### Lamb quasi-modes of a weakly curved waveguide

Wave propagation in slowly varying elastic waveguides is analysed here in terms of mutually-uncoupled quasi-modes. These are a generalization of the Lamb modes that exist in a uniform guide to the weakly non-uniform case. Quasi-modal propagation is dependent upon the wavelength and two geometrical length-scales, that of the longitudinal variations and the guide thickness. By changing these lengthscales one enters different asymptotic regimes. In this paper, the emphasis is on the mid-frequency regime when only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi-modal propagation in a canonical geometry, an arbitrarily curved plate of constant thickness. We derive practically useful asymptotic expressions of the quasi-modes of a weakly curved plate; these are particularly important since an adiabatic approximation
for this problem simply coincides with the Lamb modes of a flat plate of the same thickness.

Co-authored with Dmitri Gridin.

#### Proc. Roy. Soc. Lond A, 460, 1831-1847 2004