Structural Engineering and Mechanics

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Effects of elastic foundation on the dynamic stability of cylindrical shells

  • Ng, T.Y. (Institute of High Performance Computing, National University of Singapore) ;
  • Lam, K.Y. (Institute of High Performance Computing, National University of Singapore)
  • Published : 1999.08.25
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Abstract

A formulation for the dynamic stability analysis of cylindrical shells resting on elastic foundations is presented. In this previously not studied problem, a normal-mode expansion of the partial differential equations of motion, which includes the effects of the foundation as well as a harmonic axial loading, yields a system of Mathieu-Hill equations the stability of which is analyzed using Bolotin's method. The present study examines the effects of the elastic foundation on the instability regions of the cylindrical shell for the transverse, longitudinal and circumferential modes.

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References

  1. Akoz, A.Y. and Kadloglu, F. (1996), "The mixed finite element solution of circular beam on elastic foundation", Computers and Structures, 60, 643-651. https://doi.org/10.1016/0045-7949(95)00418-1
  2. Bolotin, V.V. (1964), The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco.
  3. Chandrasekharappa, G. (1992), "Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation", Computers and Structures, 44, 609- 618. https://doi.org/10.1016/0045-7949(92)90393-E
  4. Chang, T.P. (1994), "Deterministic and random vibration of an axially loaded Timoshenko beam resting on an elastic foundation", Journal of Sound and Vibration, 178, 55-66. https://doi.org/10.1006/jsvi.1994.1467
  5. De Rosa, M.A. (1995), "Free vibrations of Timoshenko beams on two-parameter elastic foundation", Computers and Structures, 57, 151-156. https://doi.org/10.1016/0045-7949(94)00594-S
  6. Eslami, M.R. and Ayatollahi, M.R. (1993), "Modal analysis of shell of revolution on elastic foundation", International Journal of Pressure Vessels and Piping, 56, 351-568. https://doi.org/10.1016/0308-0161(93)90005-E
  7. GuIer, K. and Celep, Z. (1995), "Static and dynamic responses of a circular plate on a tensionless elastic foundation", Journal of Sound and Vibration, 183, 185-195. https://doi.org/10.1006/jsvi.1995.0248
  8. Kuo, Y.H. and Lee, S.Y. (1994), "Deflection of nonuniform beams resting on a nonlinear elastic foundation", Computers and Structures, 51, 513-519. https://doi.org/10.1016/0045-7949(94)90058-2
  9. Lam, K.Y. and Ng, T.Y. (1998), "Dynamic stability analysis of cylindrical shells subjected to conservative periodic axial loads using different thin shell theories", Journal of Sound and Vibration, (in press).
  10. Lee, H.P. (1996), "Dynamic stability of a tapered cantilever beam on an elastic foundation subjected to a follower force", International Journal of Solids and Structures, 33, 1409-1424. https://doi.org/10.1016/0020-7683(95)00108-5
  11. Lee, S.Y., Lin, J.C. and Hsu, K.C. (1996), "Elastic instability of a beam resting on an elastic foundation subjected to a partially tangential force", Computers and Structures, 59, 983-988. https://doi.org/10.1016/0045-7949(95)00317-7
  12. Lee, S.Y. and Yang, C.C. (1993), "Non-conservative instability of a Timoshenko beam resting on Winkler elastic foundation", Journal of Sound and Vibration, 162, 177-184. https://doi.org/10.1006/jsvi.1993.1110
  13. Lee, S.Y. and Yang, C.C. (1994), "Non-conservative instability of non-uniform beams resting on an elastic foundation", Journal of Sound and Vibration, 169, 433-444. https://doi.org/10.1006/jsvi.1994.1027
  14. Librescu, L. and Lin, W.Q. (1997), "Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation", International Journal of Non-Linear Mechanics, 32, 211- 225. https://doi.org/10.1016/S0020-7462(96)00057-1
  15. Naidu, N.R. and Rao, G.V. (1995), "Vibrations of initially stressed uniform beams on a two-parameter elastic foundation", Computers and Structures, 57, 941-943. https://doi.org/10.1016/0045-7949(95)00090-4
  16. Naidu, N.R. and Rao, G.V. (1996), "Free vibration and stability behaviour of uniform beams and columns on nonlinear elastic foundation", Computers and Structures, 58, 1213-1215. https://doi.org/10.1016/0045-7949(95)00224-3
  17. Ng, T.Y. and Lam, K.Y. (1998), "Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories", Acta Mechanica, (in press).
  18. Ng, T.Y., Lam, K.Y. and Reddy, J.N. (1998a), "Dynamic stability analysis of cross-ply laminated cylindrical shells", International Journal of Mechanical Sciences, (in press).
  19. Ng, T.Y., Lam, K.Y. and Reddy, J.N. (1998b), "Parametric resonance of a rotating cylindrical shell subjected to periodic axial loading" , Journal of Sound and Vibration, (in press).
  20. Omurtag, M.H., Ozutok, A. and Akoz, A.Y. (1997), "Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential", International Journal for Numerical Methods in Engineering, 40, 295-317. https://doi.org/10.1002/(SICI)1097-0207(19970130)40:2<295::AID-NME66>3.0.CO;2-2
  21. Paliwal, D.N., Gupta, R. and Jain, A. (1993), "Stress analysis of ellipsoidal shell on an elastic foundation", International Journal of Pressure Vessels and Piping, 56, 229-242. https://doi.org/10.1016/0308-0161(93)90095-B
  22. Paliwal, D.N. (1994), "Large deflection in a shallow spherical shell on an elastic foundation under a concentrated load at the centre", International Journal of Pressure Vessels and Piping, 57, 131-133. https://doi.org/10.1016/0308-0161(94)90046-9
  23. Paliwal, D.N., Pandey, R.K. and Nath, T. (1996), "Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations", International Journal of Pressure Vessels and Piping, 69, 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
  24. Qin, Q.H. (1993), "Nonlinear analysis of Reissner plates on an elastic foundation by the BEM", International Journal of Solids and Structures, 30, 3101-3111. https://doi.org/10.1016/0020-7683(93)90141-S
  25. Qin, Q.H. (1995), "Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation", Computer Methods in Applied Mechanics and Engineering, 122, 379-392. https://doi.org/10.1016/0045-7825(94)00730-B
  26. Raju, K.K. and Rao, G.V. (1993a), "Effect of a non-linear elastic foundation on the mode shapes in stability and vibration problems of uniform columns/beams", Journal of Sound and Vibration, 160, 369-371. https://doi.org/10.1006/jsvi.1993.1031
  27. Raju, K.K. and Rao, G.V. (1993b), "Vibrations of initially stressed beams and plates around transition values of elastic foundation stiffness", Journal of Sound and Vibration, 161, 378-384. https://doi.org/10.1006/jsvi.1993.1081
  28. Zhou, D. (1993), "General solution to vibrations of beams on variable Winkler elastic foundation", Computers and Structures, 47, 83-90. https://doi.org/10.1016/0045-7949(93)90281-H

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