Surface Wave Solutions Research Articles

Rayleigh wave in a micropolar thermoelastic medium without energy dissipation

Article history: Received 6 April, 2015 Accepted 19 October 2015 Available online 19 October 2015 The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium. A frequency equation is obtained for Rayleigh wave in the medium. The non-dimensional speed of the propagation of Rayleigh wave is computed for a specific model of the material and are shown graphically against frequency and non-dimensional parameter. © 2016 Growing Science Ltd. All rights reserved.

Multiple surface wave solutions on linear viscoelastic media

We study the generic dispersion relation of surface waves on a semi-infinite viscoelastic medium bounded by a 2D viscoelastic interface, including the effects of gravitation, surface tension and bending rigidity. The classical Rayleigh, capillary-gravity and Lucassen wave solutions result as limiting cases. We identify an additional solution that differs from all previously described waves in that gravitation, surface tension and bulk shear viscosity must simultaneously be nonzero, and which exists on a pure air-water interface. For a surfactant monolayer on water, the number of coexisting wave solutions switches between one and three, depending on interfacial compressibility and frequency.

Rayleigh wave in a thermoelastic solid half-space with impedance boundary conditions

In the present paper, the Rayleigh wave in a generalized thermoelastic solid half-space is considered with impedance boundary conditions. The governing equations of homogeneous and isotropic generalized thermoelastcity are solved for general surface wave solutions. The general solutions in the half-space satisfy the required radiation conditions. These solutions also satisfy the required impedance boundary conditions at the free surface of the half-space to obtain the secular equation for wave speed of Rayleigh wave for the cases of thermally insulated surface and isothermal surface. The non-dimensional wave speed is computed for a relevant material data to observe the effects of impedance parameters and frequency.

Wave propagation in an incompressible transversely isotropic thermoelastic solid

In the present paper, the equations of motion and heat conduction equation of an incompressible transversely isotropic thermoelastic solid are formulated in view of Lord and Shulman theory on generalized thermoelastcity. The equations of motion and heat conduction equation reduce to two coupled equations in temperature and a scalar function depending on displacement. Plane harmonic solution of these coupled equations shows the existence of two homogeneous plane waves. These coupled equations are also solved for surface wave solutions which satisfy the required radiation conditions in the half-space. The surface wave solutions satisfy the appropriate boundary conditions at traction-free thermally insulated or isothermal surface of half-space and a secular equation of Rayleigh wave speed is obtained for thermally insulated case and isothermal case. For thermally insulated case, the numerical values of non-dimensional speed of Rayleigh wave are computed by using Iteration method. The wave speeds of plane waves and Rayleigh wave are illustrated graphically to observe the effects of transverse isotropy, material constants, frequency, angle of propagation and thermal relaxation in time.

Comment on “Effect of surface wave inversion non-uniqueness on 1D seismic ground response analysis” by Roy et al.

We discuss a paper dealing with the effect of surface wave solution non-uniqueness on 1D seismic site response analysis. We address some issues on the numerical simulations of seismic site response, specifically the correct definition of input motion. If a consistent framework is adopted, the solution non-uniqueness has negligible effect in amplification and acceleration response spectra for the presented dataset, confirming previous studies on the same topic.

Kinetic Theory of Electrostatic Surface Waves in a Magnetized Plasma Slab

The dispersion relation of electrostatic surface waves propagating in a magnetized plasma slab is derived from Vlasov-Poisson equations under the specular reflection boundary condition. We consider the case that the static magnetic field is parallel to the plasma-vacuum interface and the surface wave propagates obliquely to the magnetic field on the parallel plane. We find that the specular reflection boundary conditions on the plasma slab-vacuum boundaries can be satisfied, even in a magnetized plasma, by simple extension of the electric potential into the vacuum region, due to the inherent symmetry of the distribution function. Utilizing an invariance property of the kinetic surface wave solution, it is shown that the two-mode structure of the surface wave yields the symmetric and anti-symmetric modes. The kinetic dispersion relation is checked against the dispersion relations obtained from fluid equations and shows complete agreement.

Verification of surface wave solutions obtained by the reciprocity theorem

Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper.

Propagation of Rayleigh Wave in a Thermoelastic Solid Half-Space with Microtemperatures

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous thermoelastic solid half-space with microtemperatures. The governing equations of the thermoelastic medium with microtemperatures are solved for surface wave solutions. The particular solutions in the half-space are applied to the required boundary conditions at stress-free thermally insulated surface to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The non-dimensional speed of Rayleigh wave is computed numerically and presented graphically to reveal the dependence on the frequency and microtemperature constants.

Terahertz surface plasmon waveguide based on a one-dimensional array of silicon pillars

We experimentally demonstrate a three-dimensional plasmonic terahertz waveguide by lithographically patterning an array of sub-wavelength pillars on a silicon substrate. Doped silicon can exhibit conductive properties at terahertz frequencies, making it a convenient substitute for conventional metals in plasmonic devices. However, the surface wave solution at a doped silicon surface is usually poorly confined and lossy. Here we demonstrate that by patterning the silicon surface with an array of sub-wavelength pillars, the resulting structure can support a terahertz surface mode that is tightly confined in both transverse directions. Further, we observe that the resonant behavior associated with the surface modes depends on the dimensions of the pillars, and can be tailored through control of the structural parameters. We experimentally fabricated devices with different geometries, and characterized the performance using terahertz time-domain spectroscopy. The resulting waveguide characteristics are confirmed using finite element numerical simulations, and we further show that a simple one-dimensional analytical theory adequately predicts the observed dispersion relation.

Propagation of Rayleigh Wave in a Two-Temperature Generalized Thermoelastic Solid Half-Space

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous two-temperature thermoelastic solid half-space in the context of Lord and Shulman theory of generalized thermoelasticity. The governing equations of a two-temperature generalized thermoelastic medium are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The speed of Rayleigh wave is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.

Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

Rayleigh Wave in a Rotating Initially Stressed Piezoelectric Half-Space

The governing equations of an initially stressed rotating piezoelectric medium are solved for surface wave solutions. The appropriate solutions in the half-space of the medium satisfy the required boundary conditions to obtain the frequency equation of Rayleigh wave for charge free as well as electrically shorted cases. The non-dimensional speed of the Rayleigh wave is computed numerically for particular examples of Lithium niobate and PZT-5H ceramics. The effects of rotation and initial stress are observed graphically on the non-dimensional speed of the Rayleigh wave.

On Rayleigh Wave in Two-Temperature Generalized Thermoelastic Medium without Energy Dissipation

In this paper, Rayleigh surface wave is studied at a stress free thermally insulated surface of a two-temperature thermoelastic solid half-space in absence of energy dissipation. The governing equations of two-temperature generalized thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The non-dimensional speed is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.

On Rayleigh wave in generalized magneto-thermoelastic media with hydrostatic initial stress

Abstract. The governing equations of generalized magneto-thermoelasticity with hydrostatic initial stress are solved for surface wave solutions. The particular solutions in the half-space are applied to the boundary conditions at the free surface of the half-space to obtain the frequency equation of Rayleigh wave. The frequency equation is approximated for small thermal coupling and small reduced frequency. The velocity of propagation and amplitude-attenuation factor of Rayleigh wave are computed numerically for a particular material. Effects of magnetic field and hydrostatic initial stress on the velocity of the propagation and amplitude-attenuation factor are shown graphically.

Grains of SAWs: Associating quasi-particles to surface acoustic waves

This work aims at showing how to associate quasi-particles in inertial or non-inertial motion with surface-wave solutions, especially for Rayleigh and Bleustein–Gulyaev surface waves on elastic or piezoelectric substrates (by way of examples). Perturbations of various kinds (surface energy, connection to an external fluid or an external electric field, viscosity of the substrate) are also envisaged. The technique employed for this is based on the exploitation of the conservation equations for energy and wave-momentum deduced via Noether’s theorem or by direct computation, and associated with the basic field equations of which we already know the analytic continuum solutions. Volume integration of the conservation laws is then performed over a volume representative of the surface wave motion.

Waves in Warm Constant-Density Cylindrical Electron Beams

A dispersion equation is derived for waves in a warm constant-density cylindrical electron beam where electrons exhibit 3-D orbits in a uniform magnetic field and where the rigid-rotor beam model has transverse temperatures confined to the beam interior to provide a cold sharp beam edge suitable for matching RF fields. The equation solutions for surface waves in a warm beam emitted from a magnetically shielded gun can be obtained immediately from solutions for surface waves in a cold beam. Validation of such warm-beam solutions was made using TWT hot-test data and particle-in-cell-code simulations. Standard transcendental-equation solutions are found for surface waves in warm small-vorticity beams and space-charge waves in warm large-vorticity beams. Reduced plasma frequencies are increased for surface waves and decreased for space-charge waves by increasing the transverse-temperature thermal parameter. Beam temperatures were included in a Pierce-theory determinantal equation in the small-transverse-wavenumber limit.

Comment on ‘Shear wave profiles from surface wave inversion: the impact of uncertainty on seismic site response analysis’

We discuss a study on the effect of surface wave solution non-uniqueness on seismic site response. The inversion approach used in the considered paper may lead to a significant overestimation of the uncertainties due to solution non-uniqueness. We also address the numerical simulation of seismic site response. We apply a consistent framework to a synthetic dataset to show that, contrary to what is claimed in the considered study, the solution non-uniqueness has negligible effect in this specific case.

Reply to comment on ‘Shear wave profile from surface wave inversion: the impact of uncertainty on seismic site response analysis’

Socco et al (2012 J. Geophys. Eng. 9 241) comment on our study about the effect of non-uniqueness of surface wave solutions on seismic site response analysis. In particular, they refer to the approach we adopted for the selection of equivalent shear wave velocity profiles and argue that it leads to overestimation of the uncertainty due to the inherent ill-posedness of the problem. Moreover, for one of the synthetic cases of our original paper, they calculate a different set of equivalent velocity profiles, retrieving the corresponding amplification spectra. From these results, Socco et al claim that their general conclusion that the impact of solution non-uniqueness on seismic response simulations is negligible. In this reply we demonstrate that (a) the uncertainty bounds used by Socco et al in their prediction analysis, as a consequence of their surface wave inversion procedure, are unreasonably narrow; (b) consequently, their shaking predictions appear to suffer no impact from their underestimated uncertainty; and (c) their presented case shows an amplification spectrum that is only the result of assuming the existence of a bedrock at 150 m that causes resonance of the overlying layer—practically independent of the details of the S-wave velocity distribution.

Rayleigh Wave in a Rotating Magneto-Thermo-Elastic Half-Plane

The governing equations of generalized magneto- thermoelas- ticity with hydrostatic initial stress and rotation are solved for surface wave solutions. The particular solutions are applied to the boundary con- ditions at a free surface of a half-space to obtain the frequency equation of Rayleigh wave. For numerical purpose, the frequency equation is ap- proximated for small thermal coupling. The velocity of propagation and amplitude-attenuation factor of Rayleigh wave are computed numerically for a particular material. Effects of rotation, magnetic field, hydrosta- tic initial stress and relaxation time on the velocity of propagation and amplitude-attenuation factor are shown graphically.

Propagation behavior of SH waves in layered piezoelectric plates

In this study, the propagation of SH waves in a coupled plate consisting of a piezoelectric layer and an elastic layer is analytically investigated. The piezoelectric material is polarized in the z-axis direction and perfectly bonded to an elastic layer. The mathematical model of the SH wave propagation in this plate is based on the type of surface wave solution. Dispersion relations with respect to phase velocity are obtained for electrically open and mechanically free. Numerical examples are provided to illustrate graphically and compare the variations of the phase and group velocities versus the wave number for the different layers. The thickness ratio and the properties of the two layers have a significant effect on the propagation of SH waves. The conclusions are meaningful both theoretically and practically for the design of high-performance surface acoustic wave (SAW) devices.