Surface Displacement Amplitudes Research Articles

Optical and microstructural characterization of multilayer Pb(Zr0.52Ti0.48)O3 thin films correlating ellipsometry and nanoscopy

Optical and microstructural characteristics of sol–gel-deposited multilayer Pb(Zr0.52Ti0.48)O3 thin films were investigated employing several analytical techniques both invasive and non-destructive types. Optical responses probed by variable angle spectroscopic ellipsometry (VASE) were used to derive the optical properties and geometrical parameters of the multilayer thin films. STEM and TEM studies were performed to verify the nano-structural specifics and to correlate the results obtained using VASE. Crystallographic orientation and epitaxial interrelations of the layers were also investigated using selected area diffraction patterns with compositional profiles derived from energy dispersive X-ray analysis. Ferroelectric domain switching of the sol–gel-deposited films were studied by Piezoelectric Force Microscopy (PFM) revealing both the polarization–electric field hysteresis (P-E loop) relation and the butterfly-shaped surface displacement amplitude responses. The advantages and limitations of the non-invasive VASE characterization technique in terms of resolving a multilayer structure of thin films were explored in detail.

Microfluidic Injector Simulation With FSAW Sensor for 3-D Integration

This paper presents a possible creation of the optimized liquid sensors for the inkjet nozzles. The proposed focused surface acoustic wave (FSAW) device utilizing aluminum nitride (AlN) single crystal as the piezoelectric substrate is based on the pressure variation due to the continuous droplet ejector. The design, specification, and numerical simulation results are described. Comparisons between the output response of the conventional and concentric structures indicate a more efficient operation of the multiple-segment focused interdigital transducer (FIDT) structure. According to the angular spectrum of the plane wave theory, the amplitude field of FIDTs is calculated through that of straight interdigital transducers. The 3-D integrated model of the FSAW device has a number of advantages, such as the enhancement of the surface displacement amplitudes and an easier fabrication. It is able to detect the breakup appearance of the liquid in the droplet formation process. For the piezoelectric substrate AlN, it is compatible with the CMOS fabrication technology, leading to an inexpensive and reliable system. Moreover, for the proposed FIDTs with multiple straight segments, the acoustic energy is more optimized and focused near the center of the inkjet nozzle. The droplet generation process begins at an output voltage of roughly 0.074 V within 0.25 μs, and the background level of the attenuation of both the mechanical and electrical energy.

Influence of surface displacement on solid state flow induced by horizontally heterogeneous Joule heating in the inner core of the Earth

We investigate the influence of surface displacement on fluid motions induced by horizontally heterogeneous Joule heating in the inner core. The difference between the governing equations and those of Takehiro (2011) is the boundary conditions at the inner core boundary (ICB). The temperature disturbance at the ICB coincides with the melting temperature, which varies depending on the surface displacement. The normal component of stress equalizes with the buoyancy induced by the surface displacement. The toroidal magnetic field and surface displacement with the horizontal structure of Y20 spherical harmonics is given. The flow fields are calculated numerically for various amplitudes of surface displacement with the expected values of the parameters of the core. Further, by considering the heat balance at the ICB, the surface displacement amplitude is related to the turbulent velocity amplitude in the outer core, near the ICB. The results show that when the turbulent velocity is on the order of 10-1–10-2m/s, the flow and stress fields are similar to those of Takehiro (2011), where the surface displacement vanishes. As the amplitude of the turbulent velocity decreases, the amplitude of the surface displacement increases, and counter flows from the polar to equatorial regions emerge around the ICB, while flow in the inner regions is directed from the equatorial to polar regions, and the non-zero radial component of velocity at the ICB remains. When the turbulent velocity is on the order of 10-4–10-5m/s, the radial component of velocity at the ICB vanishes, the surface counter flows become stronger than the flow in the inner region, and the amplitude of the stress field near the ICB dominates the inner region, which might be unsuitable for explaining the elastic anisotropy in the inner core.

Internal-Tide Spectroscopy and Prediction in the Timor Sea

AbstractSpectral analyses of two 3.5-yr mooring records from the Timor Sea quantified the coherence of mode-0 (surface) and mode-1 (internal) tides with the astronomical tidal potential. The noncoherent tides had well-defined variance and were most accurately quantified for tidal species (as opposed to constituents) in long records (>6 months). On the continental slope (465 m), the semidiurnal mode-0 and mode-1 velocity and mode-1 pressure variance were 95%, 68%, and 56% coherent, respectively. On the continental shelf (145 m), the semidiurnal mode-0 and mode-1 velocity and mode-1 pressure variance were 98%, 34%, and 42% coherent, respectively. The response method produced time series of the semidiurnal coherent and noncoherent tides. The spectra and decorrelation time scales of the semidiurnal tidal amplitudes were similar to those of the barotropic mean flow and mode-1 eigenspeed (~4 days), suggesting local mesoscale variability shapes noncoherent tidal variability. Over long time scales (>30 days), mode-1 sea surface displacement amplitudes were positively correlated with mode-1 eigenspeed on the shelf. At both moorings, internal tides were likely modulated during both generation and propagation. Self-prediction using the response method enabled about 75% of semidiurnal mode-1 sea surface displacement to be predicted 2.5 days in advance. Improved prediction models will require realistic tide–topography coupling and background variability with both short and long time scales.

An experimental setup for contactless measurement of the velocity of Rayleigh waves and the surface displacement amplitude

An experimental setup is described on which acoustic pulses were recorded from a small surface area. The setup consists of a contactless electromagnetic-acoustic receiver in which the inductor is two thin straight parallel conductors that are positioned a small distance from each other. The velocity of a Rayleigh wave was determined in the 2–10 MHz frequency range. At these frequencies, the length of a surface acoustic wave was varied from 600 to 240 μm and the minimal spacing for measuring the velocity of the Rayleigh wave at a frequency of 10 MHz was 500 μm. A new method for measurement of the time interval between two acoustic pulses is proposed.

Solution of dynamic Green׳s function for unsaturated soil under internal excitation

The closed form three-dimensional Green׳s function of a semi-infinite unsaturated poroelastic medium subjected to an arbitrary internal harmonic loading is derived, with consideration of capillary pressure and dynamic shear modulus varying with saturation. By applying the Fourier expansion techniques and Hankel integral transforms to the circumferential and radial coordinates, respectively, the general solution for the governing partial differential equations is obtained in the transformed domain. A corresponding boundary value problem is formulated. The integral solutions for the induced displacements, pore pressure and net stress are then determined considering the continuity conditions. The formulas are compared with the degenerated solution of saturated soils and confirmed. Numerical results reveal that the response of the unsaturated half-space depends significantly on the saturation by altering dynamic shear modulus to account for the effects of matric suction on soil stiffness. Slight differences between the results occur if only the saturation is taken into account. Moreover, a large source-depth results in a pronounced contribution to the reduction of surface displacement amplitudes. The analytical solutions concluded in the study offer a broader application to dynamic response associated with axi-symmetric and asymmetric conditions.

Air-pulse OCE for assessment of age-related changes in mouse cornea in vivo

We demonstrate the use of phase-stabilized swept source optical coherence elastography (PhS-SSOCE) to assess the relaxation rate of deformation created by a focused air-pulse in tissue-mimicking gelatin phantoms of various concentrations and mouse corneas of different ages in vivo. The results show that the relaxation rate can be quantified and is different for gels with varying concentrations of gelatin and mouse corneas of different ages. The results indicate that gel phantoms with higher concentrations of gelatin as well as older mouse corneas have faster relaxation rates indicating stiffer material. This non-contact and non-invasive measurement technique utilizes low surface displacement amplitude (in µm scale) for tissue excitation and, therefore, can be potentially used to study the biomechanical properties of ocular and other sensitive tissues.

Surface Wave Propagation in an Elastic Layer Lying over a Thermodiffusive Elastic Half-Space with Imperfect Boundary

The present investigation is to study the surface wave propagation with an imperfect boundary between a homogenous isotropic thermoelastic diffusive half-space and an isotropic elastic layer of finite thickness. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness, and welded contact. The amplitude of surface displacements, temperature change, concentration, and the specific loss of energy are computed numerically. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. Some special cases of interest are also deduced and compared with known results.

An Analytic Solution for the Diffraction of Plane P Waves by a Cylindrical Inclusion in Half Space

This paper presents an analytic solution for the diffraction of plane P waves by a cylindrical inclusion in half space by Fourier-Bessel wave function expansion method, in which the flat surface of half space is approximated by a large curved surface. The equation can be constructed by the continue boundary and the free surface condition. Based on parametric analysis, the impact of the inclusion on surface displacement amplitude is discussed. It is illustrated that there is large difference of the diffraction characteristics between the hard inclusion and soft inclusion. The displacement response depends strongly on the incident angle and frequency. The diffraction effect can be ignored with large embedded depth of the inclusion.

A Study of the Vibration Impact of Underground Circular Structure on the Surrounding Buildings

The finite element model with artificial boundary was used to simulate dynamic response of an underground circular structure (tunnel, cavern) and displacement of the ground surface under incidence of Rayleigh wave, and to quantitatively analyze the effects of incident wavelength, diameter of structure, and liner stiffness on ground surface displacement amplification. The numerical results show that, the surface displacement amplitude with a tunnel can be 1.3 times of that for the case of without the tunnel. It is suggested that the effects of a tunnel on ground motion should be considered when the tunnel is planned and designed.

A study of fundamental solution in orthotropic thermodiffusive elastic media

The present investigation is to study the fundamental solution for two dimensional problem in orthotropic thermodiffusive elastic medium. After applying the dimensionless quantities, we have derived the most general expression for displacements, concentration, temperature, normal and tangential stress. The general solution for a point heat source on the surface of a semi infinite orthotropic thermodiffusive plane has been obtained. A special case of interest is also deduced from the general expression in the absence of diffusion effect. The amplitude of surface displacements, temperature change and concentration are computed and presented graphically to depict the effect of diffusion.

Scattering of Plane Sh-Wave From a Partially Debonded Shallow Cylindrical Elastic Inclusion

ABSTRACTThe scattering of plane SH-wave from a partially debonded shallow cylindrical elastic inclusion in half space is investigated in this paper by complex function method and expansion method of wave function. The debonding regions are considered as multiple arc-shaped interface cracks with non-contacting faces. Firstly, in the inclusion district, the standing wave function in the elastic inclusion with unknown coefficients which satisfies the boundary condition is constructed and generated into the Fourier series; in the half space, the stress and displacement boundary condition around the elastic inclusion can be modeled as the same as the standing wave function in the elastic inclusion. Then, a set of infinite algebraic equations can be obtained around the same boundary and the solution of problem can be gained. In the end, numerical examples of the surface displacement are provided and discussed. It is found that the interface cracks can raise the surface displacement amplitudes to a certain degree.

Scattering of SH Waves by Truncated Semicircular Canyon

The judicious region-matching technique is adopted to derive a series solution for shear horizontal waves scattering from a truncated semicircular canyon on the ground surface. A circular-arc auxiliary boundary is introduced to divide the analyzed region into two subregions. The antiplane motion of each subregion is represented in terms of an infinite series of cylindrical wavefunctions with unknown coefficients. By employing the Graf’s addition formula, boundary conditions on the curved canyon surface and continuity conditions on the auxiliary boundary, the unknown coefficients can be determined. Two modifications of the present theoretical derivation are done for the semicircular canyon and free surface cases. The plotted results reveal how the surface displacement amplitudes are influenced by varying the truncation depth.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (II): Numerical results and discussion

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated (either drained or undrained) cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

Surface brillouin scattering in opaque thin films

Simulations of surface Brillouin scattering (SBS) spectra of TiN, TiAlN, TiC and SiC thin hard films on silicon and diamond substrates have been carried out over a range of film thickness from 5nm to 1000nm. The simulations are based on the elastodynamic Green's function method that predicts the surface displacement amplitudes of acoustic phonons. These simulations provide information essential to understand and analyze experimental data emerging from SBS experiments currently in progress. There are striking differences in the simulated SBS spectra depending on the respective elastic properties of the film and the substrate. In fast on slow situations, the Rayleigh mode is accompanied by broadened resonances; in slow on fast situations, several orders of Sezawa modes are observed together with the Rayleigh mode and sharper resonances. In each case, use of a diamond substrate clearly provides optimal slow on fast conditions. Experimental studies are on process to demonstrate these effects. The velocity dispersion of the modes as a function of the product of surface wavevector and thickness (k//d) has also been simulated, allowing the elastic constants of the films to be determined.

Diffraction of plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space

An analytical solution for the scattering and diffraction of incident plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space is derived by the wave function expansion method. The solution is utilized to analyze the dependence of the computed surface motions on the incident frequencies, incident angles, porosity, boundary drainage and Poisson's ratio. It is shown that, depending on the incident angles, the surface displacement amplitudes around a canyon in a dry poroelastic half-space and saturated poroelastic half-space can be very different. The surface displacement amplitudes of an undrained saturated poroelastic half-space are close to those of a drained saturated poroelastic half-space. For low porosity, the surface displacement amplitudes of a saturated poroelastic half-space are almost identical to those of a dry poroelastic half-space, and drainage condition has little influence on the surface displacement amplitudes. But for high porosity, the effect of drainage condition becomes significant, and for the same porosity, the displacement amplitudes of an undrained saturated half-space will be larger than those of a drained saturated half-space. Poisson's ratio is also an important factor affecting the surface displacement amplitudes around the canyon, both in drained and undrained conditions, but leads to larger effects for an undrained saturated half-space than for a drained saturated half-space. Large pore pressures are found around the canyon and their amplitudes depend on the incident angles and frequencies. Below the surface, the amplitudes of pore pressures are less than they are at the surface, especially for high frequencies.

Scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space, modeled using the indirect boundary element method

The scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space is modeled using the indirect boundary element method in the frequency domain. The free-field responses are calculated to determine the displacements and stresses at the surface of the canyon, and fictitious distributed loads are then applied at the surface of the canyon in the free field to calculate the Green's functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions, and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of fluid saturation, boundary conditions, porosity, and soil layers on the surface displacement amplitudes and phase shifts are discussed, and some useful conclusions are obtained. It is shown that the surface displacement amplitudes due to saturation and boundary conditions, different porosities, or the presence of a soil layer can be very dissimilar, and large phase shifts can be observed. The resulting wavelengths for an undrained saturated poroelastic medium are slightly longer than those for a drained saturated poroelastic medium; and are longer for a drained saturated poroelastic medium than those for a dry poroelastic medium. As porosity increases, the wavelengths become longer; and a layered half-space produces longer wavelengths than a homogeneous half-space.

An Analytic Solution for the Three-Dimensional Diffraction of Plane SV-Waves by Hemispherical Canyon in a Fluid-Saturated Porous Medium Half Space

On the basis of the Biot dynamic theory, an analytic solution of three-dimensional scattering of incident plane SV waves by hemispherical canyons in a fluid saturated porous media half space is derived. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, the effects of frequency and angle of incident waves on the surface displacement amplitudes are discussed. These results are compared with those from the same situation but with an elastic one-phase medium. We conclude that (1) there is a significant difference between the previous single-phase model and the present two-phase model; (2) the normalized displacements on the free surface of alluvial valley are mainly dependent on the incident wave angles, the dimensionless frequency of the incident SV-waves; (3) with the increases of the incident angle, frequency, the displacements become more complicated; and the amplification of the displacement on the free surface of alluvial valley is more prominent than that modeled by single-phase.

An Analytical Solution for the Diffraction of Plane P-Waves by Three-Dimensional Hemispherical Canyon in a Fluid-Saturated Porous Media Half Space

On the basis of the Biot dynamic theory, an analytic solution of three-dimensional scattering and diffraction by hemispherical canyon “ in a fluid saturated porous media half space under plane P-waves incidence is presented. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, and the effects of frequency and angle of incident waves on the surface displacement amplitudes are discussed. These results are compared with those from the same situation but with an elastic one-phase media and two-dimensional circular cylindrical canyons in two-phase media, respectively.

Scattering of Plane SV Waves by Circular‐Arc Alluvial Valleys with Saturated Soil Deposits

AbstractOn the basis of Biot dynamic theory for saturated porous media, an analytic solution of twodimensional scattering and diffraction of plane SV waves by circular‐arc alluvial valleys with saturated soil deposits is presented using the Fourier‐Bessel series expansion technique with the deposits simulated by Biot dynamic theory for saturated porous media, and the half space assumed to be elastic single‐phase media. For incidence beyond critical angle, the surface waves generated are expanded in terms of finite Fourier series. The method is applicable to the case of a wide range of frequencies, and thus makes it preferable to the presently available numerical methods. The surface displacement amplitudes presented by numerical results show that the results depend on the angle of incidence, the dimensionless frequency of the incident SV wave.