Modal interactions in the vibrations of a heated annular plate

International Journal of Non-Linear Mechanics

Volumn 39, Issue 10, 2004, Pages 1671-1685

  Arafat, Haider N ^a   Nayfeh, Ali H ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Annular plates; Modal interactions; Non linear vibrations; Thermal load; Three to one internal resonance

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; BUCKLING; ELASTIC MODULI; MODAL ANALYSIS; NATURAL FREQUENCIES; POISSON RATIO; RESONANCE; THERMAL LOAD; VIBRATION CONTROL;

ANNULAR PLATES; MODAL INTERACTIONS; NON LINEAR VIBRATIONS; THERMAL LOADS; THREE TO ONE INTERNAL RESONANCE;

PLATES (STRUCTURAL COMPONENTS);

EID: 3242683427     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2004.02.015     Document Type: Article

References (33)

1. Nayfeh A.H. Nonlinear Interactions. 2000;Wiley, New York.
2. Sridhar S., Mook D.T., Nayfeh A.H. Non-linear resonances in the forced responses of plates, Part I. symmetric responses of circular plates J. Sound Vibration. 41:1975;359-373.
3. Sridhar S., Mook D.T., Nayfeh A.H. Non-linear resonances in the forced responses of plates, Part II. asymmetric responses of circular plates J. Sound Vibration. 59:1978;159-170.
4. Hadian J., Nayfeh A.H. Modal interaction in circular plates. J. Sound Vibration. 142:1990;279-292.
5. Lee W.K., Kim C.H. Combination resonances of a circular plate with three-mode interaction. J. Appl. Mech. 62:1995;1015-1022.
6. Yeo M.H., Lee W.K. Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate. J. Sound Vibration. 257:2002;653-665.
7. Lee W.K., Yeo M.H. Non-linear interactions in an asymmetric vibrations of a circular plate. J. Sound Vibration. 263:2003;1017-1030.
8. Lee W.K., Yeo M.H., Samoilenko S.B. The effects of the number of nodal diameters on non-linear interactions in two asymmetric vibration modes of a circular plate. J. Sound Vibration. 268:2003;1013-1023.
9. Tauchert T.R. Thermally induced flexure, buckling, and vibration of plates. Appl. Mech. Rev. 44:1991;347-360.
10. Thornton E.A. Thermal buckling of plates and shells. Appl. Mech. Rev. 46:1993;485-506.
11. von Freudenreich J. Vibration of steam turbine discs. Engineering. 119:1925;2-4; 31-34.
12. A. Stodola, Dampf- und Gas-Turbinen, 6th Edition, Springer, Berlin, 1924. (Translated from German by Loewenstein, L.C., Steam and Gas Turbines, McGraw Hill, New York, 1927).
13. Mote C.D. Free vibration of initially stressed circular disks. J. Eng. Ind. 87:1965;258-264.
14. Mote C.D. Theory of thermal natural frequency variations in disks. Int. J. Mech. Sci. 8:1966;547-557.
15. Mote C.D. Natural frequencies in annuli with induced thermal membrane stresses. J. Eng. Ind. 89:1967;611-618.
16. Fedorov V.A. Thermostability of elastically clamped variable-stiffness annular plates. Soviet Aeronaut. 19:1976;105-109.
17. Irie T., Yamada G. Thermally induced vibration of circular plate. Bull. JSME. 21:1978;1703-1709.
18. Buckens F. Vibrations in a thermally stressed thin plate. J. Thermal Stresses. 2:1979;367-385.
19. Pal M.C. Large deflections of heated circular plates. Acta Mechanica. 8:1969;82-103.
20. Pal M.C. Large amplitude free vibration of circular plates subjected to aerodynamic heating. Int. J. Solids Struct. 6:1970;301-313.
21. Pal M.C. Static and dynamic non-linear behaviour of heated orthotropic circular plates. Int. J. Non-Linear Mech. 8:1973;489-504.
22. P. Biswas, P. Kapoor, Non-linear vibrations of circular plates at elevated temperature, In: Proceedings of the Fourth International Conference on Numerical Methods in Thermal Problems, Part 2, Swansea, UK, July 15-18, (1985) pp. 1493-1501.
23. Li S.-R., Zhou Y.-H. Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates. J. Sound Vibration. 248:2001;370-386.
24. Li S.-R., Zhou Y.-H., Song X. Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass. J. Sound Vibration. 251:2002;141-152.
25. Nayfeh A.H., Faris W. Thermally induced principal parametric resonance in circular plates. Shock Vibration. 9:2002;143-150.
26. A.H. Nayfeh, W. Faris, Dynamic behavior of circular structural elements under thermal loads, In: Proceedings of the 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Norfolk, VA, April 7-10, 2003, pp. 1-9; Paper number AIAA-2003-1618.
27. Arafat H.N., Nayfeh A.H., Faris W. Natural frequencies of heated annular and circular plates. Int. J. Solids Struct. 41:2004;3031-3051.
28. Nayfeh A.H. Introduction to Perturbation Techniques. 1981;Wiley, New York.
29. Newman M., Forray M. Axisymmetric large deflections of circular plates subjected to thermal and mechanical loads. J. Aerospace Sci. 29:1962;1060-1066.
30. Hetnarski R.B. Thermal Stresses II. 1987;North-Holland, Amsterdam.
31. Boley B.A., Weiner J.H. Theory of Thermal Stresses. 1960;Wiley, New York.
32. Nayfeh A.H., Mook D.T. Nonlinear Oscillations. 1979;Wiley, New York.
33. H.N. Arafat, Nonlinear Response of Cantilever Beams, Ph.D. Dissertation, Virginia Tech, Blacksburg, VA, 1999.