Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration and stability of composite cylindrical shells containing a FG layer subjected to various loads

  • Sofiyev, A.H. (Department of Civil Engineering of Suleyman Demirel University)
  • Received : 2006.02.17
  • Accepted : 2007.03.10
  • Published : 2007.10.20
⟨ Previous Next ⟩

Abstract

The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin's method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

Keywords

References

  1. Babich, I.Y. and Kilin, V.I. (1985), 'Stability of a three-layer orthotropic cylindrical shell under axial loading', Soviet Appl. Mech., 21, 566-669 https://doi.org/10.1007/BF00887566
  2. Biesheuvel, P.M. and Verweij, H. (2000), 'Calculation of the composition profile of a functionally graded material produced by centrifugal casting', J. Am. Ceram. Soc., 83(4), 743-749 https://doi.org/10.1111/j.1151-2916.2000.tb01268.x
  3. Birman, V. (1995), 'Buckling of functionally graded hybrid composite plates', In: Proc. 10th Conf. on Eng. Mech., Boulder, USA
  4. Chandrasekaran, K. (1977), 'Torsional vibrations of some layered shells of revolution', J. Sound Vib., 55, 27-37 https://doi.org/10.1016/0022-460X(77)90579-X
  5. Chung, H. (1981), 'Free vibration analysis of circular cylindrical shells', J. Sound Vib., 74, 331-350 https://doi.org/10.1016/0022-460X(81)90303-5
  6. Donnell, L.H. (1934a), 'Stability of thin-walled tubes under torsion', NACA Tr-479
  7. Donnell, L.H. (1934b), 'A new theory for the buckling of the thin cylinders under axial compression and bending', Trans Asme, 56, 795-806
  8. Feldman, E. and Aboudi, J. (1997), 'Buckling analysis of functionally graded plates subjected to uniaxial loading', Compos. Struct., 38, 29-36 https://doi.org/10.1016/S0263-8223(97)00038-X
  9. Groves, J.F. and Wadley, H.N.G. (1997), 'Functionally graded materials synthesis via low vacuum directed vapor deposition', Compos. Part. B-Eng., 28(1-2), 57-69 https://doi.org/10.1016/S1359-8368(96)00023-6
  10. He, X.Q., Liew, K.M., Ng, T.Y. and Sivashanker, A. (2002), 'A FEM model for the active control of curved FGM shells using piezoelectric sensor/actuator layers', Int. J. Num. Meth. Eng., 54(6), 853-870 https://doi.org/10.1002/nme.451
  11. Jones, R.M. and Morgan, H.S. (1975), 'Buckling and vibration of cross-ply laminated circular cylindrical shells', AIAA J., 13(5), 664-671 https://doi.org/10.2514/3.49782
  12. Kardomateas, G.A. (1993), 'Buckling of thick orthotropic cylindrical shells under external pressure', J. Appl. Mech. ,60, 195-2002 https://doi.org/10.1115/1.2900745
  13. Kardomateas, G.A. (1993), 'Stability loss in thick transversely isotropic cylindrical shells under axial compression', J. Appl. Mech., 60(2),506-513 https://doi.org/10.1115/1.2900822
  14. Kardomateas, G.A. (1995), 'Bifurcation of equilibrium in thick orthotropic cylindrical shells under axial compression', J. Appl. Mech., 62(1), 43-52 https://doi.org/10.1115/1.2895882
  15. Kieback, B., Neubrand, A. and Riedel, H. (2003), 'Processing techniques for functionally graded materials', Mater. Sci. Eng. A-Struct. Material Prop. Micro-Struct. Process, 362(1-2), 81-105 https://doi.org/10.1016/S0921-5093(03)00578-1
  16. Kim, Y.S., Kardomateas, G.A. and Zureick, A. (1999), 'Buckling of thick orthotropic cylindrical shells under torsion', J. Appl. Mech., 66, 41-50 https://doi.org/10.1115/1.2789167
  17. Kitipornchai, S., Yang, J. and Liew, K.M. (2004), 'Semi analytical for nonlinear vibration of laminated FGM plates with geometric imperfections', Int. J. Solids Struct., 41, 2235-2257 https://doi.org/10.1016/j.ijsolstr.2003.12.019
  18. Kitipornchai, S., Yang, J. and Liew, K.M. (2006), 'Random vibration of the functionally graded laminates in thermal environments', Comput. Meth. Appl. Mech. Eng., 195, 1075-1095 https://doi.org/10.1016/j.cma.2005.01.016
  19. Koizumi, M. (1993), 'The concept of FGM', Ceramic Transactions, Functionally Gradient Mater., 34, 3-10
  20. Lam, K.Y. and Loy, C.T. (1995), 'Analysis of rotating laminated cylindrical shells by different thin shell theories', J. Sound Vib., 186, 23-35 https://doi.org/10.1006/jsvi.1995.0431
  21. Lei, M.M. and Cheng, S. (1969), 'Buckling of composite and homogeneous isotropic cylindrical shells under axial and radial loading', J. Appl. Mech., 791-798
  22. Leissa, A.W. (1973), Vibration of Shells. NASA SP-288
  23. Liew, K.M., He, X.Q., Ng, T.Y. and Kitipornchai, S. (2002), 'Active control of FGM shell subjected to a temperature gradient via piezoelectric sensor/actuator patches', Int. J. Num. Meth. Eng., 55, 653-668 https://doi.org/10.1002/nme.519
  24. Liew, K.M., Ng, T.Y. and Zhao, X. (2002), 'Vibration of axially loaded rotating cross-ply laminated cylindrical shells via ritz method', J. Eng. Mech., 128(9), 1001-1007 https://doi.org/10.1061/(ASCE)0733-9399(2002)128:9(1001)
  25. Liew, K.M., Yang, J. and Wu, Y.F. (2006), 'Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient', Comput. Meth. Appl. Mech. Eng., 195(9-12), 1007-1026 https://doi.org/10.1016/j.cma.2005.04.001
  26. 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
  27. Lu, P., Lee, H.P. and Lu, C. (2005), 'An exact solution for functionally graded piezoelectric laminates in cylindrical bending', Int. J. Mech. Sci., 47, 437-458 https://doi.org/10.1016/j.ijmecsci.2005.01.012
  28. Mandal, P. and Calladine, C.R. (2000), 'Buckling of thin cylindrical shells under axial compression', Int. J. Solid Struct., 37, 4509-4525 https://doi.org/10.1016/S0020-7683(99)00160-2
  29. Mao, R. and Lu, C.H. (1999), 'Buckling analysis of a laminated cylindrical shell under torsion subjected to mixed boundary conditions', Int. J. Solids Struct., 36, 3821-3835 https://doi.org/10.1016/S0020-7683(98)00178-4
  30. Mirfakhraei, P. and Redekop, D. (1998), 'Buckling of circular cylindrical shells by the differential quadrature method', Int. J. Pressure Vessels Piping, 75, 347-353 https://doi.org/10.1016/S0308-0161(98)00032-5
  31. Mises, R. (1929), 'Der Kritische Aussendruck Fur Allseits Belastete Cylindrisher Rohre, Festscher', Zum. 70 Geburtstage von prof. A Stodola, Zurich, 418-432. (Germany)
  32. Mortensen, A. and Suresh, S. (1995), 'Functionally graded metals and metal ceramic composites', I. Proc. Int. Mater. Rev., 40(6), 239-265
  33. Na, K.S. and Kim, J.H. (2006), 'Three-dimensional thermo-mechanical buckling analysis for functionally graded composite plates', Compos. Struct. in press
  34. Ng, T.Y., He, X.Q. and Liew, K.M. (2002), 'Finite element modeling of active control of functionally graded shells in frequency domain via piezoelectric sensors and actuators', Comput. Mech., 28(1), 1-9 https://doi.org/10.1007/s004660100264
  35. Ng, T.Y, Lam, K.Y., Liew, K.M. and Reddy, N.J. (2001), 'Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading', Int. J. Solids Struct.. 38, 1295-1309 https://doi.org/10.1016/S0020-7683(00)00090-1
  36. Park, H.C., Cho, C.M. and Choi, Y.H., (2001), 'Torsional buckling analysis of composite cylinders', AIAA J., 39, 951-955 https://doi.org/10.2514/2.1400
  37. Patel, B.P., Gupta, M.S., Loknath, M.S. and Kadu, C.P. (2005), 'Free vibration analysis of a functionally graded elliptical cylindrical shells using higher-order theory', Compos. Struct., 69, 259-270 https://doi.org/10.1016/j.compstruct.2004.07.002
  38. Pelekh, B.L. and Mamchur, I.L. (1978), 'Torsion of the laminated transversal isotropic cylindrical shells', Soviet Appl. Mech., 14, 24-28
  39. Pinna, R. and Ronalds, B.F. (2000), 'Hydrostatic buckling of shells with various boundary conditions', J. Constr. Steel. Res., 56(1), 1-16 https://doi.org/10.1016/S0143-974X(99)00104-2
  40. Pitakthapanaphong, S. and Busso, E.P. (2002), 'Self-consistent elasto-plastic stress solutions for functionally graded material systems subjected to thermal transients', J. Mech. Phys. Solids, 50, 695-716 https://doi.org/10.1016/S0022-5096(01)00105-3
  41. Pradhan, S.C. (2005), 'Vibration suppression of FGM composite shells using embedded magnetostrictive layers', Int. J. Solids Struct., 42, 2465-2488 https://doi.org/10.1016/j.ijsolstr.2004.09.049
  42. Pradhan, S.C. and Reddy, J.N. (2004), 'Vibration control of composite shells using embedded actuating layers', Smart Mater. Struct., 13, 1245-1257 https://doi.org/10.1088/0964-1726/13/5/029
  43. Pradhan, S.C., Loy, C.T., Lam, K.Y and Reddy, J.N. (2000), 'Vibration characteristics of functionally graded cylindrical shells under various boundary conditions', Appl. Acoust., 61(1), 119-129
  44. Put, S., Vleugels, J. and Van Der Biest, O. (2003), 'Micro structural engineering of functionally graded materials by electrophoretic deposition', J. Mater. Process. Technol., 143, 572-577 https://doi.org/10.1016/S0924-0136(03)00370-4
  45. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), 'Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach', Composites: Part B Eng., 37, 10-20 https://doi.org/10.1016/j.compositesb.2005.05.009
  46. Reddy, J.N. and Cheng, Z.Q. (2001), 'Three-dimensional solutions of smart functionally graded plates', J. Appl. Mech., 68, 234-241 https://doi.org/10.1115/1.1347994
  47. Reddy, J.N. and Chin, C.D. (1998), 'Thermo-mechanical analysis of functionally graded cylinders and plates', J. Thermal Stresses, 21, 593-602 https://doi.org/10.1080/01495739808956165
  48. Sachenkov, A.V. and Baktieva, L,U. (1978), 'Approach to the solution of dynamic stability problems of thin shells (in Russian)', Research on the Theory of Plates and Shells, Kazan State Univ., 13, 137-52
  49. Shahsiah, R. and Eslami, M.R. (2003), 'Thermal buckling of functionally graded cylindrical shell', J. Thermal Stresses, 26, 277-294 https://doi.org/10.1080/713855892
  50. Sheinman, I., Shaw, D. and Simitses, G.J. (1983), 'Nonlinear analysis of axially loaded laminated cylindrical shells', Comput. Struct., 16(1-4), 131-137 https://doi.org/10.1016/0045-7949(83)90155-4
  51. Shen, H.S. (2002), 'Post-buckling of shears deformable laminated cylindrical shell', Eng. Mech., 3, 296-306
  52. Shen, H.S. (2003), 'Post-buckling analysis of pressure loaded functionally graded cylindrical shells in thermal environments', Eng. Struct., 25, 487-497 https://doi.org/10.1016/S0141-0296(02)00191-8
  53. Shen, H.S. and Noda, N. (2005), 'Post-buckling of FGM cylindrical shell under combined axial and radial mechanical loads in thermal environments', Int. J. Solids Struct., 42, 4641-4662 https://doi.org/10.1016/j.ijsolstr.2005.02.005
  54. Shen, Z.J. and Nygren, M. (2002), 'Laminated and functionally graded materials prepared by spark plasma sintering', Key. Eng. Mater., 206(2), 2155-2158 https://doi.org/10.4028/www.scientific.net/KEM.206-213.2155
  55. Simitses, G.J. and Anastasiadis, J.S. (1991), 'Buckling of axially loaded, moderately-thick, cylindrical laminated shells', Compos. Eng., 1(6),375-391 https://doi.org/10.1016/0961-9526(91)90042-Q
  56. Sofiyev, A.H. (2003), 'Dynamic buckling of functionally graded cylindrical shells under non-periodic impulsive loading', Acta Mech., 165, 153-162
  57. Sofiyev, A.H. (2004), 'The stability of functionally graded truncated conical shells subjected to A-periodic impulsive loading', Int. J. Solids Struct., 41(13), 3411-3424 https://doi.org/10.1016/j.ijsolstr.2004.02.003
  58. Sofiyev, A.H., Deniz, A., Akcay, I.H. and Yusufoglu, E. (2006), 'The vibration and stability of a three-layered conical shell containing a FGM layer subjected to axial compressive load', Acta Mech. (in press)
  59. Tabiei, A. and Simitses, G.J. (1994), 'Buckling of moderately thick laminated cylindrical shells under trsion'. AIAA J., 21, 639-647
  60. Tan, D. (2000), 'Torsional buckling analysis of thin and thick shells of revolution', Int. J. Solids Struct., 37, 3055-3078 https://doi.org/10.1016/S0020-7683(99)00120-1
  61. Touloukian, Y.S. (1967), Thermo-Physical Properties of High Temperature Solid Materials, New York: Macmillan
  62. Vinson, J.R. and Sierakowski, R.L. (1986), The Behavior of Structures Composed of Composite Material. Nijhoft, Dordrecht
  63. Vodenitcharova, T. and Ansourian, P. (1996), 'Buckling of circular cylindrical shells subjected to uniform lateral pressure', Eng. Struct., 18, 604-614 https://doi.org/10.1016/0141-0296(95)00174-3
  64. Volmir, A.S. (1967), Stability of Elastic Systems, Nauka: Moscow. English Translation: Foreign Tech. Division, Air Force Systems Command. Wright-Patterson Air Force Base, Ohio, AD628508
  65. Warburton, G.B. (1965), 'Vibration of thin cylindrical shells', J. Mech. Eng. Sci., 7, 399-407 https://doi.org/10.1243/JMES_JOUR_1965_007_062_02
  66. Weingarten, V.I. (1964), 'Free vibrations of multilayered cylindrical shells', Exp. Mech., 200-205
  67. Woo, J. and Mequid, S.A. (2001), 'Nonlinear analysis of functionally graded plates and shallow shells', Int. J. Solids Struct., 38, 7409-7421 https://doi.org/10.1016/S0020-7683(01)00048-8
  68. Xue, J. and Hoo Fatt, M.S. (2002), 'Buckling of a non-uniform, long cylindrical shell subjected to external hydrostatic pressure', Eng. Struct., 24, 1027-1034 https://doi.org/10.1016/S0141-0296(02)00029-9
  69. Yang, J. and Shen, H.S. (2003), 'Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels', J. Sound. Vib., 261, 871-893 https://doi.org/10.1016/S0022-460X(02)01015-5
  70. Yang, J, Liew, K.M., Wu, Y.F. and Kitipornchai, S. (2006), 'Thermo-mechanical post-buckling of FGM cylindrical panels with temperature-dependent properties', Int. J. Solids Struct., 43, 307-324 https://doi.org/10.1016/j.ijsolstr.2005.04.001

Cited by

  1. Buckling analysis of composite panels and shells with different material properties by discrete singular convolution (DSC) method vol.161, 2017, https://doi.org/10.1016/j.compstruct.2016.10.077
  2. Effect of a functionally graded interlayer on the non-linear stability of conical shells in elastic medium vol.99, 2013, https://doi.org/10.1016/j.compstruct.2012.11.044
  3. On the Buckling of Functionally Graded Cylindrical Shells Under Combined External Pressure and Axial Compression vol.132, pp.6, 2010, https://doi.org/10.1115/1.4001659
  4. Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions vol.04, pp.11, 2014, https://doi.org/10.4236/wjm.2014.411032
  5. Vibration and stability of axially compressed truncated conical shells with functionally graded middle layer surrounded by elastic medium vol.20, pp.2, 2014, https://doi.org/10.1177/1077546312461025
  6. Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell vol.152, 2016, https://doi.org/10.1016/j.compstruct.2016.05.024
  7. Size-dependent buckling analysis of different chirality SWCNT under combined axial and radial loading based on orthotropic model vol.4, pp.6, 2017, https://doi.org/10.1088/2053-1591/aa7318
  8. Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads vol.101-102, 2015, https://doi.org/10.1016/j.ijmecsci.2015.07.025
  9. Buckling of bimorph functionally graded piezoelectric cylindrical nanoshell 2018, https://doi.org/10.1177/0954406217738033
  10. Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel vol.94, 2016, https://doi.org/10.1016/j.compositesb.2016.03.031
  11. On the size dependent buckling of anisotropic piezoelectric cylindrical shells under combined axial compression and lateral pressure vol.119, 2016, https://doi.org/10.1016/j.ijmecsci.2016.10.006
  12. Dynamic instability of three-layered cylindrical shells containing an FGM interlayer vol.93, 2015, https://doi.org/10.1016/j.tws.2015.03.006
  13. Stability and vibration of sandwich cylindrical shells containing a functionally graded material core with transverse shear stresses and rotary inertia effects vol.230, pp.14, 2016, https://doi.org/10.1177/0954406215593570
  14. On the Buckling of the Layered Cylindrical Shell with FGM Face Sheets Subjected to the Axial Load footnotemark vol.123, pp.4, 2013, https://doi.org/10.12693/APhysPolA.123.731
  15. Non-linear stability analysis of truncated conical shell with functionally graded composite coatings in the finite deflection vol.51, 2013, https://doi.org/10.1016/j.compositesb.2013.03.029
  16. Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium vol.45, pp.1, 2013, https://doi.org/10.1016/j.compositesb.2012.09.046
  17. Mechanical buckling of cylindrical shells with varying material properties vol.224, pp.8, 2010, https://doi.org/10.1243/09544062JMES1978
  18. The Stability of Cylindrical Shells Containing an FGM Layer Subjected to Axial Load on the Pasternak Foundation vol.02, pp.04, 2010, https://doi.org/10.4236/eng.2010.24033
  19. Buckling analysis of functionally graded material circular hollow cylinders under combined axial compression and external pressure vol.69, 2013, https://doi.org/10.1016/j.tws.2013.04.002
  20. Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells vol.53, pp.2, 2017, https://doi.org/10.1007/s10778-017-0804-8
  21. Thermally excited vibrations of aircraft structural elements vol.59, pp.4, 2016, https://doi.org/10.3103/S106879981604005X
  22. Influence of the 3D material tailoring on snap-through and snap-back post-buckling behaviors of steel-wire-reinforced hybrid 3D graded orthotropic shallow cylindrical panels pp.2041-2983, 2018, https://doi.org/10.1177/0954406218760062
  23. Surface energy effect on nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure vol.5, pp.4, 2018, https://doi.org/10.1088/2053-1591/aab914
  24. Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening vol.66, pp.5, 2007, https://doi.org/10.12989/sem.2018.66.5.557
  25. Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM vol.48, pp.4, 2020, https://doi.org/10.1080/15397734.2019.1646137