Relationship between plate and surface modes of a tube

A circular tube will support axially sysmetric surface acoustic waves at both surfaces, and also a pair of axially symmetric platelike modes. The two pairs of modes are analogous to similar mode pairs on a flat plate. The relationships between surface and plate modes are well known for the flat-plate geometry. It is shown here that for the tube geometry, the mode relationships are of a different kind. Whereas the high-frequency surface modes on a flat plate are superpositions of the two lowest Lamb modes, the high-frequency surface modes on a tube are in general not superpositions at all. On a tube, each surface mode is the high-frequency representative of a single platelike tube mode.

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