We investigate the possibility of secondary resonance of a spinning disk under space-fixed excitations. Von Karman’s plate model is employed in formulating the equations of motion of the spinning disk. Galerkin’s procedure is used to discretize the equations of motion, and the multiple scale method is used to predict the steady state solutions. Attention is focused on the nonlinear coupling between a pair of forward (with frequency and backward (with frequency traveling waves. It is found that combination resonance may occur when the excitation frequency is close to or When the combination resonance does occur, the frequencies of the free oscillation components are shifted slightly from the respective natural frequencies and The final response is therefore quasiperiodic. However, in the case when the excitation frequency is close to no combination resonance is possible. In the case when the excitation frequency is close to and simultaneously, internal resonance between the forward and backward modes can occur. The frequencies of the free oscillation components are exactly three times and five times that of the excitation frequency. In this special case both saddle-node and Hopf bifurcations are observed.
On the Secondary Resonance of a Spinning Disk Under Space-Fixed Excitations
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 2001; Revised Dec. 2003. Associate Editor: J. P. Cusumano.
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Chen, J., Hua, C., and Sun, C. (July 30, 2004). "On the Secondary Resonance of a Spinning Disk Under Space-Fixed Excitations ." ASME. J. Vib. Acoust. July 2004; 126(3): 422–429. https://doi.org/10.1115/1.1760562
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