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POMA - XVII International Conference on Nonlinear Elasticity in Materials
Conference Location: Cefalu, Sicily, Italy Conference Date: 1 - 7 July 2012
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Nonlinear elastic models within linearized elasticity and applications

Vojtech Kulvait

POMA Volume 16, pp. 045002 (August 2012); (9 pages)

Online Publication Date: August 14, 2012

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In this paper there are presented two nonlinear models within the area of linearized elasticity and some applications for them. First model aims to describe the degradation of linearized elastic solid by considering the Hooke's law with material moduli which depends on a concentration of a diffusing fluid. This model is solved numerically on a square sample with a elliptic hole and the fluid diffuses through the hole. Second model introduces constitutive relation where strain is nonlinear function of the stress into the framework of linearized elasticity. This model can be used to model materials for which maximal strain is a priori bounded. It has been recently shown that such models can be justified by means of implicit constitutive theory. Using this model is studied square sample with a V-notch subject to anti-plane stress. Described problems are solved using finite element method.
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43.10.Gi Editorials, Forum
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Linear and nonlinear resonant acoustic spectroscopy of micro bubble clouds

Matthieu Cavaro, Cedric Payan, Serge Mensah, Joseph Moysan, and Jean-Philippe Jeannot

POMA Volume 16, pp. 045003 (August 2012); (14 pages)

Online Publication Date: August 14, 2012

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In a 4th generation Sodium Fast nuclear Reactor (SFR), liquid sodium - the coolant - is topped by an argon cover gas. Due to this presence of argon, various phenomena can lead to gaseous microbubbles presence within sodium. This study deals with the determination of the void fraction of the bubble cloud. The first experiments are conducted with an air-water experimental set-up. A Helmholtz resonator is used as container of the microbubble cloud. First, a linear acoustic method based on the Wood model is presented. It allows a quantitative link between low frequency speed of sound and void fraction. The obtained results with and without bubbles are in accordance with expected void fractions. Then we applied Nonlinear Resonant Ultrasound Spectroscopy (NRUS). Note that the Helmholtz resonance is far below the bubble's resonant frequency. We present a model and associated numerical simulation of NRUS experiments. The objectives were to observe nonlinear behaviour and to link it with bubble's characteristics: void fraction and size. The nonlinear behaviour of the cloud is clearly observed but it is difficult to analyze due to the presence of a cavitation phenomenon. This presence makes the second objective nearly impossible to reach...at present time.
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43.25.Ed Effect of nonlinearity on velocity and attenuation
43.25.Ts Nonlinear acoustical and dynamical systems
43.25.Yw Nonlinear acoustics of bubbly liquids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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Nonlinear ultrasonic testing of carbon fibre reinforced plastics in the very high cycle fatigue regime

Ute Rabe, T. Helfen, Miriam Weikert, Sigrun Hirsekorn, Hans-Georg Herrmann, Christian Boller, Daniel Backe, Frank Balle, and Dietmar Eifler

POMA Volume 16, pp. 045004 (August 2012); (6 pages)

Online Publication Date: August 14, 2012

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Carbon fibre reinforced plastics (CFRP) are applied as a light-weight construction material. In their lifespan in service CFRP components are exposed to variable loads, which can amount to 1011 load cycles. It is therefore important to examine the fatigue of CFRP materials in the very high cycle regime (more than 107 loading cycles). In a joint project a three point bending ultrasonic fatigue testing system was developed at WKK. A high amplitude sinusoidal vibration is added to a static load. The operating frequency of the system f = 20 kHz is used for sample load case and at the same time as input for online ultrasonic monitoring of the fatigue process. CFRP plate material with a thickness of 4 mm was investigated. During the fatigue process the vibrations of CFRP samples were measured with a laser vibrometer and a microphone. The analysis methods fast Fourier, short time Fourier, and Hilbert Huang transformation were used to evaluate the linear and nonlinear spectral content of the signals. Increase of nonlinearity with increasing amount of fatigue cycles was observed. Non-destructive testing methods were used to examine the initial state as well as the different fatigue states of the samples during the loading intervals.
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43.25.Ts Nonlinear acoustical and dynamical systems
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Prediction of Static Moduli in Near Surface Jointed Rocks from Full Wave Sonic and Other Well Log Data

F. Chalupa

POMA Volume 16, pp. 045005 (August 2012); (8 pages)

Online Publication Date: August 17, 2012

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There is a well known difference between values of elastic moduli determined statically (by a rock mechanical test) and dynamically (using velocities of compressional and shear waves). Static ones are demanded as main design parameters in construction. Main disadvantages are that these measurements depend on core availability and the test itself is relatively slow and therefore expensive. Dynamic values are available from well logs, more or less continuously covering whole length of the borehole. The difference between static and dynamic moduli seems to be small in compact rocks and is increasing as the same material is being damaged. This is due to increasingly nonlinear elastic behaviour of the rock caused by damage. Effects of damage and weathering can be measured by a set of different well logging methods. The results can be used as data for suitable mathematical model to determine effective moduli which should be equivalent to static ones. Some early data from well logs and laboratory measurements on compact limestones were presented.
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43.20.Hq Velocity and attenuation of acoustic waves
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Nonlinear wave modulation spectroscopy: Quasistatic solution and experimental evidence

Jan Kober and Zdenek Prevorovsky

POMA Volume 16, pp. 045006 (August 2012); (13 pages)

Online Publication Date: August 17, 2012

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Nonlinear Wave Modulation Spectroscopy (NWMS) is one of Nonlinear Elastic Wave Spectroscopy (NEWS) methods proven as very sensitive to the variety of material damage ranging from distributed microdamage to single cracks. The experimental procedure consists of simultaneous excitation of a specimen by two harmonic waves with frequencies f0 resp. f1. Nonlinear parameters can be estimated by analysis of harmonic and intermodulation component dependencies in the response signal. The current methodology of NWMS evaluation is based on dynamic solution of classical nonlinear response and quadratic hysteretic model. This describes a case with distributed microdamage, however in case of a localized damage e.g. a single crack, a quasistatic solution is more appropriate. The quasistatic responses of the same model were computed for varying input parameters. To properly describe hysteretic response an amplitude ratio dependence of nonlinear spectral components was found to be the most fitting. By using the scaling relations, an universal way of description of nonlinear spectral components was derived. The results of theoretical analysis were supported by an experiment. A new approach of hysteretic nonlinearity evaluation was proposed.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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Multiwave imaging of the Earth's subsurface : a laboratory scale feasibility study

Thomas Gallot, Alison Malcolm, Steve Brown, Dan Burns, Michael Fehler, Thomas Szabo, and Zhenya Zhu

POMA Volume 16, pp. 045007 (August 2012); (27 pages)

Online Publication Date: August 17, 2012

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Multi-wave high resolution imaging methods have been developped in medical imaging. The feasibility of similar methods for geophysical applications has been studied. An interesting configuration is the subsurface imaging in a km scale where a compressional wavefield can be measured between 2 boreholes. A perturbation of this wavefield by shear waves created from the surface could creates a non-linear interaction. In this context, preliminary laboratory scale experiments have been performed in rocks (berea sandstones). The interaction between shear waves and compressional waves has been studied. The shear wave is generated by a shear transducer in the tens of kHz and used as a "localized pump". The localization of this pump is essential for a possible imaging application. The probe is a compressional pulse in the hundreds of kHz range. In this configuration, the delay of the ultrasounds pulse arrival, the time of flight modulation by nonlinear interaction is studied. Fast and slow nonlinear dynamics can be observed in this configuration. This experimental work is in progress.
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43.25.Dc Nonlinear acoustics of solids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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Application of nonlinear elastic resonance spectroscopy for damage detection in concrete

Loren W. Byers, Paul A. Johnson, and James A. Tencate

POMA Volume 16, pp. 045008 (September 2012); (15 pages)

Online Publication Date: September 20, 2012

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Nonlinear resonance ultrasound spectroscopy experiments were conducted on naturally aged concrete cores, one chemically and mechanically damaged by alkali-silica reactivity (ASR), and a similar sample showing little ASR damage. Both exhibited nonlinear behavior, similar to many other damaged materials. It was found that the damaged sample responds more nonlinearly, manifested by a larger resonant peak shift, i.e., modulus shift, as a function of strain amplitude. Further, as in many other materials, slow dynamics were present. The nonlinear response observed in these two concrete samples demonstrates that nonlinearity is an extremely sensitive indicator of damage. The results and story---now over two decades old---of how these experiments came about are revisited in this talk with an eye on future research and funding possibilities and to discuss lessons learned in the marketing of this research.
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43.20.Ks Standing waves, resonance, normal modes
43.25.Dc Nonlinear acoustics of solids
43.25.Gf Standing waves; resonance
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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Nonlinear ultrasound monitoring of single crack propagation in cortical bone

Sylvain Haupert, Sandra Guerard, David Mitton, Françoise Peyrin, and Pascal Laugier

POMA Volume 16, pp. 045009 (September 2012); (8 pages)

Online Publication Date: September 20, 2012

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Accumulation of bone microdamage is suspected to lead to severe impairment of mechanical properties with an increase in skeletal fragility and fracture risk. The objective of the study was to evaluate the sensitivity of nonlinear resonant ultrasound spectroscopy (NRUS) measurements to the propagation in cortical bone of a single microcrack induced by 4-point bending mechanical loading. Twelve human cortical bone specimens were machined as parallelepiped beams (50*2*2mm) to unambiguously identify resonant modes for NRUS measurements. A central notch of 600{lower case mu}m was made to control crack initiation and propagation during four-point bending loading. The nonlinear hysteretic elastic coefficient ({lower case alpha}f) was derived from NRUS measurements achieved in dry and wet conditions. Each bone specimen was probed by a swept-sine around its first compression mode, applying progressively increasing drive levels. Moreover, the buried crack length was assessed by synchrotron radiation micro-computed tomography with a spatial resolution of 1.4{lower case mu}m. Despite between-sample variability, {lower case alpha}f increased significantly in the damaged state (44.9±85.4) compared to the initial value (5.5±1.5) in the control undamaged state. Crack length was significantly correlated to the nonlinear elastic parameter {lower case alpha}f (r²=0.78, p<0.001). These results suggest that NRUS is sensitive to damage accumulation and can be used as a marker of bone damage.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
43.80.Qf Medical diagnosis with acoustics
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The role of prestress on propagation and interaction of weakly nonlinear elastic waves

Wlodzimierz Domanski

POMA Volume 16, pp. 045010 (October 2012); (6 pages)

Online Publication Date: October 15, 2012

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After the review of the results of some seminal research on the role of prestress in elasticity, propagation and interaction of weakly nonlinear elastic plane waves in an initially stressed material are considered. The model of a prestressed solid is based on the theory of invariants. The strain energy function of an initially stressed elastic material depends not only on the invariants of the strain or on the invariants of the initial stress but also on the combined invariants of both strain and initial stress. The influence of prestress on the evolution equations for the amplitudes of weakly nonlinear elastic waves, as well as on the waves' interaction coefficients, is investigated.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Ed Effect of nonlinearity on velocity and attenuation
43.25.Ts Nonlinear acoustical and dynamical systems
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Potential of the scaling subtraction and the cross-correlation methods for osseointegration monitoring

Jacques Riviere, Sylvain Haupert, Pascal Laugier, and Paul A. Johnson

POMA Volume 16, pp. 045011 (October 2012); (16 pages)

Online Publication Date: October 15, 2012

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The long-term perspective of this study is to implement in vivo some new noninvasive methods to monitor the bone prostheses sealing or osseointegration (dental implants, hip prostheses). Although the most widely used clinically, X-ray radiography suffers from low sensitivity, limiting for instance its ability to detect early loosening of a prosthesis. The potential of methods developed over the past twenty years and based on linear elasticity measurements has been shown in vitro, but their in vivo effectiveness is still questionable. The objective is to evaluate the potential of methods based on nonlinear elasticity measurement which showed greater sensitivity than the linear elastic response to the presence of weak contacts within a rigid structure, such as cracks. Two different methods called Scaling Subtraction Method and Cross-Correlation Method are compared in this study, using an experimental osseointegration mimicking model. One parameter extracted from the cross-correlation method is shown to be as sensitive as a linear clinical device subject to a thorough optimization. Further, this study shows that cross-correlation based methods are more sensitive than ones based on subtraction/addition, such like pulse inversion and derived methods.
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43.25.Dc Nonlinear acoustics of solids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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General solutions to the mechanical contact problem

Vladislav Aleshin, Koen Van Den Abeele, and Olivier Bou Matar

POMA Volume 16, pp. 045012 (October 2012); (11 pages)

Online Publication Date: October 15, 2012

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A theory for mechanical contact of solids with friction is developed for a wide range of contacting profiles and loading histories. The starting point of the approach is the normal load-displacement dependency that can be obtained via analytical solutions for regular e.g. axisymmetric profiles and via modeling for random surface topologies. Then, the Jaeger elastic principle based on similarity of equations for normal and tangential deformation allows us to obtain the tangential load-displacement relation for simple loading, i.e. for constant normal and tangential actions, and, moreover, to replace rough profiles by equivalent axisymmetric ones. Since in the presence of tangential action a zone of stick and a zone of slip appear in the contact area, the problem becomes memory dependent. An original general scheme of memory organization called memory diagram is presented. Evolutions of memory diagrams are governed by a special set of rules; the solution for a given memory diagram is purely analytical, although sometimes implicit. The range of applications can cover the contact acoustical nonlinearity, solids with cracks and geomaterials, vibrations of objects with partial contact, etc.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Ts Nonlinear acoustical and dynamical systems
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Probing materials damage at various depths by use of Time Reversal Elastic Nonlinearity Diagnostic: Application to concrete.

Cedric Payan, T. J. Ulrich, Pierre-Yves Le Bas, Tarik Saleh, and M. Guimaraes

POMA Volume 16, pp. 045013 (October 2012); (22 pages)

Online Publication Date: October 15, 2012

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In the context of license renewal in the field of nuclear energy, maintaining in service and re-qualifying existing concrete structures for the period of long term operations is challenging. This paper aims at providing some quantitative information related to the degree of micro-cracking of concrete and cement based materials in the presence of thermal damage. Time Reversal Elastic Nonlinearity Diagnostic (TREND) is based on the use of time reversal to focus energy at a prescribed location. This focused elastic wave energy is then analyzed for nonlinear frequency content. By varying the frequency content of the focused waveforms, the technique can be used to probe different depths relative to the surface, i.e., the TREND will probe the surface and penetrate to a depth defined by the wavelength of the focused waves. To validate this approach, we need reference measurements. We develop a methodology based on Resonant Ultrasound Spectroscopy, numerical simulations and Nonlinear Resonant Ultrasound Spectroscopy to get quantitative values of nonlinearity. These results are quantitatively correlated to the evolution of concrete microstructure in the presence of thermal damage. We then show the validity of using TREND at various depths by the good correlation between the nonlinearity measured using NRUS and TREND.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Gf Standing waves; resonance
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Elastic Linear and Nonlinear Behaviors in Slip Processes

Paul A. Johnson

POMA Volume 16, pp. 045014 (October 2012); (20 pages)

Online Publication Date: October 15, 2012

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In the earth there exist a spectrum of types of slip that range from stick-slip resulting in earthquakes to very slow slip with little accompanying seismic emission. Quasistatic stress changes or dynamic wave forcing may trigger all of these types of slip. We are interested in identifying the 'remote signatures' of slip in the earth, including triggered slips. An example of a remote signature are seismic waves from an earthquake that are recorded at the earth's surface. It appears that changes in earthquake occurrence time (recurrence) are another signature that can be used to infer slip and possibly distinguish triggered slip from natural slip. Velocity change and thickness or volume change are also potential signatures of interest.
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43.25.Dc Nonlinear acoustics of solids
43.40.Fz Acoustic scattering by elastic structures
43.40.Ph Seismology and geophysical prospecting; seismographs
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Improving time reversal focusing through deconvolution: 20 questions

T. J. Ulrich, Brian Anderson, Pierre-Yves Le Bas, Cedric Payan, Johannes Douma, and Roel Snieder

POMA Volume 16, pp. 045015 (October 2012); (21 pages)

Online Publication Date: October 15, 2012

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multimedia

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Time reversal is a proven technique for focusing wave energy in time and space. A known side effect of the process is the presence of temporal side lobes and spatial fringes, which can be undesirable depending upon the application. A deconvolution, also known as an inverse filter, technique has been developed to improve temporal compression of the focal signal. This presentation will explore the use of deconvolution in comparison to standard time reversal and provide insight into the process through visualizations of the wave-fields. Attention will also be given to the effect of the deconvolution technique upon nonlinear elasticity applications such as the time reversed nonlinear elasticity diagnostic (TREND).
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43.20.Bi Mathematical theory of wave propagation
43.25.Dc Nonlinear acoustics of solids
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
43.60.Tj Wave front reconstruction, acoustic time-reversal, and phase conjugation
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Macro-crack characterization in concrete by diffuse ultrasound under low frequency dynamic loading

Audrey Quiviger, Cedric Payan, Jean-Fraçois Chaix, Vincent Garnier, and Jean Salin

POMA Volume 16, pp. 045016 (October 2012); (16 pages)

Online Publication Date: October 15, 2012

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In concrete, a crack reveals a morphology comprised of an external part with a surface opening, and a completely or partially closed part below the surface with potentially partially opened zone. Conventional ultrasound methods defined by ASTM or ISO normalization are founded on low frequency waves time of flight measurement. Consequently, they are unable to detect a few centimeter scale surface breaking crack. At higher frequencies, strong multiple scattering phenomena occur due to the presence of aggregates, making impossible standard waveform analysis. The main issue of this paper is to use higher frequencies and to take advantage of multiple scattering by the study diffuse waves transport and its interaction with partial contacts along the crack. The ability of diffuse ultrasound to characterize the opened zone of the crack is shown. However, the closed part of the crack remains imperceptible. To overcome this difficulty, a low frequency dynamic loading is superimposed to diffuse waves in order to alternatively open and close portions the crack. Experimental results associated with numerical simulations show the validity of the method and should subsequently provide physical interpretations about the morphology of a real macro-crack in concrete.
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43.20.Fn Scattering of acoustic waves
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics
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The influence of external factors on the elastic properties of 3-D unconsolidated granular medium

A. Korobov, Natalia Shirgina, and Alexey Kokshaiskiy

POMA Volume 16, pp. 045017 (October 2012); (10 pages)

Online Publication Date: October 15, 2012

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The nature of propagation of elastic waves in unconsolidated granular media is appreciably different from their propagation in continuous media. State of the contacts between grains has a significant influence on elastic properties of granular media. We present the results of investigations of the influence of external factors (for example, the external variable pressure, the amplitude of the probe signal) on the elastic properties of unconsolidated granular 3-D structure. We used steel balls with a diameter of 2 mm and 4 mm, packed into a cell of the textolite as a model medium. Structure was attached by an external static force, the magnitude of which can be varied. The dependence of the velocity of longitudinal waves on static external compression of the medium was measured. The dependence of the velocity of elastic waves on the amplitude of the probe signal for different values of the external static compression was investigated. The velocity of elastic waves with increasing amplitude decreased. As the external compression increased, the dependence of the velocity of elastic waves on the amplitude of the signal weakened. We present a theoretical analysis of the experimental results.
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43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.25.Dc Nonlinear acoustics of solids
43.25.Ts Nonlinear acoustical and dynamical systems
43.35.Ty Other physical effects of sound
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Preisach-Mayergoyz space model density identification for nonlinear physical systems: "L-2" and "D-divergence" minimization methods

Jana Papoušková, Václav Kus, and Serge Dos Santos

POMA Volume 16, pp. 045018 (October 2012); (11 pages)

Online Publication Date: October 15, 2012

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Hysteresis is a phenomenon occurring in ferromagnetic and ferroelectric materials, as well as in a course of deformation of some materials, which are flexible, elastic, or compressible. One of the examples of the non-classical nonlinear materials, for which the hysteresis behavior play the key role, is the sandy rock. In electronics, the hysteresis is produced by positive feedback to avoid an oscillation. Phenomenological models describing hysteresis include Preisach-Mayergoyz space model (PM space) based approaches. It became more important during the last years in the field of Nonlinear Elastic Wave Spectroscopy (NEWS), which is in progress with the growing number of NDT technologies. Hysteresis of electromagnetic relays, which is one of the basic type of hysteresis in electronics, will be introduced. The results of the measurements used for PM Space density identification under the classical "L-2" space metric distance or using special statistical nonmetric distances called "D" - divergences originated from information theoretic concept will be presented. Employing these extended "D" - divergences leads to achieve the PM space density identification which is more robust against outliers or other measurement errors potentially present in the data sets.
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43.25.Ba Parameters of nonlinearity of the medium
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First simulations of the candy can concept for high amplitude non-contact excitation

Steven Delrue, Pierre-Yves Le Bas, T. J. Ulrich, Brian Anderson, and Koen Van Den Abeele

POMA Volume 16, pp. 045019 (October 2012); (27 pages)

Online Publication Date: October 15, 2012

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Nonlinear acoustic techniques have proven to be extremely sensitive to early stage damage detection. However, the main issue preventing widespread use of these techniques is that they require high amplitude waves to induce the nonlinear response. As an alternative to transducers bonded to the test material, a more practical realization consists of developing non-contact ultrasonic transducers capable of generating high amplitude waves. Time reversal (TR) techniques are particularly suited to concentrate sound energy at a chosen location in space and at a specific instance in time. In this paper, it is numerically demonstrated how TR and a "candy can" (i.e. a highly scattering, contained medium) can be used to create a focused, high amplitude non-contact transducer. We developed and investigated the results of a finite element model of the "candy can" concept. The model allows to demonstrate the concept in different situations and illustrates the ability to pre-calibrate the non-contact source in air. The results of the simulations allow a better insight in the new concept and will be used in a further stadium for optimization of the high amplitude non-contact source.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.20.Ks Standing waves, resonance, normal modes
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.60.Tj Wave front reconstruction, acoustic time-reversal, and phase conjugation
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Modeling nonlinear response from distributed damage and kissing bonds

Koen Van Den Abeele, Steven Delrue, Sylvain Haupert, and Vladislav Aleshin

POMA Volume 16, pp. 045020 (October 2012); (36 pages)

Online Publication Date: October 15, 2012

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A large number of models have been proposed in the field of nonlinear elastic wave propagation in damaged solids to validate experimental observations with theoretical predictions. In this contribution, we distinguish between "distributed" and "interface" implementations of nonlinearity, and deduce particular properties for the differing models. For the models of distributed damage, we prove that many of the currently suggested models can be seen as particular cases of the PM-model for specific protocols and parameters. In addition, we illustrate the potentiality of interface models to validate experimental results reported by other research groups.
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43.25.Ba Parameters of nonlinearity of the medium
43.25.Dc Nonlinear acoustics of solids
43.25.Ts Nonlinear acoustical and dynamical systems
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