Vibration analysis of FGM truncated and complete conical shells resting on elastic foundations under various boundary conditions

Journal of Engineering Mathematics

Volumn 77, Issue 1, 2012, Pages 131-145

  Sofiyev, A H ^a   Kuruoglu, N ^b  

^a SULEYMAN DEMIREL UNIVERSITY   (Turkey)

^b BAHCESEHIR UNIVERSITY   (Turkey)

Author keywords

Conical shells; Elastic foundations; FGMs; Frequency; Various boundary conditions; Vibration

Indexed keywords

CONICAL SHELL; ELASTIC FOUNDATION; FGMS; FREQUENCY; VIBRATION;

BIOLOGICAL ORGANS; BOUNDARY CONDITIONS; FUNCTIONALLY GRADED MATERIALS; GALERKIN METHODS; LOADING; VIBRATION ANALYSIS;

SHELLS (STRUCTURES);

EID: 84867996446     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-012-9535-3     Document Type: Article

References (46)

1. Seide P (1965) On the vibrations of simply supported truncated conical shells. Isr J Technol 3: 50-61.
2. Aganesov LG, Sachenkov AV (1966) Free vibration and stability of conical shells with arbitrary transverse section. Res Theory Plate Shells Kazan State Univ Kazan 4: 342-355 (in Russian).
3. Tani J (1971) Free transverse vibrations of truncated conical shells. Rep Inst High Speed Mech Tohoku Univ Jpn 24: 87-116.
4. Leissa AW (1973) Vibration of shells. NASA SP-288.
5. Irie T, Yamada G, Tanaka K (1984) Natural frequencies of truncated conical shells. J Sound Vib 92: 447-453.
6. Lam KY, Hua L (1999) Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell. J Sound Vib 223: 171-195.
7. Liew KM, Ng TY, Zhao X (2005) Free vibration analysis of conical shells via the element-free kp-Ritz method. J Sound Vib 281: 627-645.
8. Civalek O (2006) An efficient method for free vibration analysis of rotating truncated conical shells. Int J Press Vessel Pip 83: 1-12.
9. Li FM, Kishimoto K, Huang WH (2009) The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method. Mech Res Commun 36: 595-602.
10. Koizumi M (1993) The concept of FGM ceramic transactions. Funct Gradient Mater 34: 3-10.
11. Afsar AM, Sekine H (2001) Optimum material distributions for prescribed apparent fracture toughness in thick-walled FGM circular pipes. Int J Press Vessel Pip 78: 471-484.
12. Miyamoto Y, Kaysser WA, Rabin BH, Kawasaki A, Ford RG (1999) Functionally graded materials: design, processing and applications. Chapman Hall, London.
13. Loy CT, Lam KY, Reddy JN (1999) Vibration of functionally graded cylindrical shells. Int J Mech Sci 41: 309-324.
14. Pradhan SC, Loy CT, Lam KY, Reddy JN (2000) Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust 61: 111-129.
15. Woo J, Mequid SA (2001) Nonlinear analysis of functionally graded plates and shallow shells. Int J Solid Struct 38: 7409-7421.
16. Ng TY, Lam KY, Liew KM, Reddy JN (2001) Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading. Int J Solid Struct 38: 1295-1309.
17. Patel BP, Gupta MS, Loknath MS, Kadu CP (2005) Free vibration analysis of a functionally graded elliptical cylindrical shells using higher-order theory. Compos Struct 69: 259-270.
18. Batra RC, Jin J (2005) Natural frequencies of a functionally graded anisotropic rectangular plate. J Sound Vib 282: 509-516.
19. Kadoli R, Ganesan K (2006) Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. J Sound Vib 289: 450-480.
20. Najafizadeh MM, Isvandzibaei MR (2007) Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mech 191: 75-91.
21. Matsunaga H (2009) Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory. Compos Struct 88: 519-531.
22. Zhao X, Lee YY, Liew KM (2009) Thermoelastic and vibration analysis of functionally graded cylindrical shells. Int J Mech Sci 51: 694-707.
23. Naj R, Boroujerdy SM, Eslami MR (2008) Thermal and mechanical instability of functionally graded truncated conical shells. Thin-Walled Struct 46: 65-78.
24. Sofiyev AH (2009) The vibration and stability behaviors of freely supported FGM conical shells subjected to external pressure. Compos Struct 89: 356-366.
25. Tornabene F, Viola E, Inman DJ (2009) 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J Sound Vib 328: 259-290.
26. Mahmoudkhani S, Haddadpour H, Navazi HM (2010) Supersonic flutter prediction of functionally graded conical shells. Compos Struct 92: 377-386.
27. Sofiyev AH, Kuruoglu N, Halilov HM (2010) The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures. Appl Math Model 34: 1807-1822.
28. Zhao X, Liew KM (2011) Free vibration analysis of functionally graded conical shell panels by a meshless method. Compos Struct 93: 649-664.
29. Pasternak PL (1954) On a new method of analysis of an elastic foundation by means of two foundation constants. Cosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR, pp 1-56 (in Russian).
30. Kerr AD (1964) Elastic and visco-elastic foundation models. J Appl Mech 31: 491-498.
31. Gazizov BG, Zaynashev AM (1973) On the stability of truncated conical shells on an elastic foundation beyond the elasticity limit. Res Theory Plate Shells Kazan State Univ Kazan 10: 195-201 (in Russian).
32. Sun B, Huang Y (1988) The exact solution for the general bending problems of conical shells on the elastic foundation. Appl Math Mech 9: 455-469.
33. Paliwal DN, Pandey RK, Nath T (1996) Free vibration of circular cylindrical shell on Winkler and Pasternak foundation. Int J Press Vessel Pip 69: 79-89.
34. Amabili M, Dalpiaz G (1997) Free vibration of cylindrical shells with non-axisymmetric mass distribution on elastic bed. Meccanica 32: 71-84.
35. Paliwal DN, Pandey RK (1998) The free vibrations of a cylindrical shell on an elastic foundation. J Vib Acoust 120: 63-71.
36. Ng TY, Lam KY (1999) Effects of elastic foundation on the dynamic stability of cylindrical shells. Struct Eng Mech 8: 193-205.
37. Cai JB, Chen WQ, Ye GR, Ding HJ (2000) On natural frequencies of a transversely isotropic cylindrical panel on a Kerr foundation. J Sound Vib 232: 997-1004.
38. Gunawan H, Sato M, Kanie S, Mikami T (2004) Static and free vibration analysis of cylindrical shells on elastic foundation. J Struct Eng JSCE 50A: 25-34.
39. Sheng GG, Wang X (2008) Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium. J Reinf Plast Compos 27: 117-134.
40. Shen HS (2009) Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. Int J Mech Sci 51: 372-383.
41. Shah AG, Mahmood T, Naeem MN, Iqbal Z, Arshad SH (2010) Vibrations of functionally graded cylindrical shells based on elastic foundations. Acta Mech 211: 293-307.
42. Sofiyev AH, Schnack E, Korkmaz A (2009) The vibration analysis of simply supported FGM truncated conical shells resting on two-parameter elastic foundations. IRF'2009 3rd International Conference on Integrity, Reliability and Failure, Porto, Portugal, pp 277-278.
43. Sofiyev AH (2010) Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation. Mech Res Commun 37: 539-544.
44. Pitakthapanaphong S, Busso EP (2002) Self-consistent elasto-plastic stress solutions for functionally graded material systems subjected to thermal transients. J Mech Phys Solid 50: 695-716.
45. Jin ZH, Batra RC (1996) Stresses intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock. J Therm Stress 19: 317-339.
46. Reddy JN, Chin CD (1998) Thermal-mechanical analysis of functionally graded cylinders and plates. J Therm Stress 21: 593-626.