On the solution of eigenvalue problems of laminated non-homogeneous orthotropic circular shells with clamped edges subjected to hydrostatic pressure

Acta Mechanica

Volumn 212, Issue 1-2, 2010, Pages 93-114

  Sofiyev, Abdullah H ^a   Kuruoglu, N ^b   Isayev, F G ^c  

^a SULEYMAN DEMIREL UNIVERSITY   (Turkey)

^b BAHCESEHIR UNIVERSITY   (Turkey)

^c Department of Mathematics and Computer Science   (Azerbaijan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION FUNCTION; BUCKLING PRESSURE; CLAMPED EDGE; COMPATIBILITY EQUATION; CONICAL SHELL; CRITICAL STRESS; CYLINDRICAL SHELL; EIGENVALUE PROBLEM; FREE VIBRATION; ISOTROPIC MATERIALS; LAMINATED CYLINDRICAL SHELLS; MATERIAL PROPERTY; NON-HOMOGENEOUS; NONHOMOGENEITY; PIECE-WISE; SINGLE LAYER; THICKNESS DIRECTION; TRUNCATED CONICAL SHELL; UNKNOWN PARAMETERS;

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; GALERKIN METHODS; HYDRAULICS; HYDRODYNAMICS; HYDROSTATIC PRESSURE; LAMINATING; NATURAL FREQUENCIES;

SHELLS (STRUCTURES);

EID: 77952950610     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-009-0236-6     Document Type: Article

References (61)

1. D.J. Wilkins J.C.W. Bert D.M. Egle 1970 Free vibrations of orthotropic sandwich conical shells with various boundary conditions J. Sound Vib. 13 211 228 0218.73103 10.1016/S0022-460X(70)81175-0
2. K. Chandrasekaran V. Ramamurti 1982 Asymmetric free vibrations of layered conical shells J. Mech. Des. 104 453 462 10.1115/1.3256367
3. A. Kayran J.R. Vinson 1990 Free vibration analysis of laminated composite truncated circular conical shells AIAA J. 28 1259 1269 10.2514/3.25203
4. H. Wang T.K. Wang 1991 Stability of laminated composite circular conical shells under external pressure J. Appl. Math. Mech. 12 1153 1161 0747.73028 10.1007/BF02456054
5. L. Tong 1993 Free vibration of composite laminated conical shells Int. J. Mech. Sci. 35 47 61 0825.73343 10.1016/0020-7403(93)90064-2 (Pubitemid 23612197)
6. C. Shu 1996 Free vibration analysis of composite laminated conical shells by generalized differential quadrature J. Sound Vib. 194 587 604 10.1006/jsvi.1996.0379 (Pubitemid 126370865)
7. A. Korjakin R. Rikards A. Chate H. Altenbach 1998 Analysis of free damped vibrations of laminated composite conical shells Compos. Struct. 41 39 47 10.1016/S0263-8223(98)00024-5 (Pubitemid 28392465)
8. I.F.P. Correia C.M.M. Soares C.A.J. Soares J. Herskovits 2003 Analysis of laminated conical shell structures using higher order models Compos. Struct. 62 383 390 10.1016/j.compstruct.2003.09.009 (Pubitemid 37453662)
9. T.Y. Ng H. Li K.Y. Lam 2003 Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions Int. J. Mech. Sci. 45 567 587 1116.74439 10.1016/S0020-7403(03)00042- 0
10. Reddy J.N.: Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)
11. R. Heuer F. Ziegler 2004 Thermoelastic stability of layered shallow shells Int. J. Solid Struct. 41 2111 2120 1072.74029 10.1016/j.ijsolstr.2003.11. 032 (Pubitemid 38319483)
12. R. Heuer 2006 Thermo-piezoelectric flexural vibrations of viscoelastic panel-type laminates with interlayer slip Acta Mech. 181 129 138 1096.74026 10.1007/s00707-005-0299-y
13. S. Liang H.L. Chen T. Chen Y. Michael M.Y. Wang 2007 The natural vibration of a symmetric cross-ply laminated composite conical-plate shell Compos. Struct. 80 265 278 10.1016/j.compstruct.2006.05.014 (Pubitemid 46359838)
14. O. Civalek 2007 Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach J. Comput. Appl. Math. 205 251 271 1115.74058 10.1016/j.cam.2006.05.001 2324838 (Pubitemid 46656438)
15. H.W. Bargmann 2008 On the stability of thin-walled, corrugated, circular cylindrical shells under external pressure Acta Mech. 195 117 128 1136.74016 10.1007/s00707-007-0553-6
16. B. Gu Y.-W. Mai C.Q. Ru 2009 Mechanics of microtubules modeled as orthotropic elastic shells with transverse shearing Acta Mech. 207 195 209 1173.74027 10.1007/s00707-008-0121-8
17. Y. Goldfeld 2009 An alternative formulation in linear bifurcation analysis of laminated shells Thin-Walled Struct. 47 44 52 10.1016/j.tws.2008.05. 001
18. Volmir, A.S.: Stability of Elastic Systems. Moscow, Nauka (English Translation) Foreign Technology Division, Air Force Systems Command. Wright-Patterson Air Force Base, Ohio, AD628508 (1967)
19. Leissa A.W.: Vibration of Shells. NASA SP-288, Washington (1973)
20. F. Delale F. Erdogan 1983 The crack problem for a non-homogeneous plane ASME J. Appl. Mech. 50 609 614 0542.73118
21. Khoroshun, L.P., Kozlov, S.Y., Ivanov, Y.A., Koshevoi, I.K.: The Generalized Theory of Plates and Shells Non-Homogeneous in Thickness Direction. Naukova Dumka, Kiev (1988) (in Russian)
22. Baruch, M., Arbocz, J., Zhang, G.Q.: Laminated conical shells-considerations for the variations of stiffness coefficients. Report LR-671, Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands (1992)
23. R.H. Gutierrez P.A.A. Laura D.V. Bambill V.A. Jederlinic D.H. Hodges 1998 Axisymmetric vibrations of solid circular and annular membranes with continuously varying density J. Sound Vib. 212 611 622 10.1006/jsvi.1997.1418
24. I. Elishakoff 2001 Inverse buckling problem for inhomogeneous columns Int. J. Solids Struct. 38 457 464 1009.74021 10.1016/S0020-7683(00)00049-4
25. A.H. Sofiyev E. Schnack 2003 The buckling of cross-ply laminated non-homogeneous orthotropic composite conical thin shells under a dynamic external pressure Acta Mech. 162 29 40 1064.74101 10.1007/s00707-002-1001-2
26. G.J. Weng 2003 Effective bulk moduli of two functionally graded composites Acta Mech. 166 57 67 1064.74147 10.1007/s00707-003-0063-0
27. C. Massalas D. Dalamanagas G. Tzivanidis 1981 Dynamic instability of truncated conical shells with variable modulus of elasticity under periodic compressive forces J. Sound Vib. 79 519 528 0483.73038 10.1016/0022-460X(81) 90463-6 (Pubitemid 12458188)
28. P.R. Heyliger A. Julani 1992 The free vibrations of inhomogeneous elastic cylinders and spheres Int. J. Solid Struct. 29 2689 2708 0775.73140 10.1016/0020-7683(92)90112-7 (Pubitemid 23566029)
29. X. Zhang N. Hasebe 1999 Elasticity solution for a radially non-homogeneous hollow circular cylinder J. Appl. Mech. 66 598 606 10.1115/1.2791477 1723021
30. M. Jabareen M. Eisenberge 2001 Free vibrations of non-homogeneous circular and annular membranes J. Sound Vib. 240 409 429 10.1006/jsvi.2000.3249 (Pubitemid 32370195)
31. H.J. Ding H.M. Wang W.Q. Chen 2003 A solution of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermo-elastic problems J. Sound Vib. 263 815 829 10.1016/S0022-460X(02)01075-1
32. U.S. Gupta R. Lal S. Sharma 2007 Vibration of non-homogeneous circular Mindlin plates with variable thickness J. Sound Vib. 302 1 17 10.1016/j.jsv.2006.07.005 (Pubitemid 46209199)
33. R. Lal 2007 Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness, A spline technique J. Sound Vib. 306 203 214 10.1016/j.jsv.2007.05.014 (Pubitemid 47069474)
34. A.H. Sofiyev M.H. Omurtag E. Schnack 2009 The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure J. Sound Vib. 319 963 983 10.1016/j.jsv.2008.06.033
35. V.B. Chalivendra 2009 Mixed-mode crack-tip stress fields for orthotropic functionally graded materials Acta Mech. 204 51 60 1162.74015 10.1007/s00707-008-0047-1
36. Z. Mecitoglu 1996 Governing equations of a stiffened laminated inhomogeneous conical shell AIAA J. 34 2118 2225 0910.73044 10.2514/3.13360
37. A.M. Zenkour M.E. Fares 2001 Bending, buckling and free vibration of non-homogeneous composite laminated cylindrical shells using a refined first-order theory Compos. B Eng. 32 237 247 10.1016/S1359-8368(00)00060-3 (Pubitemid 32318153)
38. C.-P. Wu C.-Y. Lee 2001 Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness Int. J. Mech. Sci. 43 1853 1869 1048.74603 10.1016/S0020-7403(01)00010-8 (Pubitemid 32544286)
39. Y. Goldfeld J. Arbocz 2004 Buckling of laminated conical shells given the variations of the stiffness coefficients AIAA J. 42 642 649 10.2514/1.2765
40. S. Kitipornchai J. Yang K.M. Liew 2006 Random vibration of the functionally graded laminates in thermal environments Comput. Meth. Appl. Mech. Eng. 195 1075 1095 1115.74031 10.1016/j.cma.2005.01.016 (Pubitemid 41722566)
41. V. Tripath B.N. Singh K.K. Shukla 2007 Free vibration of laminated composite conical shells with random material properties Compos. Struct. 81 96 104 10.1016/j.compstruct.2006.08.002 (Pubitemid 46939685)
42. A.H. Sofiyev Z. Karaca 2009 The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure Eur. J. Mech. Solid A Solids 28 317 328 1156.74334 10.1016/j.euromechsol.2008.06.002
43. J. Singer 1966 Buckling of clamped conical shells under external pressure AIAA J. 4 328 337 10.2514/3.3436
44. J. Singer M. Baruch J. Reichenthal 1971 Influence of in plane boundary conditions on the buckling of clamped conical shells Isr. J. Tech. 9 127 139 0214.52006
45. Tani, J.: Free transverse vibrations of truncated conical shells. The Report Institute of High Speed Mechanics, Tohoku University, Japan, vol. 24. pp. 87-116 (1971)
46. Tani, J.: Influence of pre-buckling deformations on the buckling of truncated conical shells under external pressure. The Report Institute of High Speed Mechanics, Tohoku University, Japan, vol. 28. pp. 149-164 (1973)
47. T. Irie G. Yamada K. Tanaka 1984 Natural frequencies of truncated conical shells J. Sound Vib. 92 447 453 10.1016/0022-460X(84)90391-2 (Pubitemid 14529672)
48. K.Y. Lam H. Li 1999 On free vibration of a rotating truncated circular orthotropic conical shell Compos. Part B Eng. 30 135 144 10.1016/S1359-8368(98) 00049-3
49. Y. Wang R. Liu X. Wang 1999 Free vibration analysis of truncated conical shells by the differential quadrature method J. Sound Vib. 224 387 394 10.1006/jsvi.1999.2218
50. K.M. Liew T.Y. Ng X. Zhao 2005 Free vibration analysis of conical shells via the element-free kp-Ritz method J. Sound Vib. 281 627 645 10.1016/j.jsv.2004.01.005 (Pubitemid 40206556)
51. V.I. Weingarten 1964 Free vibration of thin cylindrical shells AIAA J. 2 717 722 10.2514/3.2405
52. Agenesov, L.G., Sachenkov, A.V.: Free vibration and stability of conical shells with arbitrary transverse section. Research on the Theory of Plates and Shells, Kazan State University, Kazan 4, pp. 342-355 (1966) (in Russian)
53. W. Soedel 1980 A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions J. Sound Vib. 70 209 217 10.1016/0022-460X(80)90325-9 (Pubitemid 11447871)
54. T. Koga 1988 Effects of boundary conditions on the free vibrations of circular cylindrical shells AIAA J. 26 1387 1394 0676.73035 10.2514/3.10052 976248
55. K.Y. Lam C.T. Loy 1995 Effect of boundary conditions on frequencies of a multi-layered cylindrical shell J. Sound Vib. 188 363 384 10.1006/jsvi.1995.0599
56. C.T. Loy K.Y. Lam C. Shu 1997 Analysis of cylindrical shells using generalized differential quadrature Shock Vib. 4 193 198
57. M.N. Naem B. Sharma 2000 Prediction of natural frequencies for thin circular cylindrical shells Proc. Inst. Mech. Eng. 214 1313 1328
58. X.M. Zhang G.R. Liu K.Y. Lam 2001 Vibration analysis of thin cylindrical shells using wave propagation approach J. Sound Vib. 239 397 403 10.1006/jsvi.2000.3139 (Pubitemid 32377070)
59. M. El-Mously 2003 Fundamental natural frequencies of thin cylindrical shells, a comparative study J. Sound Vib. 264 1167 1186 10.1016/S0022-460X(02) 01391-3
60. B. Han G.J. Simitses 1991 Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads. Part II, Numerical results Compos. Struct. 19 183 205 10.1016/0263-8223(91)90022-Q
61. H.S. Shen Q.S. Li 2002 Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions Int. J. Mech. Sci. 44 1731 1754 1032.74559 10.1016/S0020-7403(02)00056-5 (Pubitemid 34946817)