Structural Engineering and Mechanics

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Dynamic combination resonance characteristics of doubly curved panels subjected to non-uniform tensile edge loading with damping

  • Udar, Ratnakar. S. (Department of Aerospace Engineering, Indian Institute of Technology) ;
  • Datta, P.K. (Department of Aerospace Engineering, Indian Institute of Technology)
  • Received : 2005.09.22
  • Accepted : 2006.09.06
  • Published : 2007.03.10
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Abstract

The dynamic instability of doubly curved panels, subjected to non-uniform tensile in-plane harmonic edge loading $P(t)=P_s+P_d\;{\cos}{\Omega}t$ is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to simple resonances in parametrically excited doubly curved panels. Analytical expressions for the instability regions are obtained at ${\Omega}={\omega}_m+{\omega}_n$, (${\Omega}$ is the excitation frequency and ${\omega}_m$ and ${\omega}_n$ are the natural frequencies of the system) by using the method of multiple scales. It is shown that, besides the principal instability region at ${\Omega}=2{\omega}_1$, where ${\omega}_1$ is the fundamental frequency, other cases of ${\Omega}={\omega}_m+{\omega}_n$, related to other modes, can be of major importance and yield a significantly enlarged instability region. The effects of edge loading, curvature, damping and the static load factor on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which the curved panels cannot become dynamically unstable. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.

Keywords

References

  1. Argento, A (1993), 'Dynamic stability of a composite circular cylindrical shell subjected to combined axial and torsional loading', J. Compos. Mater., 29(11), 2000-2005
  2. Argento, A. and Scott, R.A. (1993), 'Dynamic instability of layered anisotropic circular cylindrical shells, part I: Theoretical development', J. Sound. Vib., 162(2), 311-322 https://doi.org/10.1006/jsvi.1993.1120
  3. Bolotin, V.V. (1964), The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco
  4. Bolotin, V.V., Grishko, A.A. and Panov, M.Y. (2002), 'Effect of damping on the postcritical behaviour of autonomous non-conservative systems', Non-Linear. Mech., 37, 1163-1179 https://doi.org/10.1016/S0020-7462(01)00148-2
  5. Cederbaum, G. (1991), 'Dynamic instability of shear-deformable laminated plates', AIAA J., 29(11), 2000-2005 https://doi.org/10.2514/3.10830
  6. Choo, Y.S. and Kim, J.H. (2000), 'Dynamic stability of rectangular plates subjected to pulsating follower forces', AIAA J., 38(2), 353-361 https://doi.org/10.2514/2.964
  7. Deolasi, P.J. and Datta, P.K. (1995), 'Effects of damping on the parametric instability behaviour of plates under localized edge loading (compression or tension)', Struct. Eng. Mech., 3(3), 229-244
  8. Deolasi, P.J. and Datta, P.K. (1997), 'Simple and combination resonances of rectangular plates subjected to nonuniform edge loading with damping', Eng. Struct., 19(12), 1011-1017 https://doi.org/10.1016/S0141-0296(97)00128-4
  9. Engel, R.S. (1991), 'Dynamic stability of an axially loaded beam on elastic foundation with damping', J. Sound Vib., 146(3), 463-477 https://doi.org/10.1016/0022-460X(91)90702-L
  10. Hsu, C.S. (1963), 'On the parametric excitation of dynamic system having multiple degrees of freedom', J. Appl. Mech., ASME, 30(3), 367-372 https://doi.org/10.1115/1.3636563
  11. Hutt, J.M. and Salam, A.E. (1971), 'Dynamic stability of plates by finite element method', J. Eng. Mech. Div , ASCE, 97, 879-899
  12. Iwatsubo, T., Sugiyama, Y. and Ogino, S. (1974), 'Simple and combination resonances of columns under periodic axial loads', J. Sound Vib., 33(2), 211-221 https://doi.org/10.1016/S0022-460X(74)80107-0
  13. Kar, R.C. and Sujata, T. (1991), 'Dynamic stability of a tapered symmetric sandwich beam', Comput. Struct., 40(6), 1441-1449 https://doi.org/10.1016/0045-7949(91)90414-H
  14. Kim, J.H. and Choo, Y.S. (1998), 'Dynamic stability of a free-free Timoshenko beam subjected to a pulsating follower force', J. Sound Vib., 216(4), 623-636 https://doi.org/10.1006/jsvi.1998.1717
  15. Lee, W.K. and Kim, C.H. (1995), 'Combination resonances of a circular plate with three-mode interaction', J. Appl. Mech., ASME, 62, 1015-1022 https://doi.org/10.1115/1.2896037
  16. Leissa, A.W. and Ayoub, E.F. (1989), 'Tension buckling of rectangular sheets due to concentrated forces', J. Eng. Mech., ASCE, 115(12), 2749-2762 https://doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2749)
  17. Leissa, A.W, Lee, J.K. and Wang, A.J. (1983), 'Vibrations of cantilevered doubly curved shallow shells', Int. J. Solids. Struct., 19(5), 411-424 https://doi.org/10.1016/0020-7683(83)90052-5
  18. Matsunaga, H. (1999), 'Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses', J. Sound Vib., 225(1), 41-60 https://doi.org/10.1006/jsvi.1999.2234
  19. Mond, M. and Cederbaum, G. (1992), 'Dynamic instability of anti-symmetric laminated plates', J. Sound Vib., 154(2), 271-279 https://doi.org/10.1016/0022-460X(92)90581-H
  20. Cederbaum, G. (1992), 'Analysis of parametrically excited laminated shells', Int. J. Mech. Sci., 34(3), 241-250 https://doi.org/10.1016/0020-7403(92)90074-Q
  21. Moorthy, J, Reddy, J.N. and Plaut, R.H. (1990), 'Parametric instability of laminated composite plates with transverse shear deformation', Int. J. Solids Struct., 26, 801-811 https://doi.org/10.1016/0020-7683(90)90008-J
  22. Nayfeh, A.H. (1973), Perturbation Methods, Wiley, New York
  23. Nayfeh, A.H. and Mook, D.T. (1979), Nonlinear Oscillations. Wiley, New York
  24. Ostiguy, G.L., Samson, L.P. and Nguyen, H. (1993), 'On the occurrence of simultaneous resonances In parametrically-excited rectangular plates', J. Vib. Acoust., 115(3), 344-352 https://doi.org/10.1115/1.2930355
  25. Saha, K.N., Kar, R.C. and Datta, P.K. (1997), 'Dynamic stability of a rectangular plate on non-homogeneous Winkler foundation', Comput. Struct., 63(6), 1213-1222 https://doi.org/10.1016/S0045-7949(96)00390-2
  26. Sahu, S.K. and Datta, P.K. (2001), 'Parametric instability of doubly curved panels subjected to non-uniform harmonic loading', J. Sound Vib., 240(1), 117-129 https://doi.org/10.1006/jsvi.2000.3187
  27. Szemplinska-Stupnicka, W. (1978), 'The generalized harmonic balance method for determining the combination resonance in the parametric dynamic systems', J. Sound Vib., 58(3), 347-361 https://doi.org/10.1016/S0022-460X(78)80043-1
  28. Takahashi, K. (1981), 'An approach to investigate the instability of the multiple degree of freedom parametric dynamic systems', J. Sound Vib., 78(4), 519-529 https://doi.org/10.1016/S0022-460X(81)80122-8
  29. Takahashi, K. and Konishi, Y. (1988), 'Dynamic stability of a rectangular plate subjected to distributed in-plane dynamic force', J. Sound Vib., 123(1), 115-127 https://doi.org/10.1016/S0022-460X(88)80082-8

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