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Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surf...
Citations
... Propagation characteristics of in-plane elastic wave dispersion relations in nanoscale piezoelectric semiconductor/phononic crystals with interface effect were studied by Guo and Wei [24]. Enzevaee and Shodja [25] investigated the propagation of the torsional wave in the piezoelectric layer within surface/interface theory. Understanding surface wave propagation in thin-film nanodevices is essential for the design and applications of Nano Electro Mechanical Systems (NEMSs). ...
... (34) and (35) in Eqs. (25) and (26), the system of ordinary differential equations are ...
This work has explored surface/interface theory-based torsional wave propagation in a piezoelec-tric fiber-reinforced composite (PFRC) layer on top of a functionally graded elastic substrate. PFRC is assumed to be composed of piezoelectric fiber and epoxy matrix. Micro-mechanical investigations have been performed to determine the coefficients of PFRC using strength of materials (SM) and rule of mixtures (RM) techniques. The dispersion relation for the torsional wave under non-classical boundary conditions is determined using surface/interface theory. The effects of surface/ interface, fiber volume fractions, and heterogeneities on the phase velocity and the mode shapes of the wave have been demonstrated graphically. ARTICLE HISTORY
... It was observed that the mechanical imperfect interface can increase the real part of the wavenumber and decrease the imaginary part of the wavenumber for the 1st and 2nd modes, while the electric or electric current imperfect interface has nearly no influence on the dispersion and attenuation curves. Under the mathematical framework of surface/interface elasticity theory, Enzevaee and Shodja formulated the propagation of the torsional surface waves in a medium consisting of a functionally graded substrate bonded to a thin piezoelectric over-layer [21]. It is observed that the surface/interface effects result in a reduction in the phase velocity and the phase velocity reduces by increasing surface/interface parameters for all modes at a specific wave number. ...
In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of biased electric fields. Then, considering the propagation of a shear horizontal wave in the piezoelectric semiconductor semi-infinite medium, two equivalent mathematical models are established. In the first mathematical model, the Schottky junction is theoretically treated as an electrically imperfect interface, and an interface characteristic length is utilized to describe the interface effect of the Schottky junction. To legitimately confirm the interface characteristic length, a second mathematical model is established, in which the Schottky junction is theoretically treated as an electrical gradient layer. Finally, the dispersion and attenuation curves of shear horizontal waves are numerically calculated using these two mathematical models to discuss the influence of the Schottky junction on the dispersion and attenuation characteristics of shear horizontal waves. Utilizing the equivalence of these two mathematical models and the above numerical results, the numerical value of the interface characteristic length is reliably legitimately confirmed; this value is independent of the thickness of the upper metal layer, the doping concentration of the lower n-type piezoelectric semiconductor substrate, and biasing electric fields. Only the biasing electric field parallel to the Schottky junction can provide an evident influence on the attenuation characteristics of shear horizontal waves and enhance the interface effect of the Schottky junction. Since the second mathematical model is also a validation of our previous mathematical model established through the state transfer equation method, some numerical results calculated using these two mathematical models are compared with those obtained using the previous method to verify the correctness and superiority of the research work presented in this paper. Since these two mathematical models can better calculate the dispersion and attenuation curves of high-frequency waves in micro- and nano-scale piezoelectric semiconductor materials, the establishment of mathematical models and the revelation of physical mechanisms are fundamental to the analysis and optimization of micro-scale resonators, energy harvesters, and amplifications.
... Based on Equation (11), the circumferential mechanical displacement component u θ is decoupled with the radial and axial mechanical displacement components u r and u z , the electric potential φ, and charge carrier concentration perturbation c. Therefore, there are two independent radially propagated cylindrical SAW in this PSC semi-infinite medium, i.e., the radially polarized cylindrical SAW related to u r , u z , φ, and c and the circumferential polarized cylindrical SAW, i.e., torsional SAW [32][33][34][35][36][37][38][39], only related to u θ . As the circumferential polarized cylindrical SAW is decoupled with the piezoelectric and semiconductor effects, only the radially polarized cylindrical SAW is discussed in this paper. ...
This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are mathematically derived. Then, based on these basic equations and the transfer matrix method, two equivalent mathematical models are established concerning the propagation of radially propagated cylindrical surface acoustic waves in this piezoelectric semiconductor semi-infinite medium. Based on the surface and interface effect theory, the homo- or hetero-junction is theoretically treated as a two-dimensional electrically imperfect interface in the first mathematical model. To legitimately confirm the interface characteristic lengths that appear in the electrically imperfect interface conditions, the homo- or hetero-junction is equivalently treated as a functional gradient thin layer in the second mathematical model. Finally, based on these two mathematical models, the dispersion and attenuation curves of radially propagated cylindrical surface acoustic waves are numerically calculated to discuss the influence of the homo- and hetero-junctions on the dispersion and attenuation characteristics of radially propagated cylindrical surface acoustic waves. The interface characteristic lengths are legitimately confirmed through the comparison of dispersion and attenuation curves calculated using the two equivalent mathematical models. As piezoelectric semiconductor energy harvesters usually work under elastic deformation, the establishment of mathematical models and the revelation of physical mechanisms are both fundamental to the analysis and optimization of micro-scale surface acoustic wave resonators, energy harvesters, and acoustic wave amplification based on the propagation of surface acoustic waves.
... Модели поверхностной упругости были распространены на тела со связанностью механических и электрических полей. Соответствующие динамические задачи об установившихся колебаниях пьезоэлектрических полуограниченных сред с дополнительной поверхностной связанностью электромеханических полей рассматривались в [24][25][26][27][28][29][30][31], а аналогичные задачи для магнитоэлектрических сред -в [32 -34]. Как отмечалось в [35; 36], такие модели могут быть как электромеханически связанными, так и несвязанными. ...
In this paper, symmetric and antisymmetric plane problems about the action of oscillating load on the boundary of an elastic isotropic nanothin layer are considered. The nanoscale layer thickness is considered by introducing surface stresses in accordance with the Gurtin-Murdoch theory. According to this theory, it is assumed that, in addition to external loads, surface stresses act on the layer boundaries, which are described by Hooke's “surface” law. As a result, the properties of the elastic material of the layer with nanoscale thickness become different from the properties of the material of a regular-sized body, which is typical for nanomechanics problems. A standard technique was used for the solution of formulated problems, including the application of limiting absorption principle, the Fourier transform over infinitely extended coordinate and the theory of residues for finding the inverse Fourier transform. It is shown how it is possible to obtain solutions in the form of series in natural waves, in which the wave numbers are defined as the roots of the corresponding dispersion equations. For a specific example, dispersion relations were studied and graphs of the first dispersion curves were plotted. The behavior of barrier frequencies, changes in wave numbers and zones of existence of backward waves at different nanoscale layer thicknesses are analyzed. The results of the analysis showed that for an ultrathin layer, surface effects have a significant impact on the dispersion relations, and the trends in the dispersion curves can differ significantly for different modes and layer thicknesses.
... The present result and the work of Enzevaee and Shodja(Enzevaee and Shodja, 2020). ...
... Forced torsional vibration of nanobeam via nonlocal strain gradient theory and surface energy effects under moving harmonic torque have been investigated by Hamidi et al. [9]. Enzevaee and Shodja [10] examined the torsional surface waves in a transversely isotropic FG substrate by means of interface theory. Recently, Akbarov and Bagirov Emin [11] examined the dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder with the initial inhomogeneous thermal stresses. ...
The present paper investigates the torsional wave propagation in a threefold concentric pre-stressed compounded cylinder with imperfect contact conditions. The three-dimensional linearized theory of elastic waves and the piecewise homogeneous body model has been employed to formulate the problem. The mathematical modeling has been carried out in two independent cases. In the first case, a solid cylinder encased in a hollow cylinder embedded in an infinite elastic medium has been considered. Whereas the second case comprises a hollow cylinder of finite thickness in place of a solid cylinder. By means of Murnaghan potential, the mechanical characteristics of the three materials have been used. Further, the dispersion relations for both the cases have been obtained in terms of the Bessel and modified Bessel functions. In order to validate the present findings, two particular cases have been derived that matches with the previous works. The first case is obtained by removing the outermost cylinder, while the second case has been derived by removing the imperfection in addition to that. To summarize the computations, a complete numerical simulation has been carried out, and graphical illustrations have been shown to aid the mathematical analyses.
... This was achieved by interrelating the corresponding energies obtained within the Gurtin and Murdoch surface elasticity and ab initio density functional theory (DFT) calculations. To date, although surface elasticity theory has been extensively applied to various problems of wave propagation through elastic solids [10,14,15], only a few analytical studies have been done on surface wave propagation in piezoelectric media within this theory [1,16,17]. In SAW devices, propagation of waves with high frequencies is of particular interest. ...
... Equations (14), (15), (17), and (19) together with conditions (20) and (21) lead to a system of algebraic equations for the unknown coefficients. For a non-trivial solution, the determinant of the coefficient matrix is set equal to zero, leading to the dispersion relation for the considered SH surface wave propagation with surface/interface effects. ...
Shear horizontal surface acoustic waves (SAW) propagation in an ultra-thin functionally graded piezoelectric (FGP) layer bonded to a homogeneous substrate is analytically formulated in the mathematical framework of surface/interface elasticity theory. It is assumed that the FGP over-layer is made of a hexagonal 6-mm crystal with a single axis of rotational symmetry coinciding with the axis of polarization. The mechanical and piezoelectric properties of the layer are assumed to vary linearly with thickness. The half-space is made of a transversely isotropic material. It should be mentioned that this model is of great interest in investigating SAW devices at high frequencies. Accounting for the surface/interface effects, the pertinent electromechanical dispersion relation for both cases of the electrically open and short surfaces is derived analytically using Wentzel–Kramers–Brillouin singular perturbation theory. The effects of the surface/interface parameters and the gradient parameter which indicate the variation of the piezoelectric properties of the FGP layer on the dispersion relation, the electromechanical coupling factor, displacement field, electric potential function, electric displacement field, and stress field are studied numerically, and the results are compared with those obtained from classical theory.
... The propagation theory of horizontal shear waves in cladding structures has always been one of the research hotspots of solid mechanics. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] The displacement solution of a single cladding structure excited by horizontal shear waves was derived by the integral transformation method, and it was found that the displacement magnitude depends on the excitation magnitude. [26][27][28][29][30][31][32] The freely propagating solution of horizontal shear waves in 1 the multilayer cladding structure was studied by the global matrix method and the transfer matrix method. ...
The forced propagation solution of interfacial shear stress of multilayer cladding structure excited by Love waves is derived by the integral transformation method, and the shear resonance mechanism of interfacial separation is further revealed. The coupling resonance between the excitation frequency and structure intrinsic property causes the peak of interfacial shear stress amplitude, which results in interfacial shear separation at certain frequency bands. It is found that the coupling resonance frequency of interfacial shear stress is only dependent on the inherent properties of the structure, around which the frequency band of interfacial shear separation is formed. The coupling resonance frequency decreases with the increase of the cladding thickness or shear wave velocity difference between the cladding and substrate. The influence of cladding material parameters on interfacial shear stress is greater than that of matrix material parameters. The experimental results support the theoretical analysis results. The conclusions presented could have potential applications in ultrasonic deicing/defrosting/de-sanding and/or coatings protection.
