Modes of Wave Propagation and Dispersion Relations in a Cylindrical Shell

Abstract

This paper reinvestigates the classic problem of the dispersion relations of a cylindrical shell by obtaining a complete set of analytical solutions, based on Flügge’s theory, for all orders of circular harmonics, n=0,1,2,…,∞. The traditional numerical root search process, which requires considerable computational effort, is no longer needed. Solutions of the modal patterns (eigenvectors) for all propagating (and nonpropagating) modes are particularly emphasized, because a complete set of properly normalized eigenvectors are crucial for solving the vibration problem of a finite shell under various admissible boundary conditions. The dispersion relations and the associated eigenvectors are also the means by which to construct transfer matrices used to analyze the vibroacoustic transmission in cylindrical shell structures or pipe-hose systems. The eigenvectors obtained from the conventional method in shell analysis are not as conveniently normalized as those commonly used in mathematical physics. The present research proposes a new alternative method to find eigenvectors that are normalized such that their norms equal unity. A parallel display of the dispersion curves and the associated modal patterns has been used in the discussion and shown to provide a more insightful understanding of the wave phenomena in a cylindrical shell.

Numerical modeling of the momentum and thermal characteristics of air flow in the intercooler connection hose

“…Marquez et al [15] pointed out the significance of dynamic loads originating from gas pulsations and investigated the impact of hose flexibility at the discharge side of a compressor. As modes of wave propagation and dispersion relations in a cylindrical annuli was numerically considered by Liu et al [16], Drew et al [17] experimented on the longitudinal transmission of pressure fluctuations and structural vibrations in flexible hoses. Nishimura and Matsunaga [18] also worked on the pressure wave propagation in a hydraulic hose and analyzed the interrelation of the pressure perturbation and the simultaneously excited vibration.…”

Dispersion Relations and Modal Patterns of Wave in a Cylindrical Shell

“…A continuous variation of mode patterns for all kind of wave types in the desired frequency range will be rapidly obtained, and the physical meanings of wave propagation can also be shown more clearly and straightforward [8].…”