Bending wave velocity tops out at the material’s transverse shear wave speed

Evidence

A major assumption behind Equation 1.11 is that the shear contribution to the lateral displacement is small. This is likely to be true if the radius of the bend is large with respect to the thickness of the plate, that is, at long wavelengths. However, when the radius of the bend is of a similar size to the thickness, this condition is no longer satisfied, and the wave propagated asymptotically approaches that of a transverse shear wave. This gives an upper limit on the phase velocity of a bending wave, which is equal to that of the transverse shear wave in the material. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 129

Categorization

• DEFINE: Clarifies the domain of validity for the bending wave equation and the physical ceiling on its phase velocity.
• corroborated: 4 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 129
• XREF: connects to: Bending wave speed grows as the square root of frequency; Applied forces in plates generate bending waves rather than pure shear waves — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 121