Shape of dispersion curves in the Rayleigh-Lamb spectrum (Archives of Mechanics - Test, 2004)
The following features of the symmetric Lamb modes in an elastic waveguide are well known: 1. There exists no mode with phase speed less than cR. 2. There is only one mode whose speed asymptotically approaches cR. 3. A horizontal line above c = cT (including the line c = cL) cannot be an asymptote to any of the modes. 4. Phase speed of all modes, except the lowest mode, approaches cT as the frequency becomes very large. The above features characterize the spectrum which is obtained numerically or experimentally but are not fully understood analytically. We analyze the Rayleigh-Lamb equation and provide analytical explanation for the above features.