Effect of the two-parameter elastic foundation on the critical parameters of nonhomogeneous orthotropic shells

International Journal of Structural Stability and Dynamics

Volumn 12, Issue 5, 2012, Pages

  Sofiyev, A H ^a   Schnack, E ^b   Haciyev, V C ^c   Kuruoglu, N ^d  

^a SULEYMAN DEMIREL UNIVERSITY   (Turkey)

^b KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^c INSTITUTE OF MATHEMATICS AND MECHANICS   (Azerbaijan)

^d BAHCESEHIR UNIVERSITY   (Turkey)

Author keywords

Buckling; nonhomogeneity; orthotropic shells; vibration; Winkler and Pasternak type elastic foundations

Indexed keywords

CRITICAL PARAMETER; CYLINDRICAL AND CONICAL SHELLS; DIMENSIONLESS FREQUENCY; ELASTIC FOUNDATION; NON-HOMOGENEOUS; NONHOMOGENEITY; ORTHOTROPIC SHELLS; ORTHOTROPY; THICKNESS DIRECTION; THIN-WALLED; TRUNCATED CONICAL SHELL; VIBRATION; WINKLER; YOUNG'S MODULUS;

BUCKLING; GALERKIN METHODS; HYDROSTATIC PRESSURE;

SHELLS (STRUCTURES);

EID: 84871749442     PISSN: 02194554     EISSN: 17936764     Source Type: Journal    
DOI: 10.1142/S0219455412500411     Document Type: Article

References (45)

1. P. L. Pasternak, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants (Gos. Izd. Lit. po Stroit I Arkh., Moscow, Russia, 1954).
2. A. D. Kerr, Elastic and visco-elastic foundation models, J. Appl. Mech. 31 (1964) 491-498.
3. M. I. Gorbunov-Possadov, T. A. Malikova and V. I. Solomin, Design of Structures on Elastic Foundation, 3rd edn. (Gos. Izd. Lit. po Stroit I Arkh. (Strojizdat), Moscow, USSR, 1984).
4. V. A. Bajenov, The Bending of the Cylindrical Shells in Elastic Medium (Visha Shkola, Kiev, Russian, 1975).
5. R. Yang, H. Kameda and S. Takada, Shell model FEM analysis of buried pipelines under seismic loading, Bull. Disast. Prev. Res. Inst. 38(3) (1988) 115-146.
6. D. N. Paliwal, R. K. Pandey and T. Nath, Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, Int. J. Pres. Ves. Pip. 69 (1996) 79-89. (Pubitemid 126393756)
7. D. N. Paliwal and R. K. Pandey, The free vibrations of a cylindrical shell on an elastic foundation, J. Vib. Acoust. 120 (1998) 63-71. (Pubitemid 128651959)
8. M. Amabili and G. Dalpiaz, Free vibration of cylindrical shells with non-axisymmetric mass distribution on elastic bed, Meccanica. 32 (1997) 71-84. (Pubitemid 127506346)
9. T. Y. Ng and K. Y. Lam, E®ects of elastic foundation on the dynamic stability of cylindrical shells, Int. J. Struct. Eng. Mech. 8 (1999) 193-205.
10. S. Naili, and C. Oddou, Buckling of short cylindrical shell surrounded by an elastic medium, J. Appl. Mech. ASME 67 (2000) 212-214.
11. S. L. Fok, Analysis of the buckling of long cylindrical shells embedded in an elastic medium using the energy method, J. Strain Anal. 37 (2002) 375-383. (Pubitemid 34964522)
12. H. Gunawan, M. Sato, S. Kanie and T. Mikami, Static and free vibration analysis of cylindrical shells on elastic foundation, J. Struct. Eng. JSCE A 50 (2004) 25-34.
13. K. G. Golovko, P. Z. Lugovoi and V. F. Meish, Solution of axisymmetric dynamic problems for cylindrical shells on an elastic foundation, Int. Appl. Mech. 43(12) (2007) 1390-1395.
14. H. S. Shen, Post-buckling of internal-pressure-loaded laminated cylindrical shells surrounded by an elastic medium, J. Strain Anal. 44(6) (2009) 439-458.
15. B. G. Gazizov and A. M. Zaynashev, On the stability of truncated conical shells on an elastic foundation beyond the elasticity limit, Research on the Theory of Plates and Shells, Kazan State University, Kazan, (in Russian) 10 (1973) 195-201.
16. B. Sun and Y. Huang, The exact solution for the general bending problems of conical shells on the elastic foundation, Appl. Math. Mech. Engl. Ed. 9(5) (1988) 455-469.
17. V. Nath and R. K. Jain, Orthotropic annular shells on elastic foundations, J. Eng. Mech. 3 (1980) 1242-1256.
18. H. S. Shen, Post-buckling of orthotropic plates on two-parameter elastic foundation, J. Eng. Mech. ASCE 121(1) (1995) 50-56.
19. M. H. Omurtag and F. Kadioglu, Free vibration analysis of orthotropic plates resting on Pasternak foundation by mixed finite element formulation, Comput. Struct. 67 (1998) 253-265. (Pubitemid 128420530)
20. D. N. Paliwal and S. Singh, Free vibrations of orthotropic cylindrical shell on elastic foundation, AIAA J. 37 (1999) 1135-1139.
21. D. N. Paliwal and R. K. Pandey, Free vibrations of an orthotropic thin cylindrical shell on a Pasternak foundation, AIAA J. 39(11) (2001) 2188-2191. (Pubitemid 33084953)
22. J. Tomar, D. Gupta and V. Kumar, Natural frequencies of a linearly tapered nonhomogeneous isotropic elastic circular plate resting on an elastic foundation, J. Sound Vib. 111 (1986) 1-8. (Pubitemid 17482888)
23. B. Klyachko and S. Klyachko, Symmetry in the problem of vibration of a polar-orthotrop?c non-homogeneous plate on an elastic foundation, J. Sound Vib. 201(3) (1997) 365-381. (Pubitemid 127375983)
24. A. H. Sofiyev, S. N. Keskin and Al. H. Sofiyev, E®ects of elastic foundation on the vibration of laminated non-homogeneous orthotropic circular cylindrical shells, Shock Vib. 11 (2004) 89-101.
25. A. Lal, B. N. Singh and R. Kumar, E®ect of random system properties on initial buckling of composite plates resting on elastic foundation, Int. J. Struct. Stabil. Dyn. 8(1) (2008) 103-130. (Pubitemid 351700257)
26. A. H. Sofiyev, H. M. Halilor, N. Kurooglu, Analytical solution of the dynamic behavior of non-homogenous orthotropic cylindrical shells on elastic foundations under moving loads, J. Eng. Math. 69(2011) 359-371.
27. G. G. Sheng and X. Wang, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, J. Reinforc. Plast. Compos. 27 (2008) 117-134.
28. S. C. Pradhan and T. Murmu, Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using di®erential quadrature method, J. Sound Vib. 321 (2009) 342-362.
29. P. Malekzadeh, Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations, Compos. Struct. 89 (2009) 367-373.
30. A. H. Sofiyev, E. Schnack and A. Korkmaz, The vibration analysis of simply supported FGM truncated conical shells resting on two-parameter elastic foundations, IRF'2009-3rd Int. Conf. on Integrity, Reliability and Failure, July 2009, Porto, Portugal, pp. 277-278.
31. H. S. Shen, Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium, Int. J. Mech. Sci. 51 (2009) 372-383.
32. J. Singer and R. Fershst-Scher, Buckling of orthotropic conical shells under external pressure, J. Aeronautical Quarterly 15 (1964) 151-168.
33. T. Irie, G. Yamada and K. Tanaka, Natural frequencies of truncated conical shells, J. Sound Vib. 92(3) (1984) 447-453. (Pubitemid 14529672)
34. L. P. Khoroshun, S. Y. Kozlov, Y. A. Ivanov and I. K. Koshevoi, The Generalized Theory of Plates and Shells Non-Homogeneous in Thickness Direction (Naukova Dumka, Kiev, in Russian, 1988).
35. A. Kasagi and S. Sridharan, Buckling and post-buckling analysis of thick composite cylindrical shells under hydrostatic pressure, Compos. Eng. 3 (1993) 467-487.
36. L. Tong, E®ect of axial load on free vibration of orthotropic conical shells, J. Vib. Acoust. 118 (1996) 164-168. (Pubitemid 126766857)
37. K. M. Lam and H. Li, On free vibration of a rotating truncated circular orthotropic conical shell, Compos. B: Eng. 30 (1999) 135-144.
38. K. M. Liew, T. Y. Ng and X. Zhao, Free vibration analysis of conical shells via the element-free kp-Ritz method, J. Sound Vib. 281 (2005) 627-645. (Pubitemid 40206556)
39. H. S. Shen and N. Noda, Post-buckling of pressure-loaded FGM hybrid cylindrical shell in thermal environments, Compos. Struct. 77 (2007) 546-560. (Pubitemid 44689026)
40. R. Lal, Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness: A spline technique, J. Sound Vib. 306 (2007) 203-214. (Pubitemid 47069474)
41. D. Iean and R. Quintanilla, On the deformation of inhomogeneous orthotropic elastic cylinders, Eur. J. Mech. Solid. 26 (2007) 999-1015. (Pubitemid 47411613)
42. Y. Ootao and Y. Tanigawa, Three-dimensional solution for transient thermal stresses of an orthotropic functionally graded rectangular plate, Compos. Struct. 80 (2007) 10-20. (Pubitemid 46359816)
43. A. H. Sofiyev, M. Omurtag and E. Schnack, The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure, J. Sound Vib. 319(3-5) (2009) 963-983.
44. F. M. Li, K. Kishimoto and W. H. Huang, The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method, Mech. Res. Commun. 36 (2009) 595-602.
45. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. (CRC Press, Boca Raton, FL, 2004).