Propagation Characteristics Of Rayleigh Waves Research Articles

Derivation and Application of Analytical Coupling Loss Coefficient by Transfer Function in Soil–Building Vibration

Vibrations generated by railways may undergo amplification or reduction while traversing the foundations, floors, and spans of adjacent structures. This fluctuation in the vibration intensity, identified as a building’s coupling loss, is commonly considered in vibration forecasts through the utilization of universal frequency-independent adjustment parameters. This article employs a theoretical analytical approach to investigate the propagation characteristics of Rayleigh waves in elastic foundation soil, as well as the variations at the contact surface of buildings’ foundations. Analytical expressions for the coupling loss coefficient are derived to explore the displacement transfer relationship in the soil–structure interaction. To accurately and efficiently analyze the proposed buildings and site, the entire vibration propagation system is decoupled into substructure systems for independent analytical calculations. Theoretical analytical methods are utilized to obtain the displacement transfer functions between the soil and the structures through the refraction and transmission of waves. From a theoretical perspective, a thorough understanding of the interaction between soil and buildings is achieved. The influence of various variables related to railways and foundations on the building responses is analyzed. By comparing with measured data, the correctness of the analytical form of the coupling loss coefficient is validated, filling a gap in the literature due to the lack of analytical research on displacement transfer losses in soil–structure interactions.

Effects of corrugated boundaries on Rayleigh waves in a piezoelectric semiconductor substrate covered with a metal layer

In the present work, analytical solutions for Rayleigh waves propagating in a metal covered layer over a piezoelectric semiconductor (PSC) substrate with corrugated surface and corrugated interface are obtained. The solutions of the various physical fields can be expressed as a summation of infinite harmonic waves by using the Bloch–Floquet theorem due to the existence of the periodic corrugated surface and corrugated interface. The effects of the height and contour shape of the corrugated surface and corrugated interface, the doping density of the PSC substrate and the thickness of the metal covered layer on the dispersion and attenuation curves and mode shapes of Rayleigh waves are discussed via numerical example. The results show that the existence of the corrugated surface will lead to the decrease of the phase velocity and non-monotonous change with wavenumber, besides, and significantly increases the attenuation near k0=π/Λ(k0 and Λ are the wavenumber and period, respectively). In addition, the effects of periodic corrugated surface are much greater than those of periodic corrugated interface and are closely related with the ratio of the wavelength to the structure period. Moreover, the sinusoidal corrugated surface can be used to better control the propagation characteristics of Rayleigh waves by comparison.

3D analysis of Rayleigh-type surface wave in fractured media: Insights into anisotropic characteristics

The propagation characteristics of Rayleigh waves on the surfaces of fracture-containing media have considerable theoretical and practical significance. Limitations are associated with using two-dimensional (2D) observations of Rayleigh waves to predict fracture features, because real fractures have a complex distribution inside media. Therefore, the three-dimensional (3D) propagation of Rayleigh waves in media with directional fractures is simulated in this study by combining the staggered-grid finite difference method with parallel computing. The wave velocity and amplitude of Rayleigh waves depend on the relative direction between fracture and wave path on the medium surface. That is, Rayleigh waves exhibit clearly anisotropic characteristics for a medium with directionally distributed fractures, where the degree of anisotropy is closely related to fracture parameters, such as the fracture density and fracture scale. Two new anisotropy parameters for Rayleigh waves are defined in this study: the anisotropy of the wave velocity and the anisotropy of attenuation (transmission coefficient). For a single fracture, the minor axis of the anisotropic quasi-semiellipse and the locations of discontinuities can indicate the normal direction of the fracture and the fracture distribution range, respectively. For multiple fractures, the major axis of the anisotropic quasi-semiellipse of the Rayleigh wave has almost the same direction as the main distribution of the fracture zone. This study provides theoretical support for the accurate prediction of complex fracture parameters inside media.

Effect of flow-independent viscosity on the propagation of Rayleigh wave in porous media

The propagation characteristics of Rayleigh wave near the surface of fluid-saturated poroviscoelastic medium are investigated in this paper. The effective stress in porous media is defined by the linear viscoelasticity theory based on Biot model and Kelvin-Voigt model. The dispersion equations of Rayleigh wave are derived analytically and then solved numerically to obtain its propagation speed and attenuation coefficient in the poroviscoelastic solid half-space. The effects of relaxation time and viscous coupling on the dispersion and attenuation of the Rayleigh wave as well as the body waves are discussed. The results indicate that the flow-independent viscosity has important influence on the propagation characteristics of Rayleigh waves, compared with the flow-dependent effect of viscous coupling between the pore fluid and solid skeleton.

Vibration Isolation Mechanism of Concrete Piles for Rayleigh Waves on Sand Foundations

To study the propagation characteristics of Rayleigh waves and the isolation mechanism of a single-row of piles by isolation effects, in this paper we draw a two-dimensional contour map ofζ(normalized acceleration amplitude relative to a measure close at the vibration source) using a vibration test carried out on a sand foundation. In this experiment, we study, in addition to the free field and the single pile cases, settings with two and three piles. The result shows that the vibration caused by the point source in the free field excites Rayleigh waves in a radial direction along the surface of the foundation. Meanwhile, the vibrations of the points along the propagation path on the surface of the foundation are gradually weakened. There is a steady transition when theζdrops to 0.6 and a placid decline whenζdecreases to less than 0.25. The vibration-shielded region, the strengthened region, and the strengthened strips will appear on the surface of the foundation. The vibration-shielded region is located behind the piles, and the region presents a trumpet-shaped area that takes the pile as the vertex. Increasing the quantity of piles contributes to increasing the vibration isolation effect, not only that involving the degree of isolation but also for the area of the shielded area. The vibration-strengthened regions include the diffraction regions at the pile corners on both sides of the single-row of piles and the scattering region at the gaps of the piles. In addition, the composite regions are located among the vibration source and the scattering and diffraction-strengthened regions. Increasing the number of piles has little influence on the scattering and diffraction-strengthened regions but can significantly enhance the vibrations of the composite regions. In general, the vibration-strengthened strips are connected with the scattering-strengthened regions. However, in the test of a single pile, the pile is connected to the diffraction-strengthened regions near its two anterior angles.

Effect of initial stress on the propagation and attenuation characteristics of Rayleigh waves

The present investigation deals with the mathematical modelling and analytical thinking to uncover the various facets of the propagation of Rayleigh waves in an Earth’s crustal layer. This work has been carried out when the wave is passing through a pre-stressed anisotropic layer of finite thickness, lying over a semi-infinite medium with void pores. The upper boundary plane of the crustal layer has been thought to be a free surface. Displacement components of the wave for both the media have been derived analytically. Appropriate boundary conditions have been well satisfied with the aid of displacement and stress factors in order to get the desired dispersion relation. A comparative study has been performed graphically taking anisotropic, orthotropic and isotropic strata, in order to show the impact of initial stress and thickness on the propagation characteristics of Rayleigh waves. The present work may establish a program to connect theoretical results with subject area applications.

Laser-Generated Rayleigh Waves Propagating in Transparent Viscoelastic Adhesive Coating/Metal Substrate Systems

We have established numerical models for simulating laser-generated Rayleigh waves in coating/substrate systems by a finite element method and investigated the propagation characteristics of Rayleigh waves in systems concerning the viscoelasticity and transparency of adhesive coatings. In this way, we have studied the influence of the mechanical properties of the coating, such as the elastic moduli, viscoelastic moduli, coating thickness, transparency, and coating material, on the propagation characteristics of the Rayleigh waves. The results show that the propagation characteristics of the Rayleigh waves can be divided into low- and high-frequency parts. The high-frequency propagation characteristics of the Rayleigh wave are closely related to the properties of the adhesive coating.

Propagation and attenuation of Rayleigh waves in a partially-saturated porous solid with impervious boundary

Abstract Propagation of Rayleigh waves is studied in a three-phase porous solid half-space, which is bounded above by an impervious plane surface. In this dissipative medium, Rayleigh wave propagates as an inhomogeneous wave, which decays with distance from the stress-free plane boundary. The impervious boundary restricts the flow of pore-fluids to the interior of porous solid only. This is ensured by fixing the fluid-pressure gradient in pores at boundary or with the sealing of surface pores. In either case, the existence and propagation of inhomogeneous wave are represented by a dispersion equation, which happens to be complex and irrational. This equation is rationalized into an algebraic equation of degree 24, which is solved for a numerical example. Solutions of the dispersion equation are checked to represent an inhomogeneous wave decaying with depth. Each qualified solution is resolved to define the phase velocity and attenuation coefficient of a Rayleigh wave in the medium. Numerical example compares the velocity and attenuation of Rayleigh wave in porous sandy loam for the two representations of the impervious boundary, one with sealed pores and other with no fluid-pressure gradient. Effects of saturation degree, porosity, capillary pressure, pore-fluids viscosity and frame anelasticity are observed on the propagation characteristics of Rayleigh waves. Existence of second Rayleigh wave is checked numerically. Such a wave is possible only when the porous frame is highly anelastic and saturated enough.

Rayleigh waves in a double porosity half-space

Based on the governing equations of double-porosity media extended from Biot's theory, the propagation characteristics of Rayleigh waves are discussed in this paper. Characteristic equations of Rayleigh waves in a double porosity half-space with the pervious boundary are derived by assuming that both the coupling mass coefficient ρ 23 and coupling permeability term k (12) are equal to zeros. The dispersion and attenuation properties of Rayleigh waves in a double porosity medium are analyzed numerically. The effects of the porosity and fracture permeability on the behavior of the propagation of Rayleigh waves are investigated. It is found that Rayleigh waves in a double porosity half-space are dispersive and attenuated during propagation. The Rayleigh wave speed is always less than the phase velocity of P1 and shear waves, and always higher than the phase velocity of P3 wave.

Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials

The paper is aimed at to investigate the propagation of Rayleigh waves in a homogeneous, transversely isotropic, piezothermoelastic half-space subjected to stress free, electrically shorted/charge-free and thermally insulated/isothermal boundary conditions. Secular equations for the half-space in closed form and isolated mathematical conditions in completely separate terms are derived. The secular equations for stress free piezoelectric, thermoelastic and elastic half-spaces have also been deduced as special cases from the present analysis. Finally, numerical solution of various secular equations and other relevant relations is carried out for cadmium-selenide (6 mm class) material. The dispersion curves and attenuation coefficients of wave propagation are presented graphically, in order to illustrate and compare the analytical results. The theory and numerical computations are found to be in close agreement. The coupling between the thermal/electric/elastic fields in piezoelectric materials provides a mechanism for sensing thermomechanical disturbances from measurements of induced electric potentials, and for altering structural responses via applied electric fields. Therefore, the analysis will be useful in the design and construction of temperature sensors and surface acoustic wave filter devices.

Surface Acoustic Wave Properties of La3Ta0.5Ga5.5O14 Single Crystals

The propagation characteristics of Rayleigh waves on a La3Ta0.5Ga5.5O14 (LTG) substrate were theoretically investigated for all cuts and propagation directions. The material constants, such as the elastic stiffness, piezoelectric constants and their thermal coefficients, were measured by the resonant and antiresonant frequency method. The existence of orientations with zero-temperature coefficient of delay (TCD) was calculated by computer analysis. The electromechanical coupling coefficient (k2) is about three times larger than that of ST-cut quartz. The phase velocity is approximately 2690 m/s. These results indicate a large possibility for application to wide-band intermediate-frequency surface acoustic wave (SAW) filter devices.

Analysis of Surface Acoustic Wave Properties of the Rotated Y-cut Langasite Substrate

The propagation characteristics of Rayleigh waves on a Y-rotated La3Ga5SiO14 (langasite) substrate are evaluated with the use of newly obtained material constants. The calculated phase velocity, the power flow angle (PFA), the coupling electromechanical coefficient (K2), the temperature coefficient of delay (TCD) and the diffraction coefficient (γ) are shown as contour maps. The revised numerical calculations were in much better agreement with the experimental results of the temperature characteristics on the langasite substrate with Euler angle (0°, 140°, φ). Moreover, the temperature characteristics as a function of the metal thickness were experimentally investigated. It was found that a thicker metal leads to a lower turnover temperature. Finally, an example of the frequency response of the transversal filter designed for IS95 is shown.

Characteristics of Rayleigh and Leaky Surface Acoustic WavePropagating on a La3Ga5SiO14 Substrate

The propagation characteristics of Rayleigh waves on a La3Ga5SiO14 substrate are theoretically investigated for all cuts and propagation directions. The results of the phase velocity, electro-mechanical coupling constant (K2), power flow angle (PFA) and temperature coefficient of delay (TCD) are shown as contour maps. The maximum value of K2 of a Rayleigh wave is 0.55%, and about 0.5% with zero TCD. These values are about 2–3 times larger than those of quartz. It is found that some cuts exist, which do not have a Rayleigh wave. The characteristics of leaky surface acoustic wave (SAW) on Z-cut La3Ga5SiO14 are also shown.

Optical Probing of Acoustic Surface Waves

Light diffraction by acoustic surface waves is used as a probe to study the propagation characteristics of Rayleigh waves on y-cut z-oriented LiNbO3. Both the surface deformation and the periodic variation of the index of refraction in the medium, which diffracts the transmitted light beam, are related to the particle displacements of the propagating Rayleigh waves. For the reflected beam, only the surface deformation contributes to the diffracted light. Experimental demonstrations of using the optical probe to observe the Fresnel diffraction of a rectangular interdigital transducer to measure the transmission and reflection coefficients of a transducer and to determine the propagation characteristics, such as velocity, attenuation of Rayleigh waves on a LiNbO3 substrate and on a metalized LiNbO3 substrate, will be discussed.

Optical probing of surface acoustic waves

Light diffraction by surface acoustic waves is used in studying the propagation characteristics of Rayleigh waves on y-cut z-oriented LiNbO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> . In reflection, only the surface deformation contributes to the diffracted light. In transmission, the photoelastic effect, which is incident beam polarization dependent, must also be considered. Such optical probing has been used to study the Fresnel diffraction radiation pattern of an interdigital transducer, to measure beam steering effects related to transducer misalignment on an anisotropic substrate, and to measure reflection and transmission coefficients of an electrically loaded transducer. Attenuation measurements have been made over frequencies as high as 3.5 GHz. The power dependence of attenuation and harmonic generation is also examined.