The peculiarities of the non-axisymmetric frequency spectra of finite elastic cylinders

A rigorous solution of three-dimensional boundary-value problem concerning the forced vibrations of a finite, elastic, isotropic cylinder is constructed analytically by means of the superposition method. With this solution, the resonances in non-propagating waves were investigated. Particularly, a survey of the frequency spectrum for an aluminum cylinder, vibrating with the circumferential order two, reveals the existence of a localized resonance, usually referred to as an end resonance, well below the cut-off frequency of the lowest real dispersion branch of an infinite cylinder. This phenomenon demonstrates the remarkable differences between the axisymmetric and non-axisymmetric end resonances of elastic cylinders. Comparison of the theoretical results with the experiments published elsewhere reveals an excellent agreement.