Localized bending vibrations of piezoelectric plates

Piliposian, G.T.; Ghazaryan, K.B.

doi:10.1080/17455030.2011.576712

Cited by 9 publications

(8 citation statements)

References 14 publications

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“…Most of the above results were derived using Kirchhoff plate theory. It was demonstrated that the edge waves in elastic thin plate were also theoretically predicted by Mindlin plate theory including shear deformation and rotatory inertia (Norris et al, 1998) and Ambartsumian refined plate theory considering high-order shear deformation (Piliposian and Ghazaryan, 2011). The former was proved to be in agreement with experimental and finite element results (Lagasse and Oliner, 1976;Norris et al, 1998).…”

Section: Introductionmentioning

confidence: 67%

“…Compared with elastic waves propagation in the infinite piezoelectric materials, which have been widely studied and also have been used in many engineering fields, the results related to edge waves in the thin piezoelectric plates are still limited, and some interesting properties are waiting to be further revealed. Recently, Piliposian and Ghazaryan (2011) studied the existence and propagation of bending waves localized at the free edge of a piezoelectric plate within the framework of Ambartsumian refined plate theory. The condition for existence of a localized bending wave was given.…”

Section: Introductionmentioning

confidence: 99%

“…The propagation of bending wave with multi-mode was shown. Piezoelectric plates considered in (Piliposian and Ghazaryan, 2011) and (Nie et al, 2021) are both assumed as the transversely isotropic media. In this paper, we study the propagation of bending waves localized along the free edge of a semi-infinite piezoelectric plate of orthogonal symmetry using two-variable refined plate theory (TVPT, a high-order shear deformation theory), Reissner-Mindlin refined plate theory (RMPT, a first-order shear deformation theory), and the classical plate theory (CPT).…”

Section: Introductionmentioning

confidence: 99%

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Bending waves localized along the edge of a semi-infinite piezoelectric plate with orthogonal symmetry

Nie

Lei²,

Liu³

et al. 2022

Front. Mater.

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We study the propagation of bending waves along the free edge of a semi-infinite piezoelectric plate within the framework of two-variable refined plate theory (TVPT, a high-order plate theory), Reissner-Mindlin refined plate theory (RMPT, a first-order plate theory), and the classical plate theory (CPT). The piezoelectric plate has macroscopic symmetry of orthogonal mm2 The governing equations are derived using Hamilton principle. The dispersion relations for electrically open and shorted boundary conditions at the free edge are obtained analytically. The difference in dispersion property between the three plate theories is analyzed. The numerical results show that the dispersion curves predicted by TVPT and RMPT are similar and have small difference over the complete frequency range, which means both the two theories are valid for the analysis of edge waves in a piezoelectric plate. But the wave velocity calculated by CPT is much larger than the two theories above and is no longer valid for high frequency and thick plate. The electrical boundary condition at the free edge has an insignificant effect on phase velocity and group velocity which can be ignored for the analysis of edge waves in a piezoelectric plate governed by bending deformation. The velocity of bending edge waves in a semi-infinite piezoelectric plate is positively related to that of Rayleigh surface wave in a traction-free piezoelectric half-space. The edge wave velocity can be enhanced when the piezoelectric plate is considered as one with weaker anisotropy.

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Section: Introductionmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bending waves localized along the edge of a semi-infinite piezoelectric plate with orthogonal symmetry

Nie

Lei²,

Liu³

et al. 2022

Front. Mater.

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“…In recent years, piezoelectric materials have gathered an increased amount of attention because of their application in structural health monitoring, electromechanical transducers, sensors, etc. The present study involves the extension of the previous work that has been done by Kaplunov and Nobili (Kaplunov and Nobili, 2017). This paper analyzes travelling flexural waves that propagate along the free edge of a thin piezoelectric plate, which is semi-infinite and supported by two parametric Pasternak elastic foundations.…”

Section: Introductionmentioning

confidence: 86%

“…In this figure, the frequency curve is plotted for a particular dimensionless nonlocal parameter a 1 = 0.4. Kaplunov and Nobili (Kaplunov and Nobili, 2017) analyzed the influence of infinite and semi-infinite Pasternak foundations on the phase velocity of edge waves on the semi-infinite isotropic plate. In the case of the piezoelectric plate, for a particular wave number, the frequency increases as the dimensionless foundation parameter β 1 varies from 1.1 × 10 −6 to 1.9 × 10 −6 within the very short range of wave number, which is the opposite characteristic of the dispersion curve that has been obtained in case of different values of the nonlocal parameter.…”

Section: Numerical Calculations and Graphical Descriptionsmentioning

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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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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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 vibrations of piezoelectric plates

Cited by 9 publications

References 14 publications

Bending waves localized along the edge of a semi-infinite piezoelectric plate with orthogonal symmetry

Bending waves localized along the edge of a semi-infinite piezoelectric plate with orthogonal symmetry

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

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