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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Elastic moduli of transversely isotropic graphite fibers and their composites

The paper demonstrates that it is possible to calculate the complete set of elastic mechanical properties for graphite-epoxy fiber-reinforced materials at any fiber-volume fraction by modifying equations previously developed to include transversely isotropic graphite-fiber properties. Experimental verification of the modified equations is demonstrated by using these equations to curve fit elastic-property data obtained ultrasonically over a range of fiber-volume fractions. Material systems under consideration are T300/5208, AS-3501 and Modomor II/LY558 graphite epoxy. Using the modified equations it is possible to extrapolate for fiber properties. From Modomor II/LY558 ultrasonic data, it is shown that five out of seven extrapolated graphite-fiber properties are consistent with the assumption that graphite fibers are transversely isotropic. Elastic properties for T300/5208 and AS-3501 are ultrasonically evaluated by propagating stress waves through six individual specimens cut at various angles from a block of unidirectional material. Particular attention is devoted to specimen dimensions. To demonstrate the need for accurately calculating or experimentally measuring all lamina elastic properties, a brief discussion is included on the effect that variations in lamina elastic properties have on calculating interlaminar stresses.

Kriz, R. D.↗
NASA NTRS2005

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Ambur, Damodar R.↗
DOE OSTI2020

Impact of nuclear reactor radiation on the performance of AlN/sapphire surface acoustic wave devices

The performance of an AlN/sapphire surface acoustic wave (SAW) delay line device was characterized in real time under irradiation inside a nuclear reactor. Both its resonant frequency and transmission efficiency were observed to respond to a change in reactor power. The response follows an exponentially saturating behavior after a step power increase, followed by an exponentially decaying recovery after reactor shutdown. A sensitivity analysis based on the governing electro-mechanical equations shows that the frequency shift can be attributed to the softening of sapphire’s elastic constants under neutron radiation. Additionally, a kinetic rate equation is adopted to interpret device response and describe its microstructural evolution. These results suggest that the AlN/sapphire SAW device remains functional under irradiation, is sensitive to neutron and gamma ray fluxes, and offers an opportunity for remote sensing and in-situ measurement of material properties when exposed to nuclear reactor environment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
NASA NTRS1983

The input mobility of an infinite circular cylindrical elastic shell filled with fluid

The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.

Fuller, C. R.↗
NASA NTRS1984

Vibration and flutter of mistuned bladed-disk assemblies

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Kaza, K. R. V.↗
NASA NTRS1984

Vibration and flutter of mistuned bladed-disk assemblies

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbufans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Rao, K.↗
NASA NTRS1972

Elastic wave propagation in a joined cylindrical-conical-cylindrical shell.

The problem of longitudinal impact of a thin finite joined shell, consisting of a cylinder-truncated cone-cylinder, is analyzed both experimentally and analytically. The model analyzed is a 1/100 scale replica of a portion of the Apollo/Saturn V vehicle. Experimental results were obtained from a drop-test system. Longitudinal and circumferential strain pulses were monitored on each section of the joined shell. The velocity of the impacter ring prior to impact was measured and used as a boundary condition in the solution of the governing partial differential equations. A bending theory, including transverse shear, radial inertia, and rotary inertia effects, was used to analyze the finite joined shell. Good agreement between analytical and experimental strain profiles was obtained.

Rose, J. L.↗
NASA NTRS1934

Impact buckling of thin bars in the elastic range for any end condition

Following a qualitative discussion of the complicated process involved in a short-period, longitudinal force applied to an originally not quite straight bar, the actual process is substituted by an idealized process for the purpose of analytical treatment. The simplifications are: the assumption of an infinitely high rate of propagation of the elastic longitudinal waves in the bar, limitation to slender bars, disregard of material damping and of rotatory inertia, the assumption of consistently small elastic deformations, the assumption of cross-sectional dimensions constant along the bar axis, the assumption of a shock-load constant in time, and the assumption of eccentricities on one plane. Then follow the mathematical principles for resolving the differential equation of the simplified problem, particularly the developability of arbitrary functions with steady first and second and intermittently steady third and fourth derivatives into one convergent series, according to the natural functions of the homogeneous differential equation.

Taub, Josef↗
DOE OSTI2023

Direct imaging of shock wave splitting in diamond at Mbar pressure

Understanding the behavior of matter at extreme pressures of the order of a megabar (Mbar) is essential to gain insight into various physical phenomena at macroscales—the formation of planets, young stars, and the cores of super-Earths, and at microscales—damage to ceramic materials and high-pressure plastic transformation and phase transitions in solids. Under dynamic compression of solids up to Mbar pressures, even a solid with high strength exhibits plastic properties, causing the induced shock wave to split in two: an elastic precursor and a plastic shock wave. This phenomenon is described by theoretical models based on indirect measurements of material response. The advent of x-ray free-electron lasers (XFELs) has made it possible to use their ultrashort pulses for direct observations of the propagation of shock waves in solid materials by the method of phase-contrast radiography. However, there is still a lack of comprehensive data for verification of theoretical models of different solids. Here, we present the results of an experiment in which the evolution of the coupled elastic–plastic wave structure in diamond was directly observed and studied with submicrometer spatial resolution, using the unique capabilities of the x-ray free-electron laser (XFEL). The direct measurements allowed, for the first time, the fitting and validation of the 2D failure model for diamond in the range of several Mbar. Our experimental approach opens new possibilities for the direct verification and construction of equations of state of matter in the ultra-high-stress range, which are relevant to solving a variety of problems in high-energy-density physics.

36 MATERIALS SCIENCE↗
NASA NTRS2020

Elastic wave analyzer for icy sub-surfaces (EWAIS) in water-bearing worlds

In this paper, we discuss the current status of the development of an elastic wave analyzer for icy sub-surface (EWAIS). We begin with an introductory overview of the necessity to develop an active elastic wave transmitter that will enable reaching distances of kilometer thru ice. It is being developed to be driven by piezoelectric transducers with a bouncing constrained mass that impacts a transmission head. The EWAIS transmits the waves at two distinct frequencies; the primary frequency at ~10 kHz for high resolution, and the secondary converted low frequency (LF) in the range of 100 to 500 Hz for long distance transmission. Sonar equation was used for the estimation of required source level, and an impact force sensor is used for the performance measurement of EWAIS prototype.

Lee, Hyeong Jae↗
DOE OSTI2023

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

Dynamic simulation↗
DOE OSTI2021

The influence of δ-(Al,Fe)OOH on seismic heterogeneities in Earth’s lower mantle

The high-pressure phases of oxyhydroxides (δ-AlOOH, ε-FeOOH, and their solid solution), candidate components of subducted slabs, have wide stability fields, thus potentially influencing volatile circulation and dynamics in the Earth’s lower mantle. Here, we report the elastic wave velocities of δ-(Al,Fe)OOH (Fe/(Al + Fe) = 0.13, δ-Fe13) to 79 GPa, determined by nuclear resonant inelastic X-ray scattering. At pressures below 20 GPa, a softening of the phonon spectra is observed. With increasing pressure up to the Fe 3+ spin crossover (~ 45 GPa), the Debye sound velocity (vD) increases. At higher pressures, the low spin δ-Fe 13 is characterized by a pressure-invariant vD. Using the equation of state for the same sample, the shear-, compressional-, and bulk-velocities (v S , v P , and v Φ ) are calculated and extrapolated to deep mantle conditions. The obtained velocity data show that δ-(Al,Fe)OOH may cause low-v Φ and low-v P anomalies in the shallow lower mantle. At deeper depths, we find that this hydrous phase reproduces the anti-correlation between v S and v Φ reported for the large low seismic velocity provinces, thus serving as a potential seismic signature of hydrous circulation in the lower mantle.

58 GEOSCIENCES↗
NASA NTRS2003

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗
DOE OSTI2021

Sound speed measurements in silver shock compressed to 300 GPa: Solid-state transition, melting, and liquid-state response

To gain insight into the thermodynamic response of shock compressed Ag states corresponding to the face-centered-cubic (fcc) to body-centered-cubic (bcc) transformation and melting observed using in-situ x-ray diffraction (XRD) measurements, we present longitudinal sound speed results and their analysis in Ag at peak stresses ranging from 60 to 300 GPa. The measured sound speeds increased linearly with density compression to 171 GPa, showing that the sound speeds (and longitudinal moduli) in the fcc and bcc phases are very similar. Between 171 and 218 GPa, the sound speed dropped significantly, consistent with the melting reported using XRD measurements in shock compressed Ag. From 218 to 300 GPa, the increasing sound speeds and Hugoniot states provide a determination of the liquid phase Ag response. In particular, determination of the Grüneisen parameter (Γ) showed that the density – Grüneisen parameter product (ρΓ) for liquid Ag is constant, but differs significantly from that for solid Ag at ambient conditions. Furthermore, the Mie- Grüneisen equation of state can be used to describe the Hugoniot and off-Hugoniot response of liquid Ag.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Mesoscale simulations of pressure-shear loading of granular tungsten carbide

Numerical simulations of pressure-shear loading of a granular material are performed using the shock physics code CTH. A simple mesoscale model for the granular material is used that consists of a randomly packed arrangement of solid circular or spherical grains of uniform size separated by vacuum. The grain material is described by a simple shock equation of state, elastic perfectly plastic strength model, and fracture model with baseline parameters for WC taken from previous mesoscale modeling work. Simulations using the baseline material parameters are performed at the same initial conditions of pressure-shear experiments on dry WC powders. Except for some localized flow regions appearing in simulations with an approximate treatment of sliding interfaces among grains, the samples respond elastically during shear, which is in contrast to experimental observations. By extending the simulations to higher shear wave amplitudes, macroscopic shear failure of the simulated samples is observed with the shear strength increasing with increasing stress confinement. The shear strength is also found to be strongly dependent on the grain interface treatment and on the fracture stress of the grains, though the variation in shear strength due to fracture stress decreases with increasing stress confinement. At partial compactions, the transverse velocity histories show strain-hardening behavior followed by formation of a shear interface that extends through the transverse dimensions of the sample. Near full compaction, no strain hardening is observed and, instead, the sample transitions sharply from an elastic response to formation of an internal shear interface. Agreement with experiment is shown to worsen with increasing confinement stress with simulations overpredicting the shear strengths measured in experiment. The source of the disagreement can be ultimately attributed to the Eulerian nature of the simulations, which do not treat contact and fracture realistically.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sound Velocities in Vanadium Reveal Complex Elastic Behavior at High Pressures

Compressional (VP) and shear (VS) wave velocities of polycrystalline vanadium were measured simultaneously up to 11.5 GPa at room temperature using ultrasonic interferometry in a multi-anvil press. Complex softening behavior in VS and resulting shear moduli are discovered, possibly revealing a precursor to the reported phase transition within 30–60 GPa. The current data enables a comprehensive assessment of the elastic and mechanical properties of vanadium at high pressures, including bulk and shear moduli, Young’s modulus, Poisson’s ratio, and Pugh’s ratio. Through fitting to the 3rd-order finite strain equations, the elastic moduli and their pressure derivatives were determined to be K S0 = 151 (2) GPa, G 0 = 46.9 (8) GPa, K$^{’}_{S0}$ = 3.47 (5), and G$^{’}_{0}$ = 0.62 (1). These experimental results allow us to compare with and benchmark the existing Steinberg–Guinan models for extrapolations to extreme pressure and temperature conditions.

36 MATERIALS SCIENCE↗