Damping Of Elastic Waves Research Articles

Expression for the granular elastic energy

Granular solid hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some drawbacks. Therefore a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from 26^{∘} to the more realistic value of 30^{∘}. (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan, and Matsuoka-Nakai-realizing each, and interpolating between them, by shifting a single scalar parameter.

Effects of cross correlations between inhomogeneities of the parameters of an isotropic medium on the spectrum and damping of elastic waves

The dispersion and damping laws have been investigated for elastic waves in an isotropic medium with one- and three-dimensional inhomogeneities of the density p(x) of the material and the elastic force constants μ(x) and λ(x) with allowance for the cross correlations between these inhomogeneities. It has been demonstrated that the positive cross correlations between μ(x) and λ(x), as well as the negative cross correlations between p(x) and μ(x) or p(x) and λ(x), lead to an enhancement of the modification of the dispersion law and an increase in the damping of waves. The positive cross correlations between p(x) and μ(x) or p(x) and λ(x), as well as the negative cross correlations between μ(x) and λ(x), result in the opposite effects: a weakening of the modification of the dispersion law and a decrease in the damping. An analysis of the results obtained in this paper and in our recent work [15] has made it possible to formulate the general regularity of the effects of cross correlations, irrespective of the physical nature of the waves: the effects of cross correlations between inhomogeneities of any two parameters of the material on the wave spectrum depend on whether both parameters related by the cross correlations belong to the same part of the Hamiltonian (i.e., if they both belong to either the kinetic part or the potential part of the Hamiltonian) or they belong to different parts of the Hamiltonian. The positive cross correlations lead to a greater modification of the dispersion law and to an increase in the damping of waves in the former case and to a decrease in these characteristics in the latter case. Correspondingly, the negative cross correlations in each of these cases result in the opposite effects. This regularity has been explained qualitatively.

Some special features of using DGS (AVG) diagrams during ultrasonic testing of welded joints

The results of development of a method and piezoelectric probes with DGS (AVG) diagrams for ultrasonic testing devices are considered. The technique is compatible with European standards for ultrasonic testing of welded joints as regards the parameters of piezoelectric probes and sensitivity tuning taking into account damping of elastic waves. The succession of operations in tuning of devices, ultrasonic testing, and evaluation of the results with DGS (AVG) diagrams is considered.

Comparison of the dynamic response of a saturated soil between two models

By comparing the dynamic responses of saturated soil to Biot’s and Yamamoto’s models, the properties of the two models have be pointed out. First of all, an analysis has been made for energy loss of each model from the basic equations. Then the damping of elastic waves in coarse sand and fine sand with loading frequency and soil’s parameters have been calculated and the representation of viscous friction and Coulomb friction in the two models has been concluded. Finally, the variations of loading wave damping and stress phase angles with water depth and soil’s parameters have been obtained as loading waves range in ocean waves.

Experience of Improving Standards and Methods for Studying the Properties of Metal Powders and Sintered Articles

Reasons are considered for improving standards in the following methods for testing powder materials: tensile, transverse bending, gas and liquid permeability, and determination of powder compact dimensions after compaction pressure removal and during sintering. Calculated data for representative specimen dimensions (cross section and thickness) for these and other test methods for sintered articles (materials) prepared from mono- and polyfraction iron powder of different sizes are confirmed by experiment. It is shown that the representative specimen dimensions prepared from monofraction powder are more than an order of magnitude less than for those prepared from polyfraction powder. The reason for this difference is considered to be the special role of individual particles (for monofraction powder) or assemblies of these particles (for polyfraction powder) in forming elementary fragments within the structure of compacts and sintered articles. Data are provided for the improved ISO 4492-1985 standard and a new GOST 29012-91 standard developed on the basis of it for precise determination of changes in the dimensions of powder compacts during pressing and sintering. Use of this method makes it possible to reveal the existence of different structural states within narrow porosity limits for powder materials. It is shown by experiment that the pulsed ultrasonic method for monitoring these structural states based on measuring the propagation rate and (or) the elastic wave damping factor, exhibits high sensitivity, it is rapid, and it may be recommended for extensive introduction and standardization in powder metallurgy.

Resonant Ultrasound Spectroscopy

When a new crystalline material is discovered, one of the first fundamental properties to be determined is the atomic structure, defined by the minimum in the free energy with respect to the positions of the atoms. Another fundamental characteristic of interest is the curvature of the free energy in the vicinity of the minimum, and this would be manifest in the elastic constants for the material. As derivatives of the free energy, elastic constants are closely connected to thermodynamic properties of the material. They can be related to the specific heat, the Debye temperature and the Gruneisen parameter (which relates the thermal expansion coefficient to the specific heat at constant volume), and they can be used to check theoretical models. Extensive quantitative connections among thermodynamic properties can be made if the elastic constants are known as functions of temperature and pressure. The damping of elastic waves provides information on anharmonicity and on coupling with electrons and other relaxation mechanisms. The elastic properties are perhaps most valuable as probes of phase transitions, such as superconductivity transitions. Clearly precise and accurate measurements of elastic constants furnish significant information about materials.

Nonlinear elastic effects of the interaction of a laser pulse with a solid

A study was made of the influence of nonlinear elastic effects on the generation of acoustic waves as a result of interaction of laser radiation with a solid. An explanation is given of the slower (compared with the predictions of the linear theory) damping of elastic waves. It is shown that the dimensions of an elastically deformed zone can be determined by an acoustic method and this can be done for any duration and time profile of a laser pulse causing such deformation.

Elastic wave damping in thin-layered saturated porous media

Monochromatic wave propagation in thin-layered saturated porous media is examined by averaging differential equations with rapidly oscillating coefficients. Particular attention is given to the transformation mechanism for the damping of such waves. Existing results in this area /1/ are extended and refined.

Effective Scattering and Damping of Elastic Waves in Multi‐Component Mixtures

AbstractScattering of elastic waves propagating in a strongly heterogeneous medium with aggregate topology is considered within a modified effective‐medium procedure. The calculations are restricted to long wavelengths or low frequencies and are based on results obtained in a previous paper for the fluctuations of a static strain field. Explicit results are presented for isotropic components and spherical grains. In particular, effective differential and total cross‐sections for the grains of different components are discussed. For non‐dissipative media the total cross‐sections are related to the damping rates of longitudinal and transverse waves. Numerical examples for the damping rates and the angular dependence of the differential cross‐sections are presented for some binary mixtures. In strongly heterogeneous media near the percolation threshold high values of the scattering rates and a nearly isotropic distribution are obtained.

Effect of cyclic loading on the parameters of elastic wave propagation in piezoelectric ceramics

1. Diagnostic methods based on elastic waves can be used for estimating fatigue changes in piezoelectric ceramics. 2. The degree of fatigue damage in piezoelectric ceramic specimens can be determined with respect to the extent of elastic wave damping. 3. The method of estimating the damage based on surface waves is more promising, since it allows recording of fatigue damage of lesser magnitude in comparison with the method based on volume waves. 4. In order to improve the resolving power of the method of fatigue damage diagnostics based on elastic waves, it is necessary to reduce the effective width of opposed-pin transducers for surface acoustic waves.

Electromagnetic damping of elastic waves: Experimental results

The passage of an elastic wave causes straining and translation in the transmitting material. If a magnetic field is applied, and the medium is an electrical conductor, some of the energy of the wave is dissipated by the flow of electrical eddy currents. Usually the amount of energy lost is very small, but it may be greatly increased if the applied field is strongly non-uniform.Laboratory experiments are described which demonstrate this effect for standing elastic waves in a metal bar. The applied magnetic field changes from almost zero to its full strength over a distance which is short compared to the length of the standing wave. The result of this strong non-uniformity is that the energy lost due to the translation of the bar in the field greatly exceeds the energy lost due to the straining of the bar in the field.The dependence of the attenuation of the waves by the magnetic field is investigated for variation in frequency of vibration, bar thickness, and field gradient.