Extensional edge modes in elastic plates and shells

Abstract

The recently discovered undamped localized mode at the end of an elastic strip is demonstrated to be particularly relevant in the plane stress setting, where it exists for the Poisson ratio 0.29. This paper also emphasizes the difference between low-frequency edge modes, typically characterized by low variation across the plate (or shell) thickness, and high-frequency edge modes, whose natural frequencies are of the order of thickness resonance frequencies.

Edge waves and resonance on elastic structures: An overview

“…In particular, the edge resonance in a strip under plane stress in which all the edges are traction free cannot easily be related to the quasi-Rayleigh standing wave as in the above example. In this case, however, it is readily deduced 3 [29] that the real eigenfrequencies appear for ν = 0 and ν ≈ 0.29. The latter value seems to be more relevant to engineering materials than its counterpart ν ≈ 0.2248 in the theory of plane strain.…”

“…This clearly demonstrates the correspondence of the cut-on for each higher-order three-dimensional edge mode with an edge resonance. Finally, the antisymmetric modes for this set of mixed face conditions are obtained from (29) simply by replacing n with n + 1/2 and interchanging the sines and cosines. In this case, since the wavenumber is then given by ξ 3d = K 2 − (n + 1/2) 2 π 2 /h 2 , it is clear that there is no propagating mode for Kh < π/2.…”

Antisymmetric feature-guided ultrasonic waves in thin plates with small radius transverse bends from low-frequency symmetric axial excitation

“…The first is the topic of guided waves localized to the edge of the plates with a constant cross-section, of which the work of Onoe 10 and Torvik,11 in rectilinear plates are pioneering early examples; this area has been investigated by several workers until recently. [12][13][14] This strand of research perhaps fed into and branched off into the investigation of the effects on guided waves of topographic features such as triangular and rectangular ridges and cut-outs. Such topics received much attention in the 1970s from the electronic devices community.…”

“…[10][11][12][13][14] Extensional and pseudo-Rayleigh type of edge modes have been identified in rectilinear plates subject to plane stress conditions. However, the flexural (Shear Horizontal) type of edge waves arising in plane strain conditions and more sensitive to the thickness of the plate have been the most widely studied type of edge waves.…”

An Overview of Stress-Strain Analysis for Elasticity Equations

“…The basic and historical literature about the stress-strain relationship for propagation of elastic waves in kinds of medium is given by some eminent researchers [52][53][54][55][56][57]. Kaplunov, Pichugin and Rogersion [58][59][60] have discussed the propagation of extensional edge waves in in semi-infinite isotropic plates, shells and incompressible plates under the influence of initial stresses. The theory of boundary layers in highly anisotropic and/or reinforced elasticity is studied by Hool, Kinne and Spencer [61,62].…”