Elastic bending wave on the edge of a semi-infinite plate reinforced by a strip plate

Abstract

Elastic waves localised near the edge of a semi-infinite plate reinforced by a strip plate are considered within the framework of the 2D classical theory for plate bending. The boundary value problem for the strip plate is subject to asymptotic analysis, assuming that a typical wavelength is much greater than the strip thickness. As a result, effective conditions along the interface corresponding to a plate reinforced by a beam with a narrow rectangular cross-section are established. They support an approximate dispersion relation perturbing that for a homogeneous plate with a free edge. The accuracy of the approximate dispersion relation is tested by comparison with the numerical data obtained from the ‘exact’ matrix relation for a composite plate. The effect of the problem parameters on the localisation rate is studied.

Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation

“…), on returning to the original coordinates equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) may be recast as…”

“…Other recent developments include studies of bending edge waves on plates supported by elastic foundations, see [19] and [20], as well as plates with the reinforced edge, see [21], [22], and a recent work [23].…”

Flexural waves at the edge of nonlocal elastic plate associated with the Pasternak foundation

“…On the other hand, Norris et al (1998) has described the fascinating history of the discovery of edge waves. Alzaidi et al (Alzaidi et al, 2019a(Alzaidi et al, , 2019b studied the edge wave on thin isotropic plate structures reinforced with strip plate and beam. Fu (Fu, 2003) proved the existence of such a kind of wave in an anisotropic plate with a unique solution.…”

“…In 1960, Konenkov (1960) demonstrated that a thin elastic plate can produce a flexural wave, guided by the free edge of the plate, within the framework of classical plate theory. In spite of Konenkov’s contributions, the flexural edge wave was independently discovered after 14 years by Thurston and McKenna (Thurston and McKenna, 1974), and Sinha (Sinha, 1974). The displacement vector components of this surface acoustic wave are perpendicular to the plane of the wave propagation.…”

Wave Mode Control of Cantilever Slab Structure of T‐Beam Bridge with Large Aspect Ratio

“…At present, in the research of wave control, the research object is mostly simplified as a flexible beam, and some literature are simplified as plate structure to implement the bending wave control [5,6]. e wave control method can be used to control the propagation of waves in one-dimensional structures, such as bending waves in beams, and axial waves in rods.…”