Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science in Engineering (MSE)

Department / School

Mechanical Engineering


Linear in-plane free vibration of a thin homogeneous, isotropic, and elastic rotating disk is researched in this thesis. Two dimensional theory of elasticity is employed to develop the general governing equations of motion. A constant angular velocity is assumed in this analysis. The wave equations and Bessel functions of the first and second kind are utilized to obtain the natural frequencies. Natural frequencies are found for certain combinations of nodal diameters and nodal circles, for clamping ratios of 0.001, 0.2, 0.3, 0.5, and 0.7. Results of the natural frequencies were compared to those of Burdess, Wren and Fawcett (1987) and Chen and Jhu(1996). Stiffness of the disk was found to be an important factor in the results. It was observed that the effect of clamping ratio was to increase the natural frequencies for the various modes of vibration. Effects of rotational speed on the natural frequencies were seen to depend on the clamping ratio, mode of vibration and type of circumferential wave occurring.

Library of Congress Subject Headings

Disks, Rotating -- Vibration



Number of Pages



South Dakota State University