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

Althobaiti, Saad; Nikonov, Anatolij; Приказчиков, Д. А.

doi:10.2140/jomms.2021.16.543

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…Duan and Kirby (Duan and Kirby, 2021) studied a threedimensional numerical model for the bending wave at the free edge of a plate. The existence of such kind of wave in an orthotropic plate has been presented by Althobaiti et al (2021) andThompson et al (2002). The influence of the Winkler foundation on flexural-type edge wave propagation is demonstrated by Kaplunov et al (2016).…”

Section: Introductionmentioning

confidence: 85%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Manna

Som

2022

Journal of Vibration and Control

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In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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

Manna

Som

2022

Journal of Vibration and Control

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“…The qualitative behavior of the bending wave on an elastic plate reinforced by a strip beam and plate is investigated by Alzaidi et al [25,26]. Althobati et al [27] demonstrate that the bending edge wave exhibits the parabolic-elliptic nature on an orthotropic plate supported with the Winkler foundation. Some other contributions towards the mathematical development of bending edge wave can be found in the recent works [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

“…Althobati et al. [27] demonstrate that the bending edge wave exhibits the parabolic‐elliptic nature on an orthotropic plate supported with the Winkler foundation. Some other contributions towards the mathematical development of bending edge wave can be found in the recent works [28–32].…”

Section: Introductionmentioning

confidence: 99%

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Som,

Manna

2024

Z Angew Math Mech

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This study investigates the localized wave propagation at the free edge of a thin semi‐infinite Magneto‐Electro‐Elastic (MEE) plate. The plate is supported by a two‐parameters elastic foundation. Biot's porosity theory is considered to formulate the porosity in the model, and the pore structure is saturated with an incompressible fluid. The Kirchhoff–Love plate theory determines the plate displacement field. A non‐homogeneity in the material parameters is considered, which varies with the spatial coordinate along the thickness direction of the plate. In order to illustrate the impacts of the surface elements on bending wave propagation, the model incorporates the surface elasticity theory. The short circuit boundary conditions are implemented to derive the general form of the potential function connected with the electric and magnetic fields, respectively. The dispersion relation for bending edge wave on a MEE fluid‐saturated porous plate is obtained by considering a sinusoidal waveform, which propagates along the free edge of the plate. A numerical method named Finite Difference (FD) scheme is employed to analyze the stability of the numerical scheme and also extract the expression of the velocity profiles of the bending edge wave in the absence of the pore structure. The impacts of the various parameters included in the considered model are examined using a numerical example, from which conclusions regarding their sensitivity are derived.

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Localized bending waves along the edge of a piezoelectric sandwich plate

et al. 2023

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

Cited by 5 publications

References 31 publications

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

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

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Localized bending waves along the edge of a piezoelectric sandwich plate

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