INNOVATIONS IN NONLINEAR ACOUSTICS: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum
838(2006); http://dx.doi.org/10.1063/1.2210309View Description Hide Description
We outline the area of “nonclassical” nonlinear acoustics that deals with media exhibiting anomalously strong elastic nonlinearity, including hysteresis, conditioning, and slow dynamics. The entire range of behaviors we term nonlinear, nonlinear, nonequilibrium dynamics (NND). The link between the diverse materials that exhibit NND appears to be the presence of “damage” at many scales, ranging from order 10−8 m to 10−1 m at least. The “damage” may be distributed as in granular materials or isolated, as in a sample with a single crack. As to the precise physical origin of the behavior, it is relatively clear in granular media for instance (Hertz‐Mindlin interaction physics); however, in other materials the origin is less clear. We believe it to be due to shear sliding, related to crack and possibly dislocation dynamics as well as other, as yet unidentified physical processes. Because the origin of the behavior is related to damage, damage diagnostics in solids, nonlinear nondestructive evaluation, follows naturally. New areas of research and application have appeared recently. For instance, NND plays a significant role in earthquake strong ground motion and potentially to earthquake source dynamics. Medical applications are in development as well as nonlinear imaging methods as well as applications to locating landmines.
838(2006); http://dx.doi.org/10.1063/1.2210310View Description Hide Description
Fundamental nonlinearity results from the fact that the interatomic potential function is not a parabola. It determines the third order elastic constants. The means of measuring fundamental nonlinearity in cubic crystals is discussed, as well as conclusions that can be drawn from the measurements. Since many cubic crystals had been measured, an attempt was made to expand the measurements to crystals of other symmetries by measuring LiNbO3. Elasticity is not responsible for nonlinearity in LiNbO3, but LiNbO3 appears to produce a nonclassical nonlinearity. Structural inhomogeneity of ferroelectric LiNbO3 may be the cause. Among the phenomena discussed are non‐exponential echo patterns which cannot be explained by nonparallelism of the sample surfaces and acoustic memory; unusual temperature dependence of ultrasonic attenuation and its temperature hysteresis; amplitude characteristics of ultrasonic attenuation.
838(2006); http://dx.doi.org/10.1063/1.2210311View Description Hide Description
Deviations from linear elasticity in consolidated rocks have been measured by acoustic methods and by quasistatic application of stress since the early 1900s. We have used elastic neutron scattering to probe a large volume (on a grain‐size scale) of a variety of consolidated rocks under dynamic and quasi‐static conditions. Differences between macroscopic external strain and average atomic‐scale strain were determined. Nonlinear behavior is intimately related to strain magnitudes so the microscopic distribution of strain is important. Our results indicate that a very small volume (< 5%) of the rock is responsible for almost all of the nonlinear response of the bulk rock. We discuss our results and possible future experiments.
838(2006); http://dx.doi.org/10.1063/1.2210312View Description Hide Description
When subjected to externally applied forces consolidated granular media (CGM), take a Berea sandstone as example, are elastically soft, unusually nonlinear, and have hysteresis with end point memory. In response to a variety of transient external disturbances CGM exhibit slow dynamics, e.g. log(t) recovery of the strain following a step change in applied pressure. These elastic properties have led to a bricks (sand grains) and mortar (bond system) picture to describe the physics of the system. Because the grains are thermally anisotropic, temperature drives the bond system altogether differently than applied stress. Consequently temperature provides the means to probe new features in the elastic response of CGM. I describe an experiment/analysis in which the temperature, used to probe the elastic state of a CGM, reveals unusual behavior. The elastic state of CGM at fixed applied stress and temperature, is a function of the applied stress protocol and the temperature protocol. Working at constant stress I find that all aspects of the elastic response to temperature exhibit behavior which presents a broad range of time scales, i.e. slow dynamics, and the response to a transient temperature disturbance is asymmetric in the sign of ΔT(t).
838(2006); http://dx.doi.org/10.1063/1.2210313View Description Hide Description
In the presence of cracked defects, material nonlinear response is determined by local contact dynamics which strongly depends on the amplitude of acoustic wave. At moderate driving amplitude, the contact acoustic nonlinearity suggests a fully deterministic scenario of higher harmonic generation and/or wave modulation. Unlike classical nonlinear materials, these effects feature much higher efficiency, specific dynamic characteristics, modulated spectra, and unconventional acoustic waveform distortion. At higher excitation, the contact vibrations acquire a dynamic instability which is a forerunner of transition to chaos. Such a dynamics is interpreted on the basis of nonlinear resonance phenomena for a defect conceived as a set of coupled oscillators. It is shown to result in a decay of external excitation into either a combination frequency pair or a subharmonic mode. For higher‐order contact nonlinearity, the nonlinear spectrum expands considerably to include the ultra‐subharmonic and ultra‐frequency pair modes. Experiments show that even a moderate acoustic excitation of realistic cracked defects gives rise to the instability vibration modes which exhibit threshold behavior and distinctive hysteretic dynamics. All the modes‐contributors to such non‐classical nonlinear spectra display a high localization in the areas of nonlinear contacts and visualize readily various fractured defects in solids. The case studies presented include Hi‐tech and constructional materials and demonstrate their applicability for defect‐selective imaging in nonlinear NDE.
838(2006); http://dx.doi.org/10.1063/1.2210314View Description Hide Description
Obtained theoretical relationship shows that the strength of concrete increases if the nonlinear parameter decreases. Experimental data proved that modulus of elasticity, ultrasound pulse velocity and nonlinear parameter are independent characteristics of concrete. Two nondestructive patent methods based on the measurement of resonant frequency shift and phase shift are described. These nonlinear nondestructive methods can be used when conventional acoustic methods are not applicable for evaluating strength of concrete.
The relationship between static and dynamic modulus is obtained from the thermofluctuation theory and nonlinear equation of state of concrete. Corresponding relationship shows that the ratio of the static to the dynamic modulus of elasticity depends on the strength of concrete, its temperature, ratio and rate of loading, and that dynamic modulus is greater than static modulus of elasticity.
Comparative study illustrates substantial agreement between obtained relationships and existing experimental results as well as general equations given in standards.
Presented data illustrate the potential of the nonlinear approach, and indicate a new direction for nonlinear nondestructive methods of evaluating mechanical properties of concrete.
838(2006); http://dx.doi.org/10.1063/1.2210315View Description Hide Description
This talk is devoted to the memory of outstanding scientist and engineer Vadim A. Robsman who died in January 2005. Dr.Robsman was the Honored Builder of Russia. He developed and applied new methods of nondestructive testing of buildings, bridges, power plants and other building units. At the same time, he published works on fundamental problems of acoustics and nonlinear dynamics. In particular, he suggested a new equation of the 4‐th order continuing the series of basic equations of nonlinear wave theory (Burgers Eq.: 2‐nd order, Korteveg ‐ de Vries Eq.: 3‐rd order) and found exact solutions for high‐intensity waves in scattering media.
838(2006); http://dx.doi.org/10.1063/1.2210316View Description Hide Description
Some new nonclassical nonlinear acoustic phenomena in ferroelectric lithium niobate are reported last years. They are a) thermal hysteresis of nonlinear ultrasonic attenuation, b) acoustic memory, which is a strong non‐exponential echo train that may not be explained by a nonparallelism of a sample, c) acousto‐domain interaction that was detected by X‐Ray technique and consists of a reorientation of the crystal lattice substructures under nonlinear action of ultrasound, d) new class of crystal sonoluminescence, which is generated at ferroelectric surface by the acoustic vibrations. In these phenomena, the involvement of the ferroelectric domain boundaries is experimentally identified by acoustically induced evolution of the X‐ray diffraction patterns, chemical etching of the crystal surfaces, temperature characteristics of the effects observed, and by the changes in acousto‐electric properties of a sample.
In this work, we report our experiments with lithium tantalite vibrators of two different types: a) two‐dimensional multi domain array of the inversely poled ferroelectric domains in a y‐rotated cut, and b) regular vibrator made of a single crystal. We measure the amplitude characteristics of rf‐admittance (Y) of the samples in Megahertz frequency (f) range at room temperature. A strong nonlinearity is detected. The distortions in the Y(f) dependencies occur under increasing of ultrasonic excitation. These distortions are much stronger in multi domain sample with a number of so called domain walls. The experimental results allow making a conclusion on nonlinear vibrations of the domain walls in an acoustic field, and to discuss their contribution to nonlinear nonclassical phenomena.
838(2006); http://dx.doi.org/10.1063/1.2210317View Description Hide Description
Recently, a nonlinear acoustic landmine detection technique has been investigated. In this detection scheme, two tones are broadcast near a buried mine. The acoustic energy couples into the soil and causes both the mine and the surrounding soil to vibrate. Vibration sensors are then used to measure intermodulation frequencies generated in the vicinity of the mine. A comparison of the intermodulation effects above a mine to those at an off target location identifies the position of the buried target. Research indicates that the contrast ratios measured using nonlinear detection exceed those obtained using linear detection. However, the velocities produced at the intermodulation frequencies are significantly less than the velocities measured using linear detection.
The objective is to maximize the on/off target contrast ratio obtained in conjunction with nonlinear acoustic mine detection. This goal will be pursued by experimentally examining excitation methods and the resultant surface velocities at nonlinearly generated frequencies. Specifically, the impact of increasing the primary amplitudes on soil surface velocity will be examined.
Nonlinear Acoustic Experiments Involving Landmine Detection: Connections with Mesoscopic Elasticity and Slow Dynamics in Geomaterials838(2006); http://dx.doi.org/10.1063/1.2210318View Description Hide Description
The vibration interaction between the top‐plate of a buried VS 2.2 plastic, anti‐tank landmine and the soil above it appears to exhibit similar characteristics to the nonlinear mesoscopic/nanoscale effects that are observed in geomaterials like rocks or granular materials. [J. Acoust. Soc. Am. 116, 3354–3369 (2004)]. When airborne sound at two primary frequencies f 1 and f 2 (closely spaced near resonance) undergo acoustic‐to‐seismic coupling, (A/S), interactions with the mine and soil generate combination frequencies | n f 1 ± m f 2 | which affect the surface vibration velocity. Profiles at f 1, f 2, f 1 −(f 2 − f 1) and f 2 +(f 2 − f 1) exhibit single peaks whereas other combination frequencies may involve higher order modes. A family of increasing amplitude tuning curves, involving the surface vibration over the landmine, exhibits a linear relationship between the peak particle velocity and corresponding resonant frequency. Subsequent decreasing amplitude tuning curves exhibit hysteresis effects. New experiments for a buried VS 1.6 anti‐tank landmine and a “plastic drum head” mine simulant behave similarly. Slow dynamics explains the amplitude difference in tuning curves for first sweeping upward and then downward through resonance, provided the soil modulus drops after periods of high strain. [Support by U.S. Army RDECOM CERDEC, NVESD, Fort Belvoir, VA.]
838(2006); http://dx.doi.org/10.1063/1.2210319View Description Hide Description
Experimental results of ultrasonic wave propagation through unconsolidated granular materials are reported. Influence of the applied static pressure and the propagation distance on the linear and nonlinear acoustic properties is studied. The aim of this work is to understand better the linear and nonlinear acoustic propagation through granular assemblages when the wavelength is of the order of the bead diameter. In particular, the role of the so‐called force chains is currently not well understood, as well as the influence of the contact distribution of the medium. In particular, the self‐demodulation of shear wave packets with variation of the excitation amplitude is documented for different configurations of granular media (propagation distance, static pressure etc …). Modeling is currently in progress and should allow together with these results to understand better the acoustic propagation through granular assemblages.
838(2006); http://dx.doi.org/10.1063/1.2210320View Description Hide Description
This study shows for the first time the feasibility of Nonlinear Resonant Ultrasound Spectroscopy (NRUS) techniques for damage characterization in bone. Two diaphysis of bovine bone were subjected to a progressive damage experiment. Fatigue damage was progressively induced in the samples by mechanical testing in 11 steps. At each damage step, the nonlinear elastic parameter was measured using NRUS. For independent assessment of damage, high energy X‐ray CT imaging was performed, but only helped in the detection of the prominent cracks. As the amount of damage accumulation increased, a corresponding increase in the nonlinear response was observed. The measured nonlinear response is much more sensitive than the change in modulus. The results suggest that NRUS could be a potential tool for micro‐damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique.
838(2006); http://dx.doi.org/10.1063/1.2210321View Description Hide Description
In response to the demand for innovative microdamage inspection systems, with high sensitivity and undoubted accuracy, we are currently investigating the use and robustness of several acoustic and ultrasonic NDT techniques based on Nonlinear Elastic Wave Spectroscopy (NEWS) for the characterization of microdamage in aeronautical components. In this report, we illustrate the results of an amplitude dependent analysis of the resonance behaviour, both in time (signal reverberation) and in frequency (sweep) domain. The technique is applied to intact and damaged samples of Carbon Fiber Reinforced Plastics (CFRP) composites after thermal loading or mechanical fatigue. The method shows a considerable gain in sensitivity and an incontestable interpretation of the results for nonlinear signatures in comparison with the linear characteristics. For highly fatigued samples, slow dynamical effects are observed.
Nonlinear Parameter Measurement for Nondestructive Evaluation of Solids : Calibrated Phase Modulation Method838(2006); http://dx.doi.org/10.1063/1.2210322View Description Hide Description
A phase modulation method is used for Nondestructive Evaluation of solid samples. We take advantage of a self reciprocity calibration procedure to achieve quantitative measurements of the nonlinear parameters of homogeneous solids samples made of fused silica, aluminum, steel and glass, as well as inhomogeneous ones (cracked glass and quenched steel).
838(2006); http://dx.doi.org/10.1063/1.2210323View Description Hide Description
Techniques and results are described for obtaining the onset of nonlinearity of forced resonance vibrations in natural dome salt and hydrostatically pressed salt at ∼500 Hz. The technique is centered on the use of an inertially loaded vibrating bar apparatus. The onset of nonlinearity was observed at ∼10−6 strain. The attenuation (Q−1) was observed to increase while the resonant frequency decreased. Concomitant with the nonlinear behavior were asymmetries in the resonance wave and the observation of a memory effect when the samples were subjected to a large number of cycles.
838(2006); http://dx.doi.org/10.1063/1.2210324View Description Hide Description
Non‐Destructive Evaluation has been carried out on three different test objects, with three different methods based on exhibits of slow dynamics and nonlinear effects. The three diverse objects were cast iron, ceramic semi‐conductors on circuit boards, and rubber. The three approaches were Higher Harmonics detection (HH), Nonlinear Wave Modulation Spectroscopy (NWMS), and Slow Dynamics (SD). For all of the objects the three approaches were tried. The results showed that for each of the objects, a different method worked the best. The cast iron worked best with nonlinear wave modulation, the ceramic semi‐conductors worked well with the higher harmonics detection, while the rubber showed best results with slow dynamics.
Multiscale Approach For Simulating Nonlinear Wave Propagation In Materials with Localized Microdamage838(2006); http://dx.doi.org/10.1063/1.2210325View Description Hide Description
A multiscale model for the simulation of two‐dimensional nonlinear wave propagation in microcracked materials exhibiting hysteretic nonlinearity is presented. We use trigger‐like elements with a two state nonlinear stress‐strain relation to simulate microcracks at the microlevel. A generalized Preisach space approach, based on the eigenstress‐eigenstrain formulation, upscales the microscopic state relation to the mesoscopic level. The macroscopic response of the sample to an arbitrary excitation signal is then predicted using a staggered grid Elastodynamic Finite Integration Technique (EFIT) formalism. We apply the model to investigate spectral changes of a pulsed signal traversing a localized microdamaged region with hysteretic nonlinearity in a plate, and to study the influence of a superficial region with hysteretic nonlinearity on the nonlinear Rayleigh wave propagation.
838(2006); http://dx.doi.org/10.1063/1.2210326View Description Hide Description
A pseudo‐spectral time domain algorithm (PSTD) has been developed for solving elastic wave equation in nonlinear hysteretic heterogeneous solids. The hysteretic nonlinearity is introduced owing to a PM space model, based on a multiscale approach. 1D resonant bar simulations and 2D time reversal experiments in a plate with fixed boundaries are presented.
838(2006); http://dx.doi.org/10.1063/1.2210327View Description Hide Description
An approach based on the equivalent medium method is used to describe the propagation of acoustic longitudinal wave in porous viscoelastic medium. Combining the wave equation for the porous medium and the dynamic equation for micropores and using the perturbation method, equations for fundamental and second harmonic are obtained. Treating medium containing micropores as a homogeneous medium, the effective nonlinearity parameter is defined, and a formula for it is achieved. The frequency dependence of effective nonlinear parameter is studied in detail, and its low frequency limit consists with Ostrovsky’s static results.