Effect of wave propagation in nonhomogeneous elastic rod with variable density

The problem of wave propagation along a transmission system composed of an overhead wire parallel to the (plane) surface of the earth, in spite of its great technical importance, does not appear to have been satisfactorily solved.1 While a complete solution of the actual problem is impossible, on account of the inequalities in the earth's surface and its lack of conductive homogeneity, the solution of the problem, where the actual earth is replaced by a plane homogeneous semi-infinite solid, is of considerable theoretical and practical interest. The solution of this problem is given in the present paper, together with formulas for calculating inductive disturbances in neighboring transmission systems.

H/D-isotope effects in chemical wave propagation on surfaces: the O 2+H 2 and NO+H 2 reactions on Rh(110) and Rh(111)

The effect of stress wave propagation on dynamic response of square tube was investigated by the experimental and numerical simulation methods in the present paper. The square tubes were subjected to the axial impact by split Hopkinson pressure bar. And the deformation process of each square tube was recorded by a high speed camera. Typical dynamic plastic buckling phenomena were observed in the experiments. And the numerical calculation of the experimental load case was conducted to analyze the effect of the stress wave propagation on the initial buckling of the square tube. The results show that there is obvious stress wave propagation in the square tube before the buckling of the square tube. And the initial buckling starts from the rear end of the tube due to the propagation of the stress wave. The relation between the stress wave propagation and initial buckling of the square tube was also discussed.

Power flow in distribution networks with earth return

CHAPTER 3 - ELASTODYNAMIC THEORY

Wavefront shaping techniques allow one to focus light inside and through turbid media. In order to gain a better understanding how light evolves inside a scattering random medium while shaping the incident wavefront, it is beneficial to know the electromagnetic field within the entire medium, which is difficult to achieve in experiments. Here we investigate wavefront shaping techniques with numerical simulations based on Maxwell’s equations to examine various effects of wave propagation in randomly scattering media. First, we calculate numerically monochromatic plane wave solutions for a given scattering medium for different incident k-vectors. With these plane wave solutions we are able to simulate complex-shaped incident wavefronts impinging on the scattering medium. This enables us to scan and tilt the incident complex wavefront after solving Maxwell’s equations and to examine the electromagnetic field inside the medium. Due to the fact that we have access to the electromagnetic field of the plane wave illumination from different angles, it is easy to phase-optimize an incident wavefront by conjugating the known phase at a certain location. Because of the separate calculation of the plane wave solutions and the possibility to simulate different incident wavefronts by superimposing these plane wave solutions, our method is very dynamic and versatile. In summary, our simulation approach contributes to the understanding of light propagation in strongly scattering media such as biological tissue and to the improvement of medical imaging techniques.

Non-hydrostatic modeling of drag, inertia and porous effects in wave propagation over dense vegetation fields

A simple procedure, based on Love’s approximate theory [The Mathematical Theory of Elasticity (Cambridge U. P., Cambridge, England, 1927), 4th ed.] for wave propagation in a bar, is proposed in order to consider dispersive effects in wave propagation in a thin-walled, fluid-filled, elastomer tube. It is assumed that the perturbation from steady flow in the tube is small enough that a linearized theory is valid, and that the elastic modulus of the tube is small compared with the bulk modulus of the fluid so that compressibility of the fluid can be neglected. The flexural rigidity of the tube wall, the inertia of the tube wall, and the radial inertia of the fluid are taken into account, and an approximate expression for the dispersion relation for the fundamental mode is obtained. In order to investigate the dispersive effects, resulting from inclusion of the inertia and flexural rigidity of the tube wall and the radial inertia of the fluid in the model, an initial value problem is considered in detail. The fast Fourier transform is used to obtain numerical solutions for small and intermediate times. Numerical results are presented in graphical form.

In the summer of 2000, Duke University and the Kenyan power generation company, KenGen, conducted a microearthquake monitoring experiment at Longonot volcano in Kenya. Longonot is one of several major late Quaternary trachyte volcanoes in the Kenya Rift. They study was aimed at developing seismic methods for locating buried hydrothermal areas in the Rift on the basis of their microearthquake activity and wave propagation effects. A comparison of microearthquake records from 4.5 Hz, 2 Hz, and broadband seismometers revealed strong high-frequency site and wave-propagation effects. The lower frequency seismometers were needed to detect and record individual phases. Two-dozen 3-component 2- Hz L22 seismographs and PASSCAL loggers were then distributed around Longonot. Recordings from this network located one seismically active area on Longonot's southwest flank. The events from this area were emergent, shallow (<3 km), small (M<1), and spatially restricted. Evidently, the hydrothermal system in this area is not currently very extensive or active. To establish the nature of the site effects, the data were analyzed using three spectral techniques that reduce source effects. The data were also compared to a simple forward model. The results show that, in certain frequency ranges, the technique of dividing the horizontal motion by the vertical motion (H/V) to remove the source fails because of non-uniform vertical amplification. Outside these frequencies, the three methods resolve the same, dominant, harmonic frequencies at a given site. In a few cases, the spectra can be fit with forward models containing low velocity surface layers. The analysis suggests that the emergent, low frequency character of the microearthquake signals is due to attenuation and scattering in the near surface ash deposits.

Perhaps the most interesting and important deductions regarding the effects of thermodynamics on wave propagation are those concerning the basic properties of shock transition in elastic fluids given by H. BETHE and H. WEYL 1. Originally obtained for fluids not conducting heat, they are readily extended to elastic solids, simple of materials. They are crucial also in the interpretation of formulae describing the evolutionary behavior of shock waves in these various classes of materials. Basically they follow from the jump conditions expressing balance of mass, balance of linear momentum, balance of energy, entropy production and certain general properties of the consicutive response function of the pressure. It is interesting to recall these results for the case of elastic solids that do not conduct heat. The interested reader may consult the original papers for the proofs2.

Surface wave propagation effects on buried segmented pipelines

The problem of propagation of Love waves in elastic waveguides loaded on the surface by a viscous (Newtonian) liquid is important in many applications such as geophysics, seismology, investigation of the physical properties of liquids. Love wave energy is concentrated near the waveguide surface, so that Love waves are especially suited to study the material properties of surface layers. In this work, the direct problem and the inverse problem of the Love wave propagation in a layered elastic waveguides loaded with a viscous liquid have been formulated and solved. The inverse problem relies on the determination of the material parameters (e.g., the unknown value of liquid viscosity) from measurements of the dispersion curves of Love waves.

The effect of random height variations associated with a conducting surface upon the characteristics of reflected wave energy is ascertained by the methods of physical optics. Average received powers its variance, angular and frequency power spectra, and the field correlation pattern are determined in terms of the statistical parameters of the surface. Volume type problems are treated by ascertaining the effect of refractive index fluctuations within a slab upon an emergent wavefront, and then generalizing to a continuous medium. The results are applied to various problems encountered in tropospheric and ionospheric wave propagation.

A numerical scheme for calculating direct and inverse double-weighted Fourier transform (DWFT) in the problems of wave propagation in inhomogeneous media on the basis of the fast Fouriertransform algorithm is proposed. The sampling step for which it is possible to recover a continuous field without information loss is estimated. The numerical calculation data are given and the obtained results are discussed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 56, No. 7, pp. 514–523, July 2013.

Theoretical study of microwaves propagation through the atmosphere may be reduced to the `one-dimensional' problem of waves propagation in a randomly layered media with effective attenuation. The randomly stratified layer that is homogeneous on the average represents a fluctuation waveguide arising as a result of interference of multiply scattered waves.