Elliptical Particle Motion Research Articles

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.

Numerical simulation on the coupling of the elliptical particle motion and phase change

The particle sedimentation and phase change in the mushy zone are accompanied by a variety of complex transfer processes involving momentum, heat, and mass. It is very important to investigate the coupling process of particle settling and melting in the mushy zone for revealing the mechanism of the solid-liquid phase change. In this paper, the motion process and heat transfer characteristics of an elliptic particle as well as two particle interactions in the vertical channel were solved by the finite element method with the consideration of coupling of the phase change and motion. The Arbitrary Lagrangian-Euler Method (ALE) was employed to track the interface of the moving particle and fluid. Results show that the elliptical particle settles along the channel's center line vertically under gravity and undergoes phase change simultaneously. Uneven velocity and temperature fields surrounding the particle are generated by sedimentation, resulting in the particle with an irregular shape. When the initial position of the particle deviates from the center line, the particle deflects during the sedimentation and shifts both left and right in the X-direction. The different initial angles of settling also affect the sedimentation velocity and melting rate. When two particles settle simultaneously, they will lead to complex movement and heat transfer due to the interaction between each other. If the arrangement is eccentric, both particles undergo complex deflections during sedimentation, leading to different melting rates for the two particles.

Full-Scale Simulation of the Fluid–Particle Interaction Under Magnetic Field Based on IIM–IBM–LBM Coupling Method

In this article, a full-scale computational model for fluid–particle interaction under a magnetic field is developed. In this model, the fluid field is solved by the lattice Boltzmann method, and the hydrodynamic force acting on the particle is computed by the immersed boundary method . The numerical solutions of the magnetic field in the fluid–solid domain are achieved by the immersed interface method with a finite difference scheme, in which the normal and tangential jump conditions of the magnetic field intensity are applied to modify the standard finite difference scheme. The magnetic stress tensor along the fluid–particle interface can be calculated accurately. Unlike the widely used point–dipole model, the magnetic force acting on the particle is determined by the stress integration method. Numerical simulation of several numerical tests are carried out to validate the proposed model. The numerical results demonstrate the validity of the present model. Moreover, the magnetoviscous effect is studied by simulating the motion of elliptical particles under the uniform magnetic field in shear flow.

Characteristics, relationships and precision of direct acoustic-to-seismic coupling measurements from local explosions

SUMMARY Acoustic energy originating from explosions, sonic booms, bolides and thunderclaps have been recorded on seismometers since the 1950s. Direct pressure loading from the passing acoustic wave has been modelled and consistently observed to produce ground deformations of the near surface that have retrograde elliptical particle motions. In the past decade, increased deployments of colocated seismometers and infrasound sensors have driven efforts to use the transfer function between direct acoustic-to-seismic coupling to infer near-surface material properties including seismic velocity structure and elastic moduli. In this study, we use a small aperture (≈600 m) array of broadband seismometers installed in different manners and depths in both granite and sedimentary overburden to understand the fundamental nature and repeatability of seismic excitation from 1 to 15 Hz using horizontally propagating acoustic waves generated by 97 local (2–10 km) explosions. In agreement with modelling, we find that the ground motions induced by acoustic-to-seismic coupling attenuate rapidly with depth. We confirm the modelled relation between acoustic and ground motion amplitudes, but show that within one acoustic wavelength, the uncertainty in the transfer coefficient between seismic and acoustic energy at a given seismic station increases linearly with separation distance between the seismic and acoustic sensor. We attribute this observation to the rapid decorrelation of the infrasonic wavefield across small spatial scales and recommend colocating seismic and infrasound sensors for use in studies seeking to invert for near-surface material properties. Additionally, contrary to acoustic-to-seismic coupling theory and prior observations, we find that seismometers emplaced in granite do not record retrograde elliptical particle motions in response to direct pressure loading. We rule out seismometer tilt effects as a likely source of this observations and suggest that existing models of acoustic-to-seismic excitation may be too simplistic for seismometers placed in high rigidity materials.

Motion and equilibrium position of elliptical and rectangular particles in a channel flow of a power-law fluid

The inertial migration of the elliptical and rectangular particles in a channel flow of a power-law fluid is studied using the lattice Boltzmann method. The numerical method and code are validated by comparing the present results with the previous ones. Effects of power-law index (n) of the fluid, particle shape, particle aspect ratio (α), blockage ratio (k) and Reynolds number (Re) on the particle trajectory and equilibrium position are discussed. The results show that the elliptical and rectangular particles will finally oscillate in a lateral equilibrium position. The distance for the particle from its initial position to the stable equilibrium position is the shortest for the rectangular particle, then followed for the elliptical particle and finally for the circular particle and square particle, the distance is the shortest for the shear-thinning fluid, then followed for the Newtonian fluid and finally for the shear-thickening fluid. This distance for the rectangular particle decreases with increasing Re, but the dependence of the distance on Re for the elliptical particle is not as obvious as that for the rectangular particle. The particle with larger aspect ratio and blockage ratio gets to the equilibrium position faster. The lateral distance from the equilibrium position to the channel centerline is reduced with increasing k, and with decreasing α for both elliptical and rectangular particles. For the particles with larger α, the lateral distance is reduced with the increase of Re, but the relationship between the lateral distance and Re for the particles with smaller α is dependent on n.

Field monitoring of the ground vibrations adjacent to an onshore wind turbine foundation

Investigations of the soil–foundation interaction behaviour of wind turbine foundations and transfer of energy from the wind to the ground have not been reported in Canada. Indeed, very few vibration monitoring studies have been conducted globally around wind farms. It has been found that turbines predominantly produce vibrations related to structural resonances and blade-passing frequencies. Energy is found to be modified with distance and is dominated by surface waves. This paper describes a study of the effect of wind–structure interaction on the behaviour of a turbine foundation and the generation of ground-based vibrations around a working commercial wind turbine in Ontario. The field monitoring system and meteorological instrumentation are described in this paper and the responses of the structure and surrounding ground due to the fluctuating wind-field are discussed. The spectral analysis shows that the higher frequency vibrations attenuate more rapidly than the lower frequency vibrations. The tilted elliptical particle motions are found to be non-Gaussian because of the non-Gaussian wind conditions. The response attenuation with distance indicates that both geometric and material attenuation may dominate the vibration attenuation in the near field and only geometric attenuation occurs in the far field.

Using multicomponent ambient seismic noise cross-correlations to identify higher mode Rayleigh waves and improve dispersion measurements

SUMMARYAmbient seismic noise cross-correlation with three-component sensors yields a nine-component empirical Green's tensor, in which four components of the radial–vertical plane contain Rayleigh waves. We exploit the retrograde elliptical nature of particle motion of the fundamental mode Rayleigh wave to correct the phase of the four radial–vertical components and stack them to obtain an average fundamental mode Rayleigh-wave time-series. This technique can suppress incoherent noise and wave packets that do not follow the targeted elliptical particle motion. The same technique can be used to isolate the first higher mode Rayleigh wave that follows prograde elliptical particle motion. We first demonstrate the effectiveness of the method on synthetic waveforms and then apply it on noise cross-correlations computed in Central California. Using this method, we isolate 1st higher mode Rayleigh waves on noise cross-correlations in the Great Valley, California, which provides new phase velocity constraints for estimating velocity structure in the sedimentary basin. We also obtain improved estimates of fundamental mode Rayleigh-wave dispersion for surface-wave tomography. The waveforms stacked assuming retrograde particle motion return at least ∼20 per cent more group velocity dispersion measurements satisfying a minimum signal-to-noise ratio (SNR) criterion than the individual components for periods ∼4–18 s. For equivalent group velocity measurements, SNR for the stacked estimate of the fundamental mode Rayleigh wave is on average 40 per cent greater than that measured on the individual components at periods less than 10 s. The technique also provides an easy way to detect large errors in sensor orientation.

New robust observables on Rayleigh waves affected by an underground cavity: from numerical to experimental modelling

The investigation and monitoring of shallow hazards due to the presence of underground cavities remain a challenge for geophysical approaches. Thus, seismic surface waves have been tested in several recent research projects in order to detect and localize voids as well as to determine their geometries. Among these works, numerous numerical studies have proved the feasibility of Rayleigh waves to detect cavities. However, most imagery processes adapted to R waves are faced with difficulties when applying them to real data. This limitation points to a major problem: the interactions between Rayleigh waves and a cavity are complex, particularly in the case of dispersing and attenuating surrounding media. Here, a combined approach based on numerical and experimental data obtained in a reduced-scale measurement bench is conducted to better understand the seismic wave propagation phenomena involved in the presence of a cavity and define robust observables that can be used in field measurements. The observables bearing the cavity signature are studied qualitatively and quantitatively on numerical and experimental recordings. The latter take into account all the propagation phenomena involved. The observations are carried out on the vertical and horizontal component of the Rayleigh wave displacement. The selected observables are studied depending on non-dimensional cavity's parameters versus the frequency, that is the wavelength-to-size ratio and the wavelength-to-depth ratio. The effects of the cavity's parameters on the observables show particularities as a function of these components, such as a higher rate of the amplitude on the horizontal component as well as a perturbation of the direct seismic surface wave amplitude above the cavity, also higher on the horizontal component. This latter feature is particularly visible on the variation of the elliptical particle motion recorded at the surface. It can be linked to the mode conversions that occur in the vicinity of the cavity and which predominate on the horizontal component when the signal is normalized.

Ross ice shelf vibrations

AbstractBroadband seismic stations were deployed across the Ross Ice Shelf (RIS) in November 2014 to study ocean gravity wave‐induced vibrations. Initial data from three stations 100 km from the RIS front and within 10 km of each other show both dispersed infragravity (IG) wave and ocean swell‐generated signals resulting from waves that originate in the North Pacific. Spectral levels from 0.001 to 10 Hz have the highest accelerations in the IG band (0.0025–0.03 Hz). Polarization analyses indicate complex frequency‐dependent particle motions, with energy in several frequency bands having distinctly different propagation characteristics. The dominant IG band signals exhibit predominantly horizontal propagation from the north. Particle motion analyses indicate retrograde elliptical particle motions in the IG band, consistent with these signals propagating as Rayleigh‐Lamb (flexural) waves in the ice shelf/water cavity system that are excited by ocean wave interactions nearer the shelf front.

Observations of elliptical particle motion in shallow water and its dependence on source depth

Acoustic particle motion that follows an elliptical path coincides with a non-zero curl of the time-averaged intensity. This vector property is also observed as curvature in intensity (energy-flux) streamlines. Measurements of the acoustic intensity field made in shallow water are presented, along with simulations of the intensity field, to demonstrate some interesting relations between acoustic intensity and elliptical particle motion. Specifically, the direction in which intensity streamlines bend (sign of the curl of intensity) corresponds to the polarization of acoustic particle motion. For a source located in water, the polarization of particle motion depends on the modes of the underwater waveguide excited at a particular source depth. By raising a source up through the water column, an abrupt change in the polarization of particle motion can occur. This effect is examined with vector sensor data collected during an experiment near Panama City, FL. For a source located in air, elliptical particle motion is most evident a few wavelengths below the sea-surface where the contribution of the lateral (evanescent) wave is significant. This effect is examined with a recording of aircraft noise on both sides of the air-water interface made near Oak Harbor, WA.

Propagation and attenuation of Rayleigh waves in generalized thermoelastic media

This study considers the propagation of Rayleigh waves in a generalized thermoelastic half-space with stress-free plane boundary. The boundary has the option of being either isothermal or thermally insulated. In either case, the dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. This dispersion equation is rationalized into a polynomial equation, which is solvable, numerically, for exact complex roots. The roots of the dispersion equation are obtained after removing the extraneous zeros of this polynomial equation. Then, these roots are filtered out for the inhomogeneous propagation of waves decaying with depth. Numerical examples are solved to analyze the effects of thermal properties of elastic materials on the dispersion of existing surface waves. For these thermoelastic Rayleigh waves, the behavior of elliptical particle motion is studied inside and at the surface of the medium. Insulation of boundary does play a significant role in changing the speed, amplitude, and polarization of Rayleigh waves in thermoelastic media.

Elliptical acoustic particle motion in underwater waveguides

Elliptical particle motion, often encountered in acoustic fields containing interference between a source signal and its reflections, can be quantified by the degree of circularity, a vector quantity formulated from acoustic particle velocity, or vector intensity measurements. Acoustic analysis based on the degree of circularity is expected to find application in ocean waveguides as its spatial dependence relates to the acquisition geometry, water column sound speed, surface conditions, and bottom properties. Vector sensor measurements from a laboratory experiment are presented to demonstrate the depth dependence of both the degree of circularity and an approximate formulation based on vertical intensity measurements. The approximation is applied to vertical intensity field measurements made in a 2006 experiment off the New Jersey coast (in waters 80 m deep) to demonstrate the effect of sediment structure on the range dependence of the degree of circularity. The mathematical formulation presented here establishes the framework to readily compute the degree of circularity from experimental measurements; the experimental examples are provided as evidence of the spatial and frequency dependence of this fundamental vector property.

Rayleigh Waves in Dissipative Poro-Viscoelastic Media

This study considers the propagation of Rayleigh waves on the stress‐free surface of a viscoelastic, porous solid saturated with viscous fluid. The surface pores have the option of being either sealed or fully opened. The dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. After rationalizing to an algebraic form, the dispersion equation is solved numerically, for exact complex roots. These roots are resolved for velocity and attenuation of the inhomogeneous propagation of Rayleigh waves in the poro‐viscoelastic solid half‐space. Effects of frame anelasticity, pore‐fluid viscosity, frequency, and pore characteristics are observed numerically on the velocities of existing Rayleigh waves. Behavior of the elliptical particle motion for these waves is studied inside and at the surface of the porous solid. With the sealing of surface pores, these waves should be more sensitive to the changes in porosity and tortuosity. An exclusive contribution of dissipation due to the anelastic frame and/or the viscous pore‐fluid is the existence of an additional inhomogeneous wave that satisfies the radiation condition for surface waves. This additional surface wave is more likely when surface pores of the dissipative porous medium are sealed.

Determination of New Zealand Ocean Bottom Seismometer Orientation via Rayleigh-Wave Polarization

Online material: Complete list of earthquakes used in this study. Three-component ground-motion recordings are critical to modern seismic analysis techniques such as receiver functions and body- and surface-wave polarization studies. Modern three-component seismometers typically resolve three axes of ground motion into one vertical and two orthogonal horizontal directions. The standard convention for installation is to orient the instrument such that one of the horizontal components is aligned with true north, taking into account the current local magnetic declination at the station. This practice can be difficult in the case of borehole instruments and practically impossible for ocean-bottom seismometers (OBS). Some deployments of OBS have used airgun shots to determine sensor orientation (Anderson et al. , 1987; Duennebier et al. , 1987); however, this is not an error- or cost-free procedure and is not always available. In these cases, determination of sensor orientation is necessary independent of human interaction with the physical instrument. The elliptical particle motion of Rayleigh waves is exploited here to calculate sensor orientation based on the statistical analysis of earthquakes recorded on OBS deployed around the south island of New Zealand. This robust method is computationally fast because synthetic seismograms are not generated and accurate source parameters are not necessary. The technique is compared with body-wave orientation results and full-waveform surface-wave orientation results. Application of this method to waveforms recorded on land stations and synthetic waveforms confirms its reliability. Surface-wave arrival azimuth is determined via polarization analysis of the Rayleigh wave recorded on a three-component sensor. Rayleigh waves exhibit retrograde elliptical particle motion, theoretically only observed on the vertical and radial components. Because it is more stable to quickly determine a linear relationship than to measure ellipticity, the polarization analysis is performed by cross correlating the vertical component with the Hilbert-transformed radial component. The 90° phase …

Multiscale Modeling of Circular and Elliptical Particles in Laminar Shear Flow

Drug delivery systems for cancer prevention and pain management have been improved related to classical cancer chemotherapy. Nanotechnology with nanoparticles offers new ways in transport of drug molecules and contrast agents by the blood flow through the circulatory system. In this study, we use multiscale mesoscopic bridging procedure of the finite elements (FE) coupled with dissipative particle dynamics (DPD) and lattice Boltzmann (LB) method to model the motion of circular and elliptical particles in a 2-D laminar flow. Four examples are considered: 1) one sedimenting cylinder in a channel, 2) two sedimenting cylinders in a channel, 3) motion of four elliptical particles in a linear shear flow, and 4) motion of circular and elliptical particle in the arterial bifurcation geometry. A good agreement with solution from the literature available was found. These results show that the multiscale approach with coupled FE and DPD/LB methods can effectively be applied to model motion of micro/nanoparticles for a drug delivery system.

Explosive Sources Prove the Validity of Homogeneous Isotropic Linear Viscoelastic Models

Abstract Intrinsic material absorption, as exemplified in the attenuation of seismic waves, is a key parameter in several seismological fields, in particular earthquake engineering. The advances of the last few decades in the theory of wave propagation in linear anelastic materials provide an opportunity to examine more completely the implications of intrinsic material absorption on seismic wave propagation. In the present paper, we analyze the records of two near-surface open quarry explosions of recently rescued, unexploded World War II bombs dropped by Allied air raids and recovered at a few meters depth close to the Milano Centrale railway station. Recordings obtained at epicentral distances of 1.4 km and 2.5 km show clear separation of body and surface waves and strong evidence for elliptical prograde particle motions for P waves. Classic elasticity theory predicts linear longitudinal motions for P waves. Hence, synthetic seismograms computed using computer codes that are based both on elasticity theory and on homogeneous attenuating waves (Herrmann and Ammon, 2002) do not account for observed particle motions. On the contrary the theory of wave propagation in homogeneous isotropic linear viscoelastic media (Borcherdt, 1971, 1973, 2009) accurately accounts for the observed characteristics of the recorded motion. Application of the theory provides empirical estimates of the inhomogeneity γ values (0≤ γ π /2) and evidence of intrinsic material absorption at low strain levels (less than 10 -6 ), as quantified by independent empirical estimates of Q -1 .

Dissipative particle dynamics simulation of circular and elliptical particles motion in 2D laminar shear flow

The dissipative particle dynamics (DPD) method is a relatively new computational method for modeling the dynamics of particles in laminar flows at the mesoscale. In this study, we use the DPD approach to model the motion of circular and elliptical particles in a 2D shear laminar flow. Three examples are considered: (i) evaluation of the drag force exerted on a circular particle moving in a stagnant fluid, (ii) rotation of an elliptical particle around its center in a shear flow, and (iii) motion of an ellipsoidal particle in a linear shear flow. For all cases, we found a good agreement with theoretical and finite element solutions available. These results show that the DPD method can effectively be applied to model motion of micro/nano-particles at the mesoscale. The method proposed can be used to predict the performances of intravascularly administered particles for drug delivery and biomedical imaging.

On Possible Plume-Guided Seismic Waves

Abstract Hypothetical thermal plumes in the Earth’s mantle are expected to have low seismic-wave speeds and thus would support the propagation of guided elastic waves analogous to fault-zone guided seismic waves, fiber-optic waves, and acoustic waves in the oceanic SOund Fixing And Ranging channel. Plume-guided waves would be insensitive to geometric complexities in the wave guide, and their dispersion would make them distinctive on seismograms and would provide information about wave-guide structure that would complement seismic tomography. Detecting such waves would constitute strong evidence of a new kind for the existence of plumes. A cylindrical channel embedded in an infinite medium supports two classes of axially symmetric elastic-wave modes, torsional and longitudinal-radial. Torsional modes have rectilinear particle motion tangent to the cylinder surface. Longitudinal-radial modes have elliptical particle motion in planes that include the cylinder axis, with retrograde motion near the axis. The direction of elliptical particle motion reverses with distance from the axis: once for the fundamental mode, twice for the first overtone, and so on. Each mode exists only above its cut-off frequency, where the phase and group speeds equal the shear-wave speed in the infinite medium. At high frequencies, both speeds approach the shear-wave speed in the channel. All modes have minima in their group speeds, which produce Airy phases on seismograms. For shear wave–speed contrasts of a few percent, thought to be realistic for thermal plumes in the Earth, the largest signals are inversely dispersed and have dominant frequencies of about 0.1–1 Hz and durations of 15–30 sec. There are at least two possible sources of observable plume waves: (1) the intersection of mantle plumes with high-amplitude core-phase caustics in the deep mantle; and (2) ScS -like reflection at the core-mantle boundary of downward-propagating guided waves. The widespread recent deployment of broadband seismometers makes searching for these waves possible.

On the propagation characteristics of tunnel surface‐waves for seismic prediction

ABSTRACTTo increase the safety and efficiency of tunnel constructions, online seismic exploration ahead of a tunnel has become a valuable tool. One recent successful forward looking approach is based on the excitation and registration of tunnel surface‐waves. For further development and for finding optimal acquisition geometries it is important to study the propagation characteristics of tunnel surface‐waves. 3D seismic finite difference modelling and analytic solutions of the wave equation in cylindrical coordinates reveal that at higher frequencies, i.e., if the tunnel‐diameter is significantly larger than the wavelength of surface‐waves, these surface‐waves can be regarded as Rayleigh‐waves confined to the tunnel wall and following helical paths along the tunnel axis. For lower frequencies, i.e., when the tunnel surface‐wavelength approaches the tunnel‐diameter, the propagation characteristics of these surface‐waves are similar to S‐waves. We define the surface‐wave wavelength‐to‐tunnel diameter ratio w to be a gauge for separating Rayleigh‐ from S‐wave excitation. For w > 1.2 tunnel surface‐waves behave like S‐waves, i.e. their velocity approaches the S‐wave velocity and the particle motion is linear and perpendicular to the ray direction. For w < 0.6 they behave like Rayleigh‐waves, i.e., their velocity approaches the Rayleigh‐wave velocity and they exhibit elliptical particle motion. For 0.6 < w < 1.2 a mixture of both types is observed. Field data from the Gotthard Base Tunnel (Switzerland) show both types of tunnel surface‐waves and S‐waves propagating along the tunnel.

An analytical solution in 2D for the motion of rigid elliptical particles with a slipping interface under a general deformation

A mathematical model for rigid inclusions with a slipping interface immersed in a general 2D homogeneous deformation is developed. Under bulk pure shear inclusions are expected to rapidly approach the stretching axis when compared to the behaviour of inclusions with no slip at the interface. The derived model predicts synthetic and antithetic motion into a stable orientation under simple shear, and thereafter the inclusion makes an antithetic angle with the shear direction. Under simple shear rotation rates can be higher or lower than those of no-slip inclusions, depending on orientation. A direct relationship between object inclination to the shear direction and the vorticity of the bulk flow is predicted. The model compares well with published analogue and numerical experiments.