Nonlinear Interactions in the Responses of Heated Annular Plates

Nonlinear modal interactions in the forced vibrations of a thermally loaded annular plate with clampedclamped immovable boundary conditions are investigated. The mechanism responsible for the interaction is a subcombination internal resonance involving the natural frequencies of the three lowest axisymmetric modes. The in-plane thermal load acting on the plate is assumed to be axisymmetric and the plate is externally excited

[1]  A. Nayfeh,et al.  Natural frequencies of heated annular and circular plates , 2004 .

[2]  Youhe Zhou,et al.  NON-LINEAR VIBRATION AND THERMAL BUCKLING OF AN ORTHOTROPIC ANNULAR PLATE WITH A CENTRIC RIGID MASS , 2002 .

[3]  Dynamic Behavior of Circular Structural Elements Under Thermal Loads , 2003 .

[4]  C. L. Zaretzky,et al.  Nonlinear flexural-flexural-torsional interactions in beams including the effect of torsional dynamics. I: Primary resonance , 1994, Nonlinear Dynamics.

[5]  J. W. Roberts,et al.  NON-LINEAR VIBRATORY INTERACTIONS IN SYSTEMS OF COUPLED BEAMS , 1986 .

[6]  M. Pal.  Static and dynamic non-linear behaviour of heated orthotropic circular plates , 1973 .

[7]  Ali H. Nayfeh,et al.  Modal interaction in circular plates , 1990 .

[8]  Vimal Singh,et al.  Perturbation methods , 1991 .

[9]  Matthew P. Cartmell,et al.  Simultaneous combination resonances in an autoparametrically resonant system , 1988 .

[10]  W. K. Lee,et al.  Non-linear interactions in asymmetric vibrations of a circular plate , 2003 .

[11]  Vibrations in a Thermally Stressed Thin Plate , 1979 .

[12]  M. Pal.  Large deflections of heated circular plates , 1969 .

[13]  Ali H. Nayfeh,et al.  Nonlinear combination resonances in cantilever composite plates , 1996 .

[14]  T. Irie,et al.  Thermally Induced Vibration of Circular Plate , 1978 .

[15]  M. Newman.  Axisymmetric Large Deflections of Circular Plates Subjected to Thermal and Mechanical Loads , 1962 .

[16]  A. H. Nayfeh,et al.  Non-linear resonances in the forced responses of plates, part 1: Symmetric responses of circular plates , 1975 .

[17]  W. K. Lee,et al.  CORRECTED SOLVABILITY CONDITIONS FOR NON-LINEAR ASYMMETRIC VIBRATIONS OF A CIRCULAR PLATE , 2002 .

[18]  T. R. Tauchert,et al.  Thermally Induced Flexure, Buckling, and Vibration of Plates , 1991 .

[19]  C. D. Mote.  Free Vibration of Initially Stressed Circular Disks , 1965 .

[20]  William Prager,et al.  Theory of Thermal Stresses , 1960 .

[21]  M. Pal.  Large amplitude free vibration of circular plates subjected to aerodynamic heating , 1970 .

[22]  M. Holmes.  Introduction to Perturbation Methods , 1995 .

[23]  A. Nayfeh,et al.  Modal Interactions in a Thermally Loaded Annular Plate , 2003 .

[24]  C. D. Mote.  Theory of thermal natural frequency variations in disks , 1966 .

[25]  Ali H. Nayfeh,et al.  Investigation of subcombination internal resonances in cantilever beams , 1998 .

[26]  A. Nayfeh,et al.  A theoretical and experimental investigation of a three-degree-of-freedom structure , 1994 .

[27]  W. K. Lee,et al.  Combination Resonances of a Circular Plate With Three-Mode Interaction , 1995 .

[29]  A. H. Nayfeh,et al.  An Experimental Investigation of Multimode Responses in a Cantilever Beam , 1997 .

[30]  The effect of the number of nodal diameters on non-linear interactions in two asymmetric vibration modes of a circular plate , 2003 .

[31]  C. D. Mote.  Natural Frequencies in Annuli With Induced Thermal Membrane Stresses , 1967 .

[32]  A. Nayfeh,et al.  Nonlinear Analysis of the Lateral Response of Columns to Periodic Loads , 1978 .