DOI QR코드

DOI QR Code

Three-dimensional free vibration analysis of functionally graded fiber reinforced cylindrical panels using differential quadrature method

  • Yas, M.H. (Department of Mechanical Engineering, Razi University) ;
  • Aragh, B. Sobhani (Department of Mechanical Engineering, Razi University) ;
  • Heshmati, M. (Department of Mechanical Engineering, Razi University)
  • 투고 : 2009.11.14
  • 심사 : 2010.11.17
  • 발행 : 2011.03.10

초록

Three dimensional solutions for free vibrations analysis of functionally graded fiber reinforced cylindrical panel are presented, using differential quadrature method (DQM). The orthotropic panel is simply supported at the edges and is assumed to have an arbitrary variation of reinforcement volume fraction in the radial direction. Suitable displacement functions that identically satisfy the simply supported boundary condition are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method to obtain natural frequencies. The main contribution of this work is presenting useful results for continuous grading of fiber reinforcement in the thickness direction of a cylindrical panel and comparison with similar discrete laminate composite ones. Results indicate that significant improvement is found in natural frequency of a functionally graded fiber reinforced composite panel due to the reduction in spatial mismatch of material properties.

키워드

참고문헌

  1. Alibeigloo, A. and Shakeri, M. (2007), "Elasticity solution for the free vibration analysis of laminated panels using the differential quadrature method", J. Compos. Struct., 81, 105-113. https://doi.org/10.1016/j.compstruct.2006.08.003
  2. Alibeigloo, A. and Shakeri, M. (2009), "Elasticity solution of static analysis of laminated cylindrical panel using differential quadrature method", J. Eng. Struct., 21, 260-267.
  3. Alibeigloo, A., Shakeri, M. and Morowat, A. (2007), "Optimal stacking sequence of laminated anisotropic cylindrical panel using genetic algorithm", Struct. Eng. Mech., 25(6), 637-652. https://doi.org/10.12989/sem.2007.25.6.637
  4. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics A review", Appl. Mech. Rev., 49, 1-28. https://doi.org/10.1115/1.3101882
  5. Bert, C.W., Jang, S.K. and Sriz, A.C. (1989), "Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature", Comput. Mech., 5(2-3), 217-226. https://doi.org/10.1007/BF01046487
  6. Bian, Z.G., Ying, J., Chen, W.Q. and Ding, H.J. (2006), "Bending and free vibration analysis of a smart functionally graded plate", Struct. Eng. Mech., 23(1), 97-113. https://doi.org/10.12989/sem.2006.23.1.097
  7. Chen, W.Q. (2005), "3-D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported", J. Compos. Struct., 69, 77-87. https://doi.org/10.1016/j.compstruct.2004.05.015
  8. Chen, W.Q. and Bian, Z.G. (2003), "Elasticity solution for free vibration of laminated beam", J. Compos. Struct., 62, 75-82. https://doi.org/10.1016/S0263-8223(03)00086-2
  9. Chen, W.Q., Bian, Z.G. and Ding, H.U. (2004), "Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells", Int. J. Mech. Sci., 46, 159-171. https://doi.org/10.1016/j.ijmecsci.2003.12.005
  10. Farid, M., Zahedinejad, P. and Malekzade, H.P. (2009), "Three dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two parameter elastic foundation using a hybrid semi-analytic, differential quadrature method", J. Mater. Design., 31(1), 2-13.
  11. Gang, S.W., Lam, K.Y. and Reddy, J.N. (1999), "The elastic response of functionally graded cylindrical shells to low-velocity", Int. J. Impact Eng., 22, 397-417. https://doi.org/10.1016/S0734-743X(98)00058-X
  12. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  13. Matsumaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2-D higher- order deformation theory", J. Compos. Struct., 84, 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006
  14. Miracle, D.B. (2001), "Aeronautical applications of metal - matrix composites ASM", Mater. Park, OH: ASM Int., 21, 1043-1049.
  15. Patel, B.P., Gupta, S.S., Loknath, M.S.B. and Kadu, C.P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", J. Compos. Struct., 69, 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002
  16. Pelletier, J.L. and Vel, S.S. (2006), "An exact solution for the steady state thermo-elastic response of functionally graded orthotropic cylindrical shells", Int. J. Solid Struct., 43(5), 1131-1158. https://doi.org/10.1016/j.ijsolstr.2005.03.079
  17. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristic of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61, 119-129.
  18. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded panels using higher-order finite-element formulation", J .Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  19. Shakeri, M., Akhlaghi, M. and Hosseini, S.M. (2006), "Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", J. Compos. Struct., 76, 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022
  20. Shen, H.S. (2009), "A comparison of buckling and post buckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators", J. Compos. Struct., 91, 375-384. https://doi.org/10.1016/j.compstruct.2009.06.005
  21. Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, Berlin.
  22. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier Stokes equations", Int. J. Numer. Meth. Fluid, 15, 791-798. https://doi.org/10.1002/fld.1650150704
  23. Vasiliev, V.V. and Morozov, E.V. (2001), Mechanics and Analysis of Composite Materials, Elsevier Science Ltd., First edition.
  24. Wang, D. and Wu, Y. (2008), "An efficient Galerkin meshfree analysis of shear deformable cylindrical panels", Interact. Multiscale Mech., 1(3), 339-355. https://doi.org/10.12989/imm.2008.1.3.339
  25. 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

피인용 문헌

  1. Nonlinear cylindrical bending analysis of E-FGM plates with variable thickness vol.16, pp.4, 2014, https://doi.org/10.12989/scs.2014.16.4.339
  2. Dynamic Analysis of Functionally Graded Fiber Reinforced Cylinders under an Impact Load by a Three Dimensional Mesh Free Approach vol.3, pp.3, 2017, https://doi.org/10.1007/s40870-017-0117-3
  3. Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube vol.49, 2013, https://doi.org/10.1016/j.matdes.2013.01.001
  4. Free vibration analysis of functionally graded fiber reinforced cylindrical panels by a three dimensional mesh-free model vol.22, pp.19, 2016, https://doi.org/10.1177/1077546315570717
  5. Three dimensional static and dynamic analysis of two dimensional functionally graded annular sector plates vol.51, pp.6, 2014, https://doi.org/10.12989/sem.2014.51.6.1067
  6. New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.719
  7. Three-Dimensional Static and Free Vibration Analysis of Carbon Nano Tube Reinforced Composite Cylindrical Shell Using Differential Quadrature Method vol.08, pp.03, 2016, https://doi.org/10.1142/S1758825116500332
  8. Aspect ratio factor for finite element method analysis of axially symmetric cylindrical shell walls vol.6, pp.4, 2014, https://doi.org/10.3846/2029882X.2014.996255
  9. Free vibration analysis of functionally graded beams with variable cross-section by the differential quadrature method based on the nonlocal theory vol.75, pp.6, 2020, https://doi.org/10.12989/sem.2020.75.6.737