Effect of Uniaxial Initial Stresses, Piezoelectricity and Third Order Elastic Constants on the Near-Surface Waves in a Stratified Half-Plane (original) (raw)
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Ultrasonics, 2012
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Meccanica, 2012
The propagation of plane vertical transverse waves at an interface of a semi-infinite piezoelectric elastic medium under the influence of the initial stresses is discussed. The free surface of the piezoelectric elastic medium is considered to be adjacent to vacuum. We assumed that the piezoelectric material is anisotropic of the type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm). For an incident of vertical transverse plane wave, four types (two for the displacement and two for the electric potential) of reflected plane waves, called quasilongitudinal (qP) and quasi-shear vertical (qSV) waves are shown to be exist. The relations governing the reflection coefficients of these reflected waves for various boundary conditions (mixed-free-fixed) are derived. It has been shown analytically that reflected coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as well as the initial stresses presented in the medium. The numerical computations of reflection coefficients for different values of initial stresses have been carried out by computer for aluminum nitride (AlN) as an example and the results are given in the form of graphs. Finally, particular cases are considered in the absence of the initial stresses and the electric potential. Some of earlier studies have been compared to the special cases and shown good agreement with them.
International Journal of Engineering Science, 2009
The existence and propagation behavior of transverse surface waves in a layered structure concerning a piezoelectric substrate and a gradient metal layer are theoretically investigated in this paper. The Wentzel-Kramers-Brillouin (WKB) method is applied to obtain the analytical solutions in the gradient metal layer. The dispersion equation for transverse surface waves in such structure is obtained in a quite simple mathematical form, where the material gradient of the metal layer assumes arbitrary functions. Effects of material gradient on three types of dispersion behavior are discussed in detail based on a proper classification. Numerical results show that the material gradient in the metal layer evidently affects the fundamental mode shape of the transverse surface waves but has negligible effects on the higher order modes.
Arabian Journal of Geosciences, 2021
This paper implements the theoretical study of propagation of Rayleigh-type surface waves in an orthotropic crystal layer of finite thickness lying on an initially stressed elastic half-space due to a point source. The boundary conditions of the model are considered properly, and the displacement components are obtained in both layers using the substitution method and the matrix method for solution (non-trivial) of the system of homogeneous linear equation. The dispersion equation is found for the seismic wave propagation in a sixth-order determinant equation form. This equation is also derived for the initial stressed elastic half-space of the free boundary. Some particular cases are considered in a relevant manner. Dispersion curves for wave number versus phase velocity are traced for the model using Mathematica software. The curves conclude that the affecting parameters have a great effect on the surface wave propagation.
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International Journal of Mathematics and Mathematical Sciences, 1988
The present work is concerned with a simple transformation rule in finding out the composite elastic coefficients of a thinly layered laminated medium whose bulk properties are strongly anisotropic with a microelastic bending rigidity. These elastic coefficients which were not known completely for a layered laminated structure, are obtained suitably in terms of initial stress components and Lame's constants xi' ui of initially isotropic solids. The explicit solutions of the dynamical equations for a prestressed thinly layered laminated medium under horizontal compression in a gravity field are derived. The results are discussed specifying the effects of hydrostatic, deviatoric and couple stresses upon the characteristic propagation velocities of shear and compression wave modes.
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Journal of Intelligent Material Systems and Structures, 2017
Wentzel-Kramers-Brillouin approximation technique serves as a powerful tool to find the particle displacements due to surface wave propagation in bedded structure with distinct material properties. This study is carried out to investigate the transference of Love-type waves in functionally graded piezoelectric material layer bonded between viscous liquid and pre-stressed piezoelectric half-space. Following the elastic wave theory, the mathematical model is established. Wentzel-Kramers-Brillouin method is applied to obtain the theoretical derivations in functionally graded piezoelectric material stratum where variation in material gradients is taken exponentially. Separation of variables method is employed to obtain the displacement components in viscous liquid and piezoelectric medium. Dispersion equations for considered surface wave are obtained in both electrically open and short cases. Profound effect of material gradient coefficient on phase velocity has been remarkably established. Some numerical examples are carried out and represented through graphs. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices.
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Acta Mechanica, 2016
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Journal of Solid Mechanics and Materials Engineering, 2010
The propagation of transverse surface waves in a functionally graded material carrying a piezoelectric layer is investigated analytically. The material properties in the substrate change gradually with the depth coordinate. We here assume that all material properties of the substrate have the same exponential function distribution along the depth direction. The dispersion equations relating phase velocity to the material gradient in the substrate for the existence of the waves are obtained in a simple mathematic form for class 6mm piezoelectric materials. It is demonstrated that the material gradient in the elastic substrate significantly affects the phase velocity and cutoff frequency of long waves but has only negligible effects on short waves. The effects of the material gradient on the penetration depth and electromechanical coupling factor, which are two parameters of practical interest, are also calculated and plotted. The significant influence of the material gradient on the wave propagation behavior provides a potential factor for designing acoustic wave devices.
A long-wave model for the surface elastic wave in a coated half-space
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010
The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional 'quasi-static' elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.
Propagation of Elastic Waves at Solid/Solid Interface
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