Flexural edge waves and Comments on “A new bending wave solution for the classical plate equation” [J. Acoust. Soc. Am. 104, 2220–2222 (1998)]

Abstract

A brief review is presented of the theory of flexural edge waves, first predicted in 1960 by Yu K. Konenkov using Kirchhoff plate theory. It is demonstrated that the flexural edge wave is also predicted by Mindlin's plate theory, and that the prediction agrees with measured data. It is noted that the edge wave was erroneously presented as a new type of bending wave solution in a recently published paper in this journal.

Flexural waves on a pinned semi-infinite thin elastic plate

“…This is the so-called Konenkov edge wave solution (after [1]) and is well documented elsewhere in the literature -see for example [4]. In order to construct such a solution consider we replace t s , associated with the scattering angle w with a value of t e > 1 in the general solution (5) and discard the incident wave.…”

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

“…It is peculiar that this wave was rediscovered several times, for more detail see Norris et al (2000) and Lawrie & Kaplunov (2012).…”

Trapped waves in thin elastic plates

“…Such trapped waves (in this context often referred to as edge waves) are important in scattering by cracks in plates, see [10], for example. They have also been shown to exist for more complex plate theories (see [11], [12], [13]) and for plates with fluid loading [14], [15]. By choosing l = π/2d or l = π/d in (3), the trapped wave is equivalent to the vibrations on a thin elastic plate confined within a semi-infinite waveguide of width 2d, and upon whose parallel sides y = 0, y = 2d the plate is freely supported (i.e.…”