Propagation Of Rayleigh Waves Research Articles

Rayleigh wave-based monitoring of mortar coating and concrete core cracking on prestressed concrete cylinder pipe under external pressure using piezoelectric lead zirconate titanate

Prestressed concrete cylinder pipe (PCCP) is a critical type of pressure pipe widely used in major water conveyance projects worldwide. As essential components of a PCCP, the mortar coating and concrete core are directly linked to its operational safety. This study employed piezoelectric lead zirconate titanate (PZT) devices as transducers to generate excitation vibrations and measure the resulting Rayleigh waves, thereby providing a means to detect cracking in and monitor the health of the mortar coating and concrete core of a prototype 1400 mm inner-diameter PCCP under external pressure. First, a theoretical analysis was conducted to define the propagation laws of Rayleigh waves. Next, a finite element analysis was undertaken to identify the tensile regions of the PCCP mortar coating and concrete core when under external pressure applied along the length of the PCCP and thereby establish the locations for the PZT devices. Experiments were subsequently conducted by incrementally increasing the external pressure load from 0 to 700 kN while monitoring the cracking in the mortar coating and concrete core using sinusoidal excitation signals with frequencies of 5, 10, and 20 kHz. The voltage amplitudes measured at each external pressure load were analysed, confirming the Rayleigh wave propagation laws and revealing that the change in the measured voltage amplitude curve aligned with the experimental observations, thereby validating the proposed measurement method. Finally, the relative percentage deviation of amplitude (RPDA) and relative percentage deviation of energy (RPDE) damage indices were established based on the voltage measurements to further evaluate the damage state of the mortar coating and concrete core. The RPDA measured at an excitation frequency of 20 kHz was best for detecting cracks in the PCCP mortar coating, whereas the RPDA and RPDE measured at excitation frequencies of 20 and 10 kHz, respectively, were best for monitoring concrete core cracking.

Rayleigh wave propagation in an initially stressed orthotropic elastic solid half-space lying under inviscid liquid and viscous liquid layers

PurposeThe purpose of this article is the propagation of Rayleigh waves in a homogeneous, isotropic, initially stressed orthotropic elastic solid half-space lying under a homogeneous, viscous, inviscid liquid layer of finite thickness.Design/methodology/approachIn the presence of both viscous and inviscid liquids, it derives the phase velocity, initial stress, and wave number-dependent frequency equation for an orthotropic elastic solid. With the help of the MATLAB program, the thickness effects of liquid layers, initial stress, and viscosity on the phase velocity and attenuation coefficient of the Rayleigh wave are explained for a particular model.FindingsThe phase velocity-dependent dispersion relation of Rayleigh waves at the interface of viscous liquid and solid half-space is a function of initial stress and wave number. Rayleigh waves along the free surface of an orthotropic elastic half-space are also derived as a particular case. The classical results of an inviscid liquid are achieved when the thickness of a viscous liquid approaches zero. Well-known classical results for initially stressed orthotropic elastic solids were also derived.Originality/valueSo far, many researchers have looked into the propagation of surface waves at the interfaces of solid–inviscid liquid, solid–solid, and multilayer interfaces. But in this article, the dispersion behavior of Rayleigh wave propagation in an initially stressed homogeneous orthotropic elastic solid half-space under a double layer of viscous liquid and inviscid liquid is studied.

Nonlinear Rayleigh wave propagation in a three-layer sandwich structure in dual-phase-lag

Plane, nonlinear Rayleigh wave propagation is investigated in a three-layer sandwich structure of a thermoelastic medium, within the frame of dual-phase-lag theory. The thermal conductivity is taken as a linear function of temperature. This induces nonlinearity in the evolution equations for the heat flux components. A particular solution is found in the form of Poincaré expansion in a small parameter that reflects the fluctuations of temperature about a steady value. This solution is discussed and plots are provided for a special case when both external faces of the structure are traction-free and under prescribed temperature regime. It is noted, in particular, that some quantities of practical interest suffer jumps at the interfaces. Some of the jumps appear only starting from the second order of approximation. The existence of jumps may be favourably used to carry out some measurements of material parameters.

Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media.

Analysis on Vibration Screening by Rayleigh Wave Propagation Through Open and In-filled Trench

Analysis on Vibration Screening by Rayleigh Wave Propagation Through Open and In-filled Trench

Acoustoelectric Effect due to an In-Depth Inhomogeneous Conductivity Change in ZnO/Fused Silica Substrates

The acoustoelectric (AE) effect induced by the absorption of ultraviolet (UV) light at 365 nm in piezoelectric ZnO films was theoretically and experimentally studied. c-ZnO films 4.0 µm thick were grown by the RF reactive magnetron sputtering technique onto fused silica substrates at 200 °C. A surface acoustic wave (SAW) delay line was fabricated with two split-finger Al interdigital transducers (IDTs) photolithographically implemented onto the ZnO-free surface to excite and reveal the propagation of the fundamental Rayleigh wave and its third harmonic at about 39 and 104 MHz. A small area of a few square millimeters on the surface of the ZnO layer, in between the two IDTs, was illuminated by UV light at different light power values (from about 10 mW up to 1.2 W) through the back surface of the SiO2 substrate, which is optically transparent. The UV absorption caused a change of the ZnO electrical conductivity, which in turn affected the velocity and insertion loss (IL) of the two waves. It was experimentally observed that the phase velocity of the fundamental and third harmonic waves decreased with an increase in the UV power, while the IL vs. UV power behavior differed at large UV power values: the Rayleigh wave underwent a single peak in attenuation, while its third harmonic underwent a further peak. A two-dimensional finite element study was performed to simulate the waves IL and phase velocity vs. the ZnO electrical conductivity, under the assumption that the ZnO layer conductivity undergoes an in-depth inhomogeneous change according to an exponential decay law, with a penetration depth of 325 nm. The theoretical results predicted single- and double-peak IL behavior for the fundamental and harmonic wave due to volume conductivity changes, as opposed to the AE effect induced by surface conductivity changes for which a single-peak IL behavior is expected. The phenomena predicted by the theoretical models were confirmed by the experimental results.

Effect of Corrugation and Imperfect Boundary on the Propagation of Rayleigh Waves in Sandy Half-Space beneath an Anisotropic Layer

Effect of Corrugation and Imperfect Boundary on the Propagation of Rayleigh Waves in Sandy Half-Space beneath an Anisotropic Layer

Study of different theories of thermoelasticity under the propagation of Rayleigh waves in thermoelastic medium

The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

Analysis of Rayleigh wave dynamic response and propagation characteristics in layered site

Rayleigh waves are crucial in earthquake engineering due to their significant contribution to structural damage. This study aims to accurately synthesize Rayleigh wave fields in both uniform elastic half-spaces and horizontally layered elastic half-spaces. To achieve this, we developed a self-programmed FORTRAN program utilizing the thin layer stiffness matrix method. The accuracy of the synthesized wave fields was validated through numerical examples, demonstrating the program’s reliability for both homogeneous and layered half-space scenarios. A comprehensive analysis of Rayleigh wave propagation characteristics was conducted, including elliptical particle motion, depth-dependent decay, and energy concentration near the surface. The computational efficiency of the self-programmed FORTRAN program was also verified. This research contributes to a deeper understanding of Rayleigh wave behavior and lays the foundation for further studies on soil-structure interaction under Rayleigh wave excitation, ultimately improving the safety and resilience of structures in seismic-prone regions.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

Rayleigh waves in nonlocal orthotropic thermoelastic medium with diffusion

AbstractThis study examines Rayleigh wave propagation dynamics in a nonlocal orthotropic medium with thermoelastic diffusion, utilizing Eringen's nonlocal elasticity theory and the Lord–Shulman hyperbolic thermoelasticity model. Normal mode analysis is used to solve the problem, deriving the frequency equation for Rayleigh waves and analyzing specific cases. The elliptical path of surface particles and its eccentricity are calculated. Graphs illustrate the relationships of propagation speed, attenuation coefficient, penetration depth, and specific loss of Rayleigh waves concerning wave number for both thermally insulated and isothermal surfaces. The results reveal that the presence of nonlocal parameters and diffusion significantly increases the values of physical variables, especially with higher wave numbers, highlighting their considerable impact on the system's dynamics.

Rayleigh Waves Propagation in a Micropolar Viscothermoelastic Half-Space with Impedance Boundary Conditions

Rayleigh Waves Propagation in a Micropolar Viscothermoelastic Half-Space with Impedance Boundary Conditions

Rayleigh wave propagation in a modified couple stress visco-thermoelastic diffusion medium

The present investigation is devoted to Rayleigh wave propagation in modified couple stress visco-thermoelastic medium with mass diffusion under Lord–Shulman and Green–Lindsay theories of thermoelasticity. After formulating the problem mathematically, the secular equation is derived for stress free, insulated, and impermeable boundary. The wave characteristics like phase velocity and attenuation coefficient have been obtained numerically by developing numerical algorithm. For a particular material, the numerically simulated results are shown graphically to display the physical meaning of the phenomenon. The current inquiry also leads to several specific cases of interest. A comparison has been conducted with the earlier findings that suggested how the additional parameters might affect the phenomena of Rayleigh waves propagating. The results obtained indicate to the strong impact for the diffusivity and viscosity of Rayleigh thermoelastic waves propagation and applicable on the related phenomenon in geology, geophysics, acoustics, astronomy, and geophysics and agreement with the physical meaning of the phenomenon.

Simulation study of Rayleigh wave inspection of subsurface white etching crack in bearing rollers

Abstract Rolling bearings are widely used in wind energy and electric vehicle industries. One of the premature failure mode due to the contact fatigue is White Etching Crack (WEC) in the subsurface. WEC occurs preferentially in the Hertzian contact region of bearings, preferentially around multi-phase inclusions containing aluminium, manganese, and sulfur. The formation process undergoes intense plastic deformation and recrystallization. Most of WECs are 100~300 μm below the contact surface in a butterfly shape. Its principal axis is 30°~50° to the rolling direction. Since the sample preparation is difficult, this simulation study enables to better understand the interaction between WEC and ultrasonic waves for a better measurement system design. Rayleigh surface wave penetrates to a depth of about an order of magnitude of one wavelength. Its energy is concentrated near the surface containing rich WEC information. The Rayleigh wave propagation process is first analyzed based on the grain scale model established. Then the immersion inspection of WEC is simulated based on the finite element method at 15 MHz in order to compromise between the detection accuracy and defect depth. Finally, by analyzing the time and frequency domain information of the scattered signals, the quantitative relationships between crack characteristics (depth, length and tilt angle) and those of Rayleigh waves (amplitude and attenuation) can be obtained. This study paves the way for the quantitatively characterization of WEC in bearing rollers with surface integrity evaluation possibility at early stage.

Application of coded excitation in the Rayleigh wave detection of aluminum plates with narrow-magnet EMAT

Abstract The poor generation efficiency causes the low signal-to-noise ratio (SNR) of the electromagnetic acoustic transducers (EMATs). The magnetic fields at the edges of the magnet are fully utilized in the narrow-magnet EMAT to generate Rayleigh waves of higher amplitudes than the conventional EMAT. This paper applies the coded excitation technology to narrow-magnet EMAT to further improve the SNR and the lift-off performance in aluminum plate detection. The main phase encoding methods are Barker code and Golay code. Compared with the conventional tone-burst excitation method, both coded excitation technologies can effectively improve the SNR of the Rayleigh wave. Theoretically, the received Rayleigh waves using the Golay-coded excitation method have no sidelobe, which is different from the case using the Barker code. Hence the Golay-coded excitation achieves higher SNR in the received ultrasonic waves. In addition, the application of the Golay-coded excitation can also effectively improve the lift-off performance of the narrow-magnet EMAT.

Rayleigh surface waves of extremal elastic materials

Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft modes, offering unprecedented opportunities for manipulating bulk waves, e.g., acting as phonon polarizers for elastic waves or invisibility cloaks for underwater acoustic waves. Despite their potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of such extremal elastic materials, have largely remained unexplored so far. In this paper, we theoretically investigate the propagation of Rayleigh waves in extremal elastic materials based on continuum theory and verify our findings with designed microstructure metamaterials based on pantographic structures. Dispersion relations and polarizations of Rayleigh waves in extremal elastic materials are derived, and the impact of higher order gradient effects is also investigated by using strain gradient theory. This study provides a continuum model for exploring surface waves in extremal elastic materials and may stimulate applications of extremal elastic materials for controlling surface waves.

Study on the interaction mechanism of laser-generated Rayleigh waves and subsurface inclined cracks

Abstract In this paper, the finite element method was used to study the reflected and transmitted waves of laser-generated Rayleigh waves from subsurface inclined cracks, the propagation paths and mode conversion mechanisms of different characteristic waves are determined. The Rayleigh wave will interact with the crack top tip and propagate back and forth along the crack surface, and be converted to shear waves at the crack top tip. The shear waves will mode-convert to Rayleigh waves at the free surface when the incidence angle of the shear wave is larger than 60°. Moreover, for the Rayleigh wave interacting with the crack bottom tip, when the crack inclined angle is less than 60°, some Rayleigh waves will travel along the crack surface to the crack top tip. When the crack inclination angle is greater than 60°, in addition to the Rayleigh waves propagating upwards along the crack surface, some Rayleigh waves convert to shear waves at the crack bottom tip and then incident on the free surface of the workpiece. Experiments were carried out to validate some of the Rayleigh wave propagation paths. The experimental results matched the theoretical arrival time well, thus verifying the reliability of the analytical wave path. The results are helpful for the quantitative detection of subsurface inclined cracks using laser ultrasonic techniques.

Magneto-thermoelastic surface waves phenomenon with voids, gravity, initial stress, and rotation under four theories

This paper addresses a significant research gap in the study of surface waves propagation in a nonhomogeneous, within a magneto-thermoviscoelastic material of higher order, initial stress, rotation, gravity effects and voids. This study provides analytical solutions for surface waves propagating through a medium consisting of a magneto-thermoelastic material with voids under the rotation, electro-magnetic field, gravity field and initial stress. The analytical solutions are derived for the displacement components, volume fraction, temperature to Stoneley and Rayleigh waves are computed numerically and presented graphically considering the external parameters impact. Furthermore, this investigates how magnetic field, voids, gravity, initial stress and fiber-reinforced parameters influence these wave phenomena. This investigation provides valuable insights into the synergistic dynamics among electric constituents, voids, Stoneley and Rayleigh waves propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies, and pioneering seismic monitoring approaches. For certain materials, numerical simulations are provided and graphically displayed. The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh and Stoneley waves propagation within this intricate material system, particularly in the presence of voids.

High load-bearing metastructure for controlling surface Rayleigh waves

Artificial metamaterials for controlling surface Rayleigh waves have been extensively studied in recent years. However, practical engineering applications of metamaterials are still limited when they lack high load-bearing capacity. For this reason, a new metamaterial called a high-load-bearing metastructure is presented, which is designed by generalized Snell’s law. The wide-bandgap performance for surface Rayleigh waves and the high load-bearing capacity of the proposed metastructure are realized by using traditional engineering materials, which provide a more flexible reference in practical engineering applications. This work can open new avenues for controlling the propagation of surface Rayleigh waves.

Rayleigh wave in nonlocal piezo-thermo-electric semiconductor medium with fractional MGT model

This paper addresses a critical gap in Rayleigh wave propagation studies within piezoelectric semiconductors. Existing research often overlooks the combined effects of piezoelectricity, semiconductivity, and thermal behavior. This work presents analytical solutions for Rayleigh waves in a novel nonlocal thermo-piezo-photo-electric semiconductor half-space, employing the fractional Moore-Gibson-Thompson model. The wave-mode method and Durand-Kerner technique are employed to extract relevant solutions from the characteristic equation, ensuring surface wave decay. Analysis is conducted for waves propagating in a stress-free, photo-excited, and isothermal boundary condition. Numerical simulations unveil phase velocity, attenuation coefficient, and particle motion, leading to a deeper understanding of wave behavior. The influence of nonlocal and fractional order parameters is meticulously investigated. These findings reveal unique phenomena that significantly advance the comprehension of Rayleigh waves in these intricate materials.