Imaginary Part Of Wave Number Research Articles

Метод обобщенного импеданса для расчета отражения и прохождения волны через многослойную структуру. Часть 2. Падение волны на прямоугольный барьер

On the basis of generalized impedance method the propagation of single-dimension wave in multi-layer structure which contains the rectangular-type barrier is investigated. The concept of single barrier as a slide which parameters are different from the parameters of all other slides of structure is introduced. It is investigated the variation of position of real negative single barrier along the length of structure. It is found that the entrance impedance along the length of structure is varied by periodic manner. It is found the analytical formulas which simulate the dependencies of real and imaginary parts of entrance media impedances from coordinate along the structure. It is found three basis regimes which correspond to different character of oscillations: regime №1 – precise periodicity, regime №2 – break periodicity, regime №3 – monotonous increasing. It is investigated the coefficient of reflection for all mentioned above cases. It is found that the reflection coefficient from barrier displacement is not depended. It is found the periodic character of changing of amplitude and phase of reflected wave and also reflection coefficient when the height of barrier is varied. For interpretation of observed dependencies it is proposed the model of resonance inside of barrier. It is investigated the special feature of wave propagation when the barrier has complex character. It is investigated the case when the real path of wave number of barrier medium is established constant but imaginary path of the same number is varied in wide boundaries. It is established that reflection coefficient started by zero when the imaginary part of wave number is equal to zero. When imaginary part of wave number increases the reflection coefficient smooth increases in limit goes to unit. The passing coefficient also smooth decreases but more quickly then reflection coefficient and in limit goes to zero. The absorb coefficient started by zero at first smooth increases and after reaching of maximum smooth decreases in limit goes to zero. It is investigated the case when real and imaginary paths of barrier medium wave number simultaneous increase in equally proportion. It is found that in this case on the smooth curves for coefficients ob reflection, passing and absorb it is putted the oscillations. The character of oscillations is explained in the frames of resonance model.

Нормальные волны в электромагнитной метакиральной изотропной среде с потерями

Plane electromagnetic waves in an isotropic absorbing chiral medium (chiral metamaterial) are considered. A system of constitutive Drude - Born - Fedorov relations with complex values of the dielectric permittivity, magnetic permeability, and the chirality parameter is used. A distinction is made between forward and backward normal waves by introducing a special parameter - the wave type identifier. Analytical expressions for real and imaginary parts of wave numbers of homogeneous normal waves are presented.

Elastic wave dispersion and attenuation caused by multiple types of disc-shaped inclusions

PurposeThe purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions.Design/methodology/approachWithin the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion.FindingsOn the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters.Originality/valueThis paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.

Alfvén Surface Waves in a Partially Ionized Resistive Medium

We study the joint effects of viscosity, resistivity and ion-neutral collisions on Alfvén surface waves propagating along a partially ionized plasma - vacuum interface. Applying boundary conditions at plasma-vacuum interface, we obtain the dispersion relation for Alfvén surface waves and solve it numerically. For different values of resistivity and neutral gas friction parameters, the variation of real and imaginary parts of wave number with viscosity parameter are shown graphically. It is found that two-mode structure of Alfvén surface waves results due to the combined effects of resistivity, viscosity and ion-neutral collisions. These results might be useful for studying the behavior of Alfvén surface waves in laboratory and space plasmas.

ANALYSIS OF FLOQUET WAVE GENERATION AND PROPAGATION IN A PLATE WITH MULTIPLE ARRAYS OF LINE ATTACHMENTS

A variety of engineering structures consist of a homogeneous “master structure”, such as a plate or shell, to which are attached multiple arrays of substructures, such as ribs or stringers. The goal of this work is to understand the effects of array impedance and spacing on energy flow in the master structure. Such an understanding may ultimately lead to a design process encompassing both the attenuation of vibrational energy and the support of static loads. Here, the vibrational response of a locally excited master structure is studied analytically for a class of structures involving an arbitrary number of substructure arrays. The approach is presented in the context of an elastic plate which is reinforced by multiple arrays of line attachments and acted upon by a line force. Extension of the analysis to other geometries and loadings is straightforward. A recursive analytical procedure is presented by which Floquet wavenumbers of a structure with p arrays are computed from the wavenumbers of a structure with p−1 of the arrays attached. In this way, the Floquet wavenumbers of any multiple array structure can be computed by first considering the master structure alone and then computing the effect of attaching each array in turn. The imaginary parts of the Floquet wavenumbers quantify the attenuation of response along the structure. In addition, the spatial response is obtained analytically as a sum of two Floquet waves through simplification and transformation of the wavenumber domain solution. By way of example, a three-array structure is considered to illustrate the recursive computation of the wavenumbers and to demonstrate the correlation between the imaginary parts of the wavenumbers and the spatial attenuation of the structural response.

Effect of Chiral Material Loss on Guided Electromagnetic Modes in Parallel-Plate Chirowaveguides

In this paper, we discuss theoretically the effects of lossy chiral material on guided electromagnetic waves in parallel-plate waveguides. The guided-wave structures filled with chiral materials have been named chirowaveguides, and their guiding properties for lossless chiral materials have been recently studied and reported in the literature. Here, we extend the analysis of chirowaveguides to the case of lossy chiral materials, and we theoretically investigate the effect of material loss on guided modes in parallel-plate chirowaveguides. Dispersion diagrams for the real and imaginary parts of wave numbers of guided modes along with their electric and magnetic field components are given and the similarities and differences of these quantities with those of the lossless chirowaveguides are addressed. These guided-wave structures can have potential applications in the design of novel devices and components, and in electromagnetic shielding. The associated theoretical analyses for lossy chirowaveguides are s...