Search NASA⌕ Search

SEARCH · Search NASA

Results for “elastic wave equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

CO 2 rock physics modeling for reliable monitoring of geologic carbon storage

Monitoring, verification, and accounting (MVA) are crucial to ensure safe and long-term geologic carbon storage. Seismic monitoring is a key MVA technique that utilizes seismic data to infer elastic properties of CO 2 -saturated rocks. Reliable accounting of CO 2 in subsurface storage reservoirs and potential leakage zones requires an accurate rock physics model. However, the widely used CO 2 rock physics model based on the conventional Biot-Gassmann equation can substantially underestimate the influence of CO 2 saturation on seismic waves, leading to inaccurate accounting. We develop an accurate CO 2 rock physics model by accounting for both effects of the stress dependence of seismic velocities in porous rocks and CO 2 weakening on the rock framework. We validate our CO 2 rock physics model using the Kimberlina-1.2 model (a previously proposed geologic carbon storage site in California) and create time-lapse elastic property models with our new rock physics method. We compare the results with those obtained using the conventional Biot-Gassmann equation. Our innovative approach produces larger changes in elastic properties than the Biot-Gassmann results. Using our CO 2 rock physics model can replicate shear-wave speed reductions observed in the laboratory. Our rock physics model enhances the accuracy of time-lapse elastic-wave modeling and enables reliable CO 2 accounting using seismic monitoring.

58 GEOSCIENCES↗

Sound velocities in shock-compressed soda lime glass: Melting and liquid-state response

Longitudinal sound velocities (and elastic moduli) were determined in soda lime glass (SLG) at peak shock stresses ranging between 40 and 90 GPa. Laser interferometry was used to obtain particle velocity histories and sound velocities by impacting SLG samples on lithium fluoride (LiF) optical windows. In all experiments, the SLG response consists of a sharp jump to a constant state followed by a release wave. The measured longitudinal sound velocities and moduli showed a marked decrease between 52 and 58 GPa, providing experimental evidence for the transformation from an amorphous solid to a liquid in shock-compressed SLG. Furthermore, the stress threshold (~55 GPa) for melting in SLG is considerably lower than the threshold reported in shock-compressed fused silica (~72 GPa), showing the effect of network-modifying cations on the onset of melting. The relative values of sound velocities, shock velocities, and the Hugoniot slopes—between 58 and 90 GPa—are fully consistent with the thermodynamic response of a shock-compressed liquid. Using the experimental results, the Grüneisen parameter (Γ) values were determined for liquid SLG to 90 GPa and then used to provide the Mie-Grüneisen equation of state for liquid SLG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermoelastic properties of tungsten at simultaneous high pressure and temperature

In this work, the compressional ( P ) and shear wave velocities ( S ) and unit cell volumes (densities) of polycrystalline tungsten (W) have been measured simultaneously up to 10.5 GPa and 1073 K using ultrasonic interferometry in conjunction with x-ray diffraction and x-radiography techniques. Thermoelastic properties of W were derived using different methods. We obtained the isothermal bulk modulus K T 0 = 310.3(1.5) GPa, its pressure derivative K ' T 0 = 4.4(3), its temperature derivative at constant pressure ( ∂ K T / ∂ T ) P = – 0.0138 ( 1 ) GPa K – 1 and at constant volume ( ∂ K T / ∂ T ) V = – 0.0050 GPa K – 1 , the thermal expansion α ( 0, T ) = 1.02(27) × 10 –5 + 7.39(3.2) × 10 –9 T (K –1 ), as well as the pressure derivative of thermal expansion ( ∂ α / ∂ P ) T = – 1.44 ( 1 ) × 10 – 7 K – 1 GP a – 1 based on the high-temperature Birch–Murnaghan equation of state (EOS), the Vinet EOS, and thermal pressure approach. Finite strain analysis allowed us to derive the elastic properties and their pressure/temperature derivatives independent of the choice of pressure scale. A least-squares fitting yielded K S 0 = 314.5(2.5) GPa, K S 0 ' = 4.45(9), (∂ K S /∂ T ) P = – 0.0076(6) GPa K –1 , G 0 = 162.4(9) GPa, G 0 ' = 1.8(1), (∂ G /∂ T ) P = – 0.0175(9) GPa K –1 , and α 298 K = 1.23 × 10 – 5 K – 1 . Fitting current data to the Mie–Grüneisen–Debye EOS with derived θ 0 = 383.4 K yielded γ 0 = 1.81 ( 6 ) and q = 0.3 . The thermoelastic parameters obtained from various approaches are consistent with one another and comparable with previous results within uncertainties. Our current study provides a complete and self-consistent dataset for the thermoelastic properties of tungsten at high P – T conditions, which is important to improve the theoretical modeling of these materials under dynamic conditions.

36 MATERIALS SCIENCE↗

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.

Qin, Zhanming↗

Noise transmission into semicylindrical enclosures through discretely stiffened curved panels

An analytical study of sound transmission into semicylindrical enclosures through discretely stiffened curved elastic panels is presented. The transmitted sound is estimated by solving the acoustic wave equation for the interior acoustic field, a Galerkin-like method being used. This solution is then coupled to the vibration of the stiffened panels. The response characteristics of these panels are determined by using a modal analysis where the modes are obtained by the finite element-strip method. Numerical results include spectra of the interior sound pressure due to white noise, turbulent boundary layer and propeller noise inputs.

Chang, M. T.↗

Seismic strain energy partitioning: estimating the strain energy of seismic body waves.

This report details a method to estimate the energy content of various types of seismic body waves. The method is based on the strain energy of an elastic wavefield and Hooke’s Law. We present a detailed derivation of a set of equations that explicitly partition the seismic strain energy into two parts: one for compressional (P) waves and one for shear (S) waves. We posit that the ratio of these two quantities can be used to determine the relative contribution of seismic P and S waves, possibly as a method to discriminate between earthquakes and buried explosions. We demonstrate the efficacy of our method by using it to compute the strain energy of synthetic seismograms with differing source characteristics. Specifically, we find that explosion-generated seismograms contain a preponderance of P wave strain energy when compared to earthquake-generated synthetic seismograms. Conversely, earthquake-generated synthetic seismograms contain a much greater degree of S wave strain energy when compared to explosion-generated seismograms.

58 GEOSCIENCES↗

Impact on multilayered composite plates

Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.

Kim, B. S.↗

Shear wave generation by mode conversion in picosecond ultrasonics: Impact of grain orientation and material properties

Abstract Picosecond ultrasonics has seen wide application in the investigation of interfaces in semiconductors and 3D imaging in biological systems. Shear ultrasonic waves are important for elastic constant and grain orientation measurement in ceramic materials. In this study, we investigate the impact of grain orientation and material's elastic properties on the generation efficiency of shear waves by mode conversion at a transducer thin film/substrate interface. The solution of acoustic wave equations suggests that crystal grain orientation has a strong impact on the generated shear wave amplitude. This dependence is found to be closely related to the magnitude of longitudinal component of wave displacements. The applicability of analytical model is validated by the experimental results from time‐domain Brillouin scattering. Moreover, material properties determine acoustic wave amplitudes based on the acoustic mismatch model and, particularly, large elastic anisotropy defined by Zener ratio favors strong shear waves. In the light of this analysis, several recommendations on suitable grain orientations and film materials are made to facilitate shear wave detection.

Wang, Yuzhou↗

In Situ Determination of Thermoelastic Properties of Magnesite at High Pressure and Temperature With Implications to Seismic Detectability of Moderately Carbonated Lithologies in the Earth's Mantle

Abstract Subduction of carbonate‐bearing oceanic plates into Earth's interior recycles carbon from the surface to the deep mantle. The subducted carbonates can significantly affect mantle properties and dynamics. Magnesite is recognized as one of the major potential carbon hosts in the deep mantle because of its stability up to deep lower mantle conditions. However, despite many previous studies on the equation of state and elastic properties of magnesite, large discrepancies still exist for its elastic moduli and their pressure and temperature derivatives. Here we report in situ density and elastic wave velocity measurements on a natural magnesite at simultaneous high pressure‐temperature conditions up to ∼8 GPa–1073 K in a multi‐anvil apparatus using ultrasonic and synchrotron X‐ray techniques. Global fitting of the data set to finite strain equations yieldsK S0 = 114.0 ± 1.2 GPa, = 4.9 ± 0.3, = (−0.019 ± 0.002) GPa/K,G 0 = 68.6 ± 0.4 GPa,G′ = 1.6 ± 0.1, and = (−0.018 ± 0.001) GPa/K. Compared to other major upper mantle and transition zone minerals, magnesite has intermediateV P , the lowestV S , and the lowest density. Thus, magnesite possesses higherV P /V S ratio than other mantle minerals in normal mantle regions, whereas this feature is less pronounced in subduction zone environments. Modeling of the velocity profiles of carbonated lithologies along different geotherms suggests that moderately‐enriched magnesite domains are unlikely to be detected seismically in the Earth's mantle.

Geochemistry & Geophysics↗

Dynamics of film

The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.

Zak, M.↗

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.↗

Sound velocities of iron-nickel (Fe90Ni10) alloy up to 8 GPa and 773 K: The effect of nickel on the elastic properties of bcc-iron at high P-T

Sound velocities of iron and iron-based alloys at high pressure and high temperature are crucial for understanding the composition and structure of Earth’s and other telluric planetary cores. In this study, we performed ultrasonic interferometric measurements of both compressional (ν P ) and shear (ν S ) velocities on a polycrystalline body-centered-cubic (bcc)-Fe 90 Ni 10 up to 8 GPa and 773 K. The elastic moduli and their pressure and temperature derivatives are derived from least-square fits to third-order finite strain equations, yielding K S0 = 154.2(8) GPa, G 0 = 73.2(2) GPa, K' S0 = 4.6(2), G' 0 = 1.5(1), ∂K S /∂T = –0.028(1) GPa/K, and ∂G/∂T = –0.023(1) GPa/K. Furthermore, a comparison with literature data on bcc-Fe suggests that nickel not only decreases both P and S wave velocities but also weakens the temperature effects on the elastic moduli of Fe-Ni alloys.

36 MATERIALS SCIENCE↗

Implications of Sound Velocities of Natural Topaz on the Seismic L–Discontinuity

Compressional and shear wave velocities of topaz have been measured by ultrasonic interferometry in a multi-anvil apparatus up to 13 GPa at room temperature. By fitting the measured velocities under pressure to finite strain equations, the elastic moduli of topaz and their pressure derivatives were obtained, yielding K S0 = 165.5 (25) GPa, K S ' = 2.9 (1), G 0 = 116.5 (17) GPa, and G' = 1.0 (1). Modeling of the velocity profiles of subducted sediments suggests that at 8 GPa (~240 km depth) the P- and S- wave velocities of the subducted sediments exhibit a first order increase of 10% and 11%, respectively. Furthermore, the comparison between seismic observations and velocity contrasts of sediment + MORB model at 240 km shows dehydration of a 1.5–3.9 km thick sediment layer can potentially contribute to the seismically observed Lehmann discontinuity in Tonga, Japan, Philippine Sea, South America, Indonesia, and South Shetland subduction zones.

36 MATERIALS SCIENCE↗

Sound Velocities of Stishovite at Simultaneous High Pressure and High Temperature Suggest an Eclogite‐Rich Layer Beneath the Hawaii Hotspot

Compressional and shear wave velocities of polycrystalline stishovite (SiO 2 ) have been measured at simultaneous high pressures and temperatures up to 14.5 GPa and 800°C. By fitting velocities to the finite strain equations, the elastic moduli and density were determined to be K S0 = 306.6(46) GPa, $K$$^{′}_{S}$ = 4.92(10), ∂K S /∂T = −0.024(1) GPa/K, G 0 = 229.0(34) GPa, G′ = 1.07(10), ∂G/∂T = −0.017(1) GPa/K, ρ 0 = 4.287(2) g/cm 3 . Our modeling suggested that, in the eclogite, coesite-stishovite transition can increase P and S wave velocities by 2.4% and 3.5%, respectively. A comparison between geophysical observations and our model shows that the coesite-stishovite phase transition in the eclogite can potentially be responsible for the occurrence of the X discontinuity beneath Hawaii. In addition, our current results suggest an eclogite-rich layer between 340 and 450 km depth beneath Hawaii. The eclogite concentration at the top and bottom of the layer is 41–55 vol% and >77 vol%, respectively.

36 MATERIALS SCIENCE↗