Affiliation:
1. Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617
Abstract
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 ωmn¯) and backward (with frequency ωmn) traveling waves. It is found that combination resonance may occur when the excitation frequency is close to 2ωmn+ωmn¯,ωmn+2ωmn¯, or 1/2ωmn¯+ωmn. When the combination resonance does occur, the frequencies of the free oscillation components are shifted slightly from the respective natural frequencies ωmn¯ and ωmn. The final response is therefore quasiperiodic. However, in the case when the excitation frequency is close to 1/2ωmn¯−ωmn, no combination resonance is possible. In the case when the excitation frequency is close to 1/3ωmn and 1/2ωmn¯−ωmn 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.
Reference14 articles.
1. Benson, R. C., and Bogy, D. B., 1978, “Deflection of a Very Flexible Spinning Disk Due to a Stationary Transverse Load,” ASME J. Appl. Mech., 45, pp. 636–642.
2. Cole, K. A., and Benson, R. C., 1988, “Fast Eigenfunction Approach for Computing Spinning Disk Deflections,” ASME J. Appl. Mech., 55, pp. 453–457.
3. Ono, K., and Maeno, T., 1987, “Theoretical and Experimental Investigation on Dynamic Characteristics of a 3.5-Inch Flexible Disk Due to a Point Contact Head,” Tribology and Mechanics of Magnetic Storage Systems, 3, SP.21, (STLE), pp. 144–151.
4. Jiang, Z. W., Chonan, S., and Abe, H., 1990, “Dynamic Response of a Read/Write Head Floppy Disk System Subjected to Axial Excitation,” ASME J. Vibr. Acoust., 112, pp. 53–58.
5. Chen, J. S., and Hsu, C. M., 1997, “On the Transient Response of a Spinning Disk Under a Space-Fixed Step Load,” ASME J. Appl. Mech., 64, pp. 1017–1019.
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