Elastic wave propagation

Numerical Modeling of Elastic Wave Propagation in Inhomogeneous Anisotropic Media. 

P. Constance Yang, Charles H. Norris, and Yehuda Stavsky, Elastic Wave Propagation In Heterogeneous Plates, International Journal of Solids and Structures, October 1966, pp. 665-684. 

Non-destructive methods include holographic interferometry, resistance transducers, stress-sensitive covers, and other similar techniques. In practice, the following physical methods of non-destructive monitoring of residual stresses are commonly used X-ray diffraction, measurement of dielectric properties, and ultrasonic control. The main purpose of these methods is to monitor the structural transformations or distortions taking place as a result of residual stresses and local deformations. However, the application of methods such as X-ray diffraction to measure distortions in unit cel dimensions, ultrasonics to measure elastic wave propagation velocities, etc., all encounter numerous experimental problems. Therefore, in ordinary laboratory conditions only quantitative estimations of residual stresses can be obtained. 

Figure 2.1 Pictorial representations of elastic waves in solids. Motions of groups of atoms ate depicted in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, Vp, are shown below each sketch, (a) Bulk longitudinal (compressional) wave in unbounded solid, (b) Bulk transverse (shear) wave in unbounded solid, (c) Surface acoustic wave (SAW) in semi-infinite solid, where wave motion extends below the surface to a depth of about one wavelength, (d) Waves in thin solid plates.

According to Karapetyan the coefficient q is, in turn, related with the elastic wave propagation parameters in a cellular material aral foam morphology by the following formula ... 

Classical theory of elasticity (see, for example [4,5]) contains the fundamental equations required to describe elastic waves propagation. Although real objects have atomic structure, the medium in which the waves propagate is regarded as a continuum. It means that the wavelength should be large enough with respect to the distance between molecules or atoms. Further we will discuss crystals, therefore, most of the variables will be tensors. 

Acoustic and elastic properties are directly concerned with seismic wave propagation in marine sediments. They encompass P- and S-wave velocity and attenuation and elastic moduli of the sediment frame and wet sediment. The most important parameter which controls size and resolution of sedimentary structures by seismic studies is the frequency content of the source signal. If the dominant frequency and bandwidth are high, fine-scale structures associated with pore space and grain size distribution affect the elastic wave propagation. This is subject of ultrasonic transmission measurements on sediment cores (Sects. 2.4 and 2.5). At lower frequencies larger scale features like interfaces with different physical properties above and below and bed-forms like mud waves, erosion zones and ehatmel levee systems are the dominant structures imaged... 

Parra, J.O., 1991. Analysis of elastic wave propagation in stratified fluid-filled porous media for interwell systemic applications, Journal of the Acoustic Society of America 90 pp. 2557-2575. 

As has been shown previously by us [3] and independently by Tarasov [4], an allowance for the regularity of elastic wave propagation in crystals gives a Debye-type expression in which the exponent is one (n — 1) for one-dimensional structures (filaments), two (n = 2) for laminar structures, and three (n = 3) for isotropic space structures. In all the intermediate cases, the exponent n will have an intermediate value. However, in contrast to Tarasov, we did not consider the behavior of filaments or layers and their interaction with each oiher, but the special features of occupation by figurative points corresponding to the excitation of vibrations in the phase k space of anisotropic substances. 

Yokomichi H, Ikeda I and Matsuoka K (1964) Elastic wave propagation due to cracking of concrete. Cement Concrete Japan 212 2-6... 

Fracture in a material takes place with the release of stored strain energy, which is consumed by nucleating new external surfaces (cracks) and emitting elastic waves, which are defined as AE waves. The elastic waves propagate inside a material and are detected by an AE sensor. Except for contactless sensors, AE sensors are directly attached on the surface as shown in Fig. 3.1. 

Sonic and ultrasonic test methods use elastic waves propagating in solid or fluid media and are classified into active and passive methods. The former requires emission of waves into the test object the latter, waves emitted by the material itself... 

Lane, H., Kettil, R, Enelund, M., Ekevid, T. Wiherg, N.-E. 2007b. Absorbing Boundary Layers for Elastic Wave Propagation. Presented at the 8th International Conference on Computational Plasticity, Barcelona, Spain, September 5-8, 2007. 

Provided a source model, the second necessary component for a simulation is the material model, which defines the mechanical properties of the propagating media in the modeling domain. The most basic 3D material model used for elastic wave propagation simulations defines the material density (p) and seismic velocities of P and S waves... 

The theory of linear elasticity (see, for example, Landau and Lifshitz, 1%5) gives the basis for the description of elastic wave propagation. Linear elasticity is given in case of a linear relationship between stress and strain. Rocks are—in general— non-linear but for sufficiently small changes of stress as during a wave propagation, linearity can be assumed. 

Geertsma, I., Smith, D.C., 1961. Some aspects of elastic wave propagation in fluid saturadet porous solids. Geophysics 26, 169 181. 

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