Wave Propagation Experiments Research Articles

Attenuation and Dispersion Characteristics of Longitudinal Waves Propagating in Viscoelastic Rods

The shape of a stress wave in a thin viscoelastic rod changes as it propagates because of attenuation and dispersion that mainly depend on the material damping. In a thick viscoelastic rod, however, the shape of the stress wave is also affected by a geometrical factor, such as a rod diameter. Pochhammer-Chree theory as well as Love theory is developed for viscoelastic rods of finite thickness in order to study geometrical effects on the attenuation and dispersion properties. Applying the Fourier transformation to both theories, attenuation and dispersion properties are evaluated in the frequency domain. Several wave propagation experiments are performed on polymethyl methacrylate (PMMA) rod specimens to evaluate the analytical results. Analytical solutions of the transient response are obtained to examine three-dimensional effects on axial strain-time histories. In addition, the applicability of Elementary theory is discussed.

Rain Attenuation at 103 GHz in Millimeter Wave Ranges

We have conducted a millimeter wave propagation experiment at 103 GHz (2.9 mm) on a propagation path of 390 m. The results were compared with the rain attenuation calculations from the Marshall-Palmer, Best, Joss-Thomas-Waldvogel and Weibull distributions for raindrop-size. It has been shown that the Weibull distribution has a good agreement with the experiments.

Ultrasonic Characterization and Inspection of Open Cell Foams

The nondestructive characterization of the material properties and the detection of hidden discontinuities in a highly porous, open cell, carbon foam using ultrasonics are presented. The propagation of ultrasonic waves in carbon foam specimens and their relationship with the elastic properties of the material are studied through theoretical modeling and laboratory experiments. The geometric and the overall elastic properties of the material are determined from microscopic data and wave propagation experiments performed under dry and fluid coupling conditions. A broadband, hybrid system based on laser generation and air-coupled detection of ultrasound is first employed for primary wave (P-wave) characterization. Significant discontinuities within the specimen are then detected using a narrowband, air-coupled ultrasonic setup as well as an automated fluid-coupled real-time intelligent ultrasonic setup. The use of the discrete wavelet transform is investigated as an effective tool for signal denoising in air-coupled ultrasonic probing of the foams. A simple, one-dimensional model, based on a periodic spring-mass system and a previously developed homogenization theory, is used to predict the wave speed.

On the estimation of complex modulus and Poisson's ratio using longitudinal wave experiments

In this paper we consider different least-squares-based approaches for estimating the complex Young's modulus and the complex Poisson's ratio of a viscoelastic material using a longitudinal wave propagation experiment. We present a statistical analysis of different estimation approaches and compare their performances. The analytical covariance expressions are validated using experimental data.

A Petrov?Galerkin finite element scheme for the regularized long wave equation

A Petrov-Galerkin finite element method (FEM) for the regularized long wave (RLW) equation is proposed. Finite elements are used in both the space and the time domains. Dispersion correction and a highly selective dissipation mechanism are introduced through additional streamline upwind terms in the weight functions. An implicit, conditionally stable, one-step predictor–corrector time integration scheme results. The accuracy and stability are investigated by means of local expansion by Taylor series and the resulting equivalent differential equation. An analysis based on a linear Fourier series solution and the Von Neumann’s stability criterion is also performed. Based on the order of the analytical approximations and of the domain discretization it is concluded that the scheme is of third order in the nonlinear version and of fourth order in the linear version. Three numerical experiments of wave propagation are presented and their results compared with similar ones in the literature: solitary wave propagation, undular bore propagation, and cnoidal wave propagation. It is concluded that the present scheme possesses superior conservation and accuracy properties.

Time reversed wave propagation experiments in chaotic micro-structured cavities

The elastic wave propagation in strongly scattering solid-state cavity consisting of a thin micro-patterned silicon wafer is studied experimentally. The chaotic behavior is induced by the irregular boundary of the cavity and/or by fabricating patterns of small holes in the wafer by laser machining. The pattern and hole size are designed with length scales matching the wavelength ⩽1 MHz and induce multiple scattering within the wafer bounds. Regular patterns of holes add phononic band like dispersion properties to the system. Elastic waves obey under very general conditions time reversal and reciprocity symmetry. In the cavity system the strong mode mixing in the wafer between shear and compression waves, the strong anisotropy of silicon, and even small dissipation is not destroying the time reversal and reciprocity symmetry in the system. We present a systematic study of the quality of the time-reversal signal as function of the chosen time interval and the position in the recorded signal. Also the influence of time dilatation, i.e. stretching and compressing the time scale of the re-emitted signal, is studied.

On the use of flexural wave propagation experiments for identification of complex modulus

In this paper, we investigate the nonparametric estimation of the frequency dependent complex modulus of a viscoelastic material. The strains due to flexural wave propagation in a bar specimen are registered at different cross sections. The time domain data is transformed into frequency domain using discrete Fourier transform and a nonlinear least squares algorithm is then employed to estimate the complex modulus at each frequency. Inherent numerical problems due to associated ill-conditioned matrices are treated with special care. An analysis of the quality of the nonlinear least squares estimate is also carried out. The validity of the theoretical results are confirmed by numerical studies and experimental tests.

White's model for wave propagation in partially saturated rocks: Comparison with poroelastic numerical experiments

We use a poroelastic modeling algorithm to compute numerical experiments of wave propagation in White's partial saturation model. The results are then compared to the theoretical predictions. The model consists of a homogeneous sandstone saturated with brine and spherical gas pockets. White's theory predicts a relaxation mechanism, due to pressure equilibration, causing attenuation and velocity dispersion of the wavefield. We vary gas saturation either by increasing the radius of the gas pocket or by increasing the density of gas bubbles. Despite that the modeling is two dimensional and interaction between the gas pockets is neglected in White's model, the numerical results show the trends predicted by the theory. In particular, we observe a similar increase in velocity at high frequencies (and low permeabilities). Furthermore, the behavior of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The modeling results show more dissipation and higher velocities than White's model due to multiple scattering and local fluid‐flow effects. The conversion of fast P‐wave energy into dissipating slow waves at the patches is the main mechanism of attenuation. Differential motion between the rock skeleton and the fluids is highly enhanced by the presence of fluid/fluid interfaces and pressure gradients generated through them.

Quasiperiodic Bloch-like states in a surface-wave experiment.

Bloch-like surface waves associated with a quasiperiodic structure are observed in a classic wave propagation experiment which consists of pulse propagation with a shallow fluid covering a quasiperiodically drilled bottom. We show that a transversal pulse propagates as a plane wave with quasiperiodic modulation, displaying the characteristic undulatory propagation in this quasiperiodic system and reinforcing the idea that analogous concepts to Bloch functions can be applied to quasicrystals under certain circumstances.

A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: Numerical examples

Numerical aspects of the grain level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of grain level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.

On merging empirical models for the lower ionosphere of auroral and non-auroral latitudes

The quiet ionosphere at high latitudes should in principle behave in a similar manner as the non-auroral ionosphere, i.e. controlled by the solar zenith angle, solar activity and season. Independent empirical models for auroral-zone and non-auroral latitudes have been developed over many years based on different sets of data; notably at high latitudes the small number of data from rocket borne wave propagation experiments was recently complemented by a much larger number of incoherent scatter data (EISCAT). The discontinuities between the two models are interpreted in terms of differences in the composition of the neutral atmosphere in the two latitude regions. Procedures are suggested to merge the non-auroral model which is defined up to 60° with the auroral model established with data taken at 70°.

System Identification Techniques for Estimating Material Functions from Wave Propagation Experiments

Material properties of an elastic material are characterized by the elastic modulus, which is real-valued and constant. For viscoelastic materials, such as plastics and polymers, the relation between stress and strain is instead dynamic, and characterized by the complex-valued and frequency-dependent complex modulus. In this article it is described how system identification techniques can be used to determine the complex modulus using strain data from wave propagation experiments in a test specimen. Modeling, derivation of estimators, and analysis of their numerical and statistical properties are included. Several practical examples are presented using real-world data, and a number of extensions are outlined.

Shallow water acoustic wave propagation experiments between three rigid bottom mounted acoustic sonar towers

Shallow water acoustic wave propagation experiments were conducted between three bottom mounted 5-m tall towers as a part of the SWAT (Shallow Water Acoustic Technology) 2000 Experiment. Each sonar tower was self-contained to support a broadband sound transmitter and a hydrophone 5 m above seafloor. The Gold code of 1023 digits with a center frequency of 5.5 kHz was transmitted from each tower at 2- and 20-min intervals. The three towers were located in a triangle with ranges of 3, 4, and 5 km in the SS and OS sites. The results show a large difference in propagation characters. In the SS site, the peaks of arrivals are scattered over 10–15 ms from the first arrival peak. The envelopes of these signals are not stable during the 32-h experiment period. However, in the OS site the peak arrival is almost single within the 3-ms width. Also, the structure of arrival is very simple and includes the tidal effect. Parabolic equation (PE) model results based on CTD and bottom observation data indicate that there is a waveguide providing stable transmission just above the seafloor in the OS site. Comparison between acoustics data and broadband PE results will be discussed. [Work supported by ONR 321OA.]

Parametric identification of viscoelastic materials from time and frequency domain data

In this paper a parametric model of the elasticity modulus of a viscoelastic material (polypropylene) is determined by measured strains from wave propagation experiments. The identification of the model parameters is carried out both in the time and in the frequency domain. The advantages and limitations of either approach is discussed. Our main result is that a good representation of the elasticity modulus can be obtained by a general standard linear solid with three elements or seven free parameters. The model is valid over the same frequency range as that of the data, which in the present case extends from 100 Hz to 10 kHz. Such a model makes it possible to perform direct time simulations by time-stepping algorithms.

Non-parametric identification of viscoelastic materials from wave propagation experiments

We investigate how the frequency-dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated from wave propagation experiments. The strains at different sections of a bar specimen are measured as functions of time. The time series are transformed into the frequency domain, where a non-parametric identification is made. A thorough analysis of the quality of the non-parametric estimate is made, in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived. The validity of these expressions are confirmed by numerical studies and real experiments.

Charged particle measurements in the polar summer mesosphere obtained by the DROPPS sounding rockets

Two Black Brant V sounding rocket payloads (DROPPS) were flown as part of the DROPPS/MIDAS program from the Andøya Rocket Range, Norway, during July 1999. One of these payloads was launched during the presence of PMSE, and the other flight occurred during NLC conditions. Both payloads were equipped to measure a number of different electrodynamic parameters of the mesosphere and lower thermosphere. A fixed-bias Langmuir probe observed small-scale structure in electron concentration. Significant electron depletions (more than an order of magnitude) were measured in a narrow altitude region during both flights. Layers of a thickness between 300 and 1400 meters were observed with very sharp transitions at the edges of the layers. These electron depletions do not appear to be artifacts produced by electrode collisions with large positive particulates. Absolute electron density concentrations were determined by a multiple-frequency radio wave propagation experiment. In addition, ion conductivities, mobilities, and number densities were determined by a Gerdien condenser. In this paper, we report on the instrumentation and the preliminary observations of the charged particle environment.

Identification of Viscoelastic Materials

The frequency-dependent complex modulus for a linearly viscoelastic material is estimated from wave propagation experiments. In these experiments, strains at different sections of a bar specimen are measured as functions of time. The time series are then transformed into the frequency domain, where the identification is made. Two identification techniques, a non-parametric and a parametric, are considered in the paper. Analyses of the quality of the estimates given by the two different techniques are carried out, and approximate expressions for the covariance matrices of the complex modulus are provided. The validity of these expressions are confirmed by numerical studies as well as by real experiments. A comparison between the results of the non-parametric and parametric approaches is made. The results of the comparison are that the parametric model describes the complex modulus quite well and that the variances for the parametric estimates are considerably smaller.

CASSE — The ROSETTA Lander Comet Acoustic Surface Sounding Experiment — status of some aspects, the technical realisation and laboratory simulations

In 2003 the ROSETTA space mission to Comet 46P/Wirtanen will be launched by the European Space Agency (ESA). On board of the spacecraft there will be a Lander platform, which opens for the first time the possibility to carry out “in situ” measurements on a comet surface. The ROSETTA Lander experiment CASSE aims to investigate the outermost surface of the comet by means of transmitting, receiving and even passively monitoring acoustic waves in a frequency range from a few hundred to several kilohertz. In particular, by transmitting and recording compression and shear waves, the mechanical properties of the cometary surface will be investigated. To guarantee sufficient ground contact in any foreseeable surface topography, and in any composition of the material to be encountered, e.g. dust, sand, ice and mixtures of these materials, the acoustic transmitters (actuators), stacked piezoceramics, and triaxial commercial piezoelectric accelerometers as receivers, will be integrated in each of the three feet of the ROSETTA Lander. The Lander feet thus act as antennas for the transmitters and receivers. By switching different actuators and accelerometers, an analysis of the cometary surface material will become possible by direct foot to foot transmission of the acoustic signals. Further, an in-depth sounding will allow the detection of layered structures or embedded local inhomogeneities. The ground contact of the Lander will be strengthened by a harpoon providing a fixation force up to at least 5 N per foot. This paper describes the first design of the Lander feet incorporating piezoceramic composite stacks as sound transmitters and receivers, and the experiments to test their efficiency. In the first part of this paper, the results of acoustic wave propagation experiments in ice, sand and olivine dust, performed in the laboratory are reported. These experiments verify that a signal strength of at least 20 dB above noise can be expected for acoustic wave propagation in cometary analogue materials. The second part of the paper deals with the outdoor experiments, performed with sensors integrated into the Lander feet prototypes and placed in a sand filled construction container. The experiments serve to estimate the minimal range of detectability of the sounding signals.

A numerical and experimental study of transient torsional waves in stepped circular bars

A numerical and experimental investigation into the reflection and transmission of transient torsional waves at a discontinuity of cross-section in stepped circular bars is presented. The differential equations governing the torsional motion of the stepped bar are solved by application of the method of bicharacteristics. The stability and convergence of the numerical solutions are checked by estimating the total energy in the system. The torsional elastic wave-propagation experiments for a stepped steel bar are carried out using a modified torsional Hopkinson bar. The numerical solutions for the torsional shear strain histories at several positions before and after the discontinuity of cross-section in the stepped steel bar are shown to be in reasonable agreement with the experimental data. The limitations of the classical one-dimensional torsional wave equation for thin rods are examined by determining the two-dimensional distributions of the dynamic torsional shear stresses in the vicinity of the cross-sectional discontinuity in the stepped bars. The advantages and limitations associated with the method of bicharacteristics are discussed.

Wave propagation experiments using point load excitation in a multi-layered structure

Transient wave propagation measurements on a single plate, a two-layer plate and a two-layer-on-a-half-space structure are reported. The experiments are performed using point load excitation and point detection at the surface of the structure. The experimental results are used to verify the accuracy of a new model for wave propagation in layered structures. The basis of the model is first introduced. Experimental measurements using different wave sources, plate materials and wave sensors are compared with each other and with theoretical results. The actual source functions for pencil-lead-break wave sources are obtained. Next, experiments performed on an aluminum plate bonded to a stainless steel plate are reported. Both the cases of stainless steel atop aluminum and aluminum atop stainless steel are considered. The experimental results show good agreement with the theoretical predictions. The effects of the second layer on the transient displacement of the top surface are discussed. Finally, a two-layer-on-a-half-space structure consisting of a stainless steel plate as the top layer, an aluminum plate as the second layer and a thick acrylic resin block as the half-space is studied. The presened experimental transient measurements agree with the predicted results, thus verifying the accuracy of the model.