Frequency clusters in the spectrum of annular cylinders

As the length of a traction-free annular cylinder is increased, distinct me mbers 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 cyl inder's generator, can have natural frequencies that are indistinguishable from one another within the resolution of test equipment or numerical simul ation. The three-dimensional vibration model discussed here predicts the fo rmation of narrow "frequency clusters" with the cylinder's increasing lengt h, the converged value of which bounds from below the frequencies of all mo des within a particular family. In addition to these spectral characteristi cs, 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 sp atially confined with displacements that decay rapidly away from the point of maximum response. At other driving frequencies, the response is distribu ted 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 le ngth.