Frequency Clusters in the Spectrum of Annular Cylinders

[+] Author and Article Information
K. I. Tzou, J. A. Wickert, A. Akay

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

J. Appl. Mech 65(4), 797-803 (Dec 01, 1998) (7 pages) doi:10.1115/1.2791914 History: Received November 11, 1997; Revised March 02, 1998; Online October 25, 2007


As the length of a traction-free annular cylinder is increased, distinct members within any family of radial or longitudinal shear modes have natural frequencies that asymptotically approach a common nonzero value. Such modes, potentially having significantly different numbers of nodes along the cylinder’s generator, can have natural frequencies that are indistinguishable from one another within the resolution of test equipment or numerical simulation. The three-dimensional vibration model discussed here predicts the formation of narrow “frequency clusters” with the cylinder’s increasing length, the converged value of which bounds from below the frequencies of all modes within a particular family. In addition to these spectral characteristics, frequency clusters have implications for the forced response of annular cylinders. For the particular families of modes that are of interest here, the steady-state harmonic response at frequencies near a cluster can be spatially confined with displacements that decay rapidly away from the point of maximum response. At other driving frequencies, the response is distributed more uniformly along the length of the cylinder. The derived analytical model is compared with results from laboratory measurements, and from the predictions of wave propagation theory in the limit of infinite cylinder length.

Copyright © 1998 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In