Abstract

Small amounts of irregularity are known to produce vibration localization in one-dimensional chains, but the effects on two and three dimensional systems are typically much weaker. We have considered a system with both one and two dimensional aspects, an axisymmetric, irregularly ribbed fluid-loaded cylindrical shell. A new formulation of this problem is given and each mode of the system is shown to be approximately equivilent to a nearest neighbor coupled chain with six degrees of freedom — corresponding to three left going and three right going traveling waves. Using these results all the azimuthal modes have been shown to be localized simultaneously and thus vibrational energy on an irregular cylindrical shell is Anderson localized. The slow flexural waves have been shown to localize separately from the fast waves provided the helical angle of the flexural wave is greater than about Ω1/25°, and for smaller helical angles, exponential localization is expected for distances less than a critical wave mixing length. Our results indicate that strong localization effects occur for the helical flexural waves yielding very short localization lengths of order a single rib spacing.

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