On the meaning of Lamb mode nonpropagating branches

The modes of vibration of an elastic plate are usually divided into propagating and nonpropagating kinds. While nonpropagating modes characterize local vibration nearby a perturbation source, which can be either an external force or a geometrical discontinuity, propagating modes carry energy along the waveguide and account for the vibration far away from the perturbation source. In this paper, by considering that the modes of an absorbing plate are always propagating, it is shown that each elastic mode consists of propagating and nonpropagating branches, which turn into a single propagating mode as soon as internal absorption is considered. Moreover, it is shown how introducing a little material damping leads to a rigorous differentiation of elastic modes when they are connected. A similar result can be obtained by loading the plate with a light fluid [Rokhlin et al., J. Acoust. Soc. Am. 85, 1074-1080 (1989)].