, 1984. View at Publisher · View at Google Scholar · View at Scopus
  13. K. M. Liew and C. W. Lim, “A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory,” Computer Methods in Applied Mechanics and Engineering, vol. 127, no. 1–4, pp. 145–162, 1995. View at Publisher · View at Google Scholar · View at Scopus
  14. J. N. Reddy and C. F. Liu, “A higher-order shear deformation theory of laminated elastic shells,” International Journal of Engineering Science, vol. 23, no. 3, pp. 319–330, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. T. Ye, G. Jin, Z. Su, and X. Jia, “A unified Chebyshev–Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions,” Archive of Applied Mechanics, vol. 84, no. 4, pp. 441–471, 2014. View at Publisher · View at Google Scholar
  16. A. Selmane and A. A. Lakis, “Vibration analysis of anisotropic open cylindrical shells subjected to a flowing fluid,” Journal of Fluids and Structures, vol. 11, no. 1, pp. 111–134, 1997. View at Publisher · View at Google Scholar · View at Scopus
  17. E. Asadi, W. Wang, and M. S. Qatu, “Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories,” Composite Structures, vol. 94, no. 2, pp. 494–500, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Bhimaraddi, “A higher order theory for free vibration analysis of circular cylindrical shells,” International Journal of Solids and Structures, vol. 20, no. 7, pp. 623–630, 1984. View at Publisher · View at Google Scholar · View at Scopus
  19. F. Tornabene, A. Liverani, and G. Caligiana, “FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations,” International Journal of Mechanical Sciences, vol. 53, no. 6, pp. 446–470, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. C. T. Loy and K. Y. Lam, “Vibration of thick cylindrical shells on the basis of three-dimensional theory of elasticity,” Journal of Sound and Vibration, vol. 226, no. 4, pp. 719–737, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. K. M. Liew, L. X. Peng, and T. Y. Ng, “Three-dimensional vibration analysis of spherical shell panels subjected to different boundary conditions,” International Journal of Mechanical Sciences, vol. 44, no. 10, pp. 2103–2117, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. C. W. Lim, K. M. Liew, and S. Kitipornchai, “Vibration of open cylindrical shells: a three-dimensional elasticity approach,” Journal of the Acoustical Society of America, vol. 104, no. 3, pp. 1436–1443, 1998. View at Publisher · View at Google Scholar · View at Scopus
  23. K. M. Liew, L. A. Bergman, T. Y. Ng, and K. Y. Lam, “Three-dimensional vibration of cylindrical shell panels—solution by continuum and discrete approaches,” Computational Mechanics, vol. 26, no. 2, pp. 208–221, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. A. W. Leissa and J.-H. Kang, “Three-dimensional vibration analysis of thick shells of revolution,” Journal of Engineering Mechanics, vol. 125, no. 12, pp. 1365–1371, 1999. View at Publisher · View at Google Scholar · View at Scopus
  25. J. So and A. W. Leissa, “Free vibrations of thick hollow circular cylinders from three-dimensional analysis,” Journal of Vibration and Acoustics, vol. 119, no. 1, pp. 89–95, 1997. View at Publisher · View at Google Scholar · View at Scopus
  26. J.-H. Kang and A. W. Leissa, “Three-dimensional vibrations of hollow cones and cylinders with linear thickness variations,” The Journal of the Acoustical Society of America, vol. 106, no. 2, pp. 748–755, 1999. View at Publisher · View at Google Scholar · View at Scopus
  27. D. Zhou, Y. K. Cheung, S. H. Lo, and F. T. K. Au, “3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method,” Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 13-14, pp. 1575–1589, 2003. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Zhou and S. H. Lo, “Three-dimensional free vibration analysis of doubly-curved shells,” Journal of Vibration and Control, 2013. View at Publisher · View at Google Scholar
  29. M. R. Mofakhami, H. H. Toudeshky, and S. H. Hashemi, “Finite cylinder vibrations with different end boundary conditions,” Journal of Sound and Vibration, vol. 297, no. 1-2, pp. 293–314, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. S. M. R. Khalili, A. Davar, and K. Malekzadeh Fard, “Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory,” International Journal of Mechanical Sciences, vol. 56, no. 1, pp. 1–25, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. W. Q. Chen, Z. G. Bian, and H. J. Ding, “Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells,” International Journal of Mechanical Sciences, vol. 46, no. 1, pp. 159–171, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  32. J. N. Sharma, “Three-dimensional vibration analysis of a homogeneous transversely isotropic thermoelastic cylindrical panel,” The Journal of the Acoustical Society of America, vol. 110, no. 1, pp. 254–259, 2001. View at Publisher · View at Google Scholar · View at Scopus
  33. Y. Qu and G. Meng, “Three-dimensional elasticity solution for vibration analysis of functionally graded hollow and solid bodies of revolution. Part I: theory,” European Journal of Mechanics A: Solids, vol. 44, pp. 222–233, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. P. Malekzadeh, M. Farid, P. Zahedinejad, and G. Karami, “Three-dimensional free vibration analysis of thick cylindrical shells resting on two-parameter elastic supports,” Journal of Sound and Vibration, vol. 313, no. 3–5, pp. 655–675, 2008. View at Publisher · View at Google Scholar · View at Scopus
  35. A. W. Leissa and M. S. Qatu, Vibrations of Continuous Systems, McGraw-Hill, New York, NY, USA, 2011.
  36. M. S. Qatu, Vibration of Laminated Shells and Plates, Elsevier, San Diego, Calif, USA, 2004.
  37. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York, NY, USA, 2nd edition, 2004.
  38. A. S. Saada, Elasticity: Theory and Applications, Ross Publishing, Plantation, Fla, USA, 2nd edition, 2009.
  39. M. S. Qatu, “Recent research advances in the dynamic behavior of shells: 1989–2000, part 1: laminated composite shells,” Applied Mechanics Reviews, vol. 55, no. 4, pp. 325–349, 2002. View at Publisher · View at Google Scholar · View at Scopus
  40. M. S. Qatu, “Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: homogeneous shells,” Applied Mechanics Reviews, vol. 55, no. 5, pp. 415–434, 2002. View at Publisher · View at Google Scholar · View at Scopus
  41. K. P. Soldatos, “Review of three-dimensional dynamic analyses of circular cylinders and cylindrical shells,” Applied Mechanics Reviews, vol. 47, no. 10, pp. 501–516, 1994. View at Publisher · View at Google Scholar
  42. W. L. Li, “Free vibrations of beams with general boundary conditions,” Journal of Sound and Vibration, vol. 237, no. 4, pp. 709–725, 2000. View at Publisher · View at Google Scholar · View at Scopus
  43. H. Khov, W. L. Li, and R. F. Gibson, “An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions,” Composite Structures, vol. 90, no. 4, pp. 474–481, 2009. View at Publisher · View at Google Scholar · View at Scopus
  44. G. Jin, Z. Su, S. Shi, T. Ye, and S. Gao, “Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions,” Composite Structures, vol. 108, no. 1, pp. 565–577, 2014. View at Publisher · View at Google Scholar · View at Scopus
  45. K. M. Liew, K. C. Hung, and M. K. Lim, “A continuum three-dimensional vibration analysis of thick rectangular plates,” International Journal of Solids and Structures, vol. 30, no. 24, pp. 3357–3379, 1993. View at Publisher · View at Google Scholar · View at Scopus
  46. K. M. Liew, K. C. Hung, and M. K. Lim, “Free vibration studies on stress-free three-dimensional elastic solids,” Journal of Applied Mechanics, vol. 62, no. 1, pp. 159–165, 1995. View at Publisher · View at Google Scholar · View at Scopus