General Wave Propagation Research Articles

Elastodynamics in micropolar fractal solids

This research explores elastodynamics and wave propagation in fractal micropolar solid media. Such media incorporate a fractal geometry while being modelled constitutively by the Cosserat elasticity. The formulation of the balance laws which govern the mechanics of fractal micropolar solid media is presented. Four eigenvalue-type elastodynamic problems admitting closed-form analytical solutions are introduced and discussed. A numerical procedure to solve general initial boundary value wave propagation problems in three-dimensional micropolar bodies exhibiting geometric fractality is then applied. Verification of the numerical procedure is discussed using the analytical solutions.

High order well-balanced scheme for river flow modeling

We propose a new numerical scheme based on the finite volumes to simulate the river flow in the presence of a variable bottom surface. Our approach is based on the Riemann solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave-propagation form and can be extended to an arbitrary high order accuracy. The main goal is to construct the scheme, which is well-balanced, i.e. maintains not only some special steady states, but all steady states which can occur.

A modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform one-dimensional waveguides

In this article, using the wave propagation method, the natural frequencies and mode shapes of an arbitrary non-uniform one-dimensional waveguide are calculated. The non-uniform rods and beams are partitioned into several continuous segments with constant cross-sections, for which there exists an exact analytical solution. At the end of each segment, waves in positive and negative directions are obtained in terms of waves at initial segment and subsequently, the calculations of the mode shapes become simple. By satisfying the boundary conditions, the characteristic equation is obtained and natural frequencies are calculated for both the arbitrary non-uniform rod and beam. Also, by adding waves in positive and negative directions at the end point of each segment, the mode shapes are obtained. To verify the modified wave method presented here, the frequencies and mode shapes of the rod and the beam with a polynomial cross-section having an exact analytical solution are compared and have been proven to be of high accuracy. Besides, comparisons of finite element method are also included. Therefore, this method can also be used to calculate the natural frequencies and mode shapes of rods and beams with any arbitrary variable cross-section for which no analytical solution is available. For the ‘Modified Wave Approach’ developed here, dimensions of transmission matrix remain constant if the number of segments is increased, while in general wave propagation method, dimensions of transmission matrix increase upon increasing the number of segments. Besides this novelty, this method has the advantage that it gives all the natural frequencies and mode shapes, unlike other approximate methods such as weighted residual, Rayleigh–Ritz, and finite difference methods which have their own shortcomings such as limited number of natural frequencies. Also, since each segment has an exact analytical solution, in contrast to other approximate methods, much higher accuracy is obtained even with only a few number of partitions.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.

Vibration modelling of complex waveguide structures

In this paper, a general wave propagation approach for the vibration analysis of three-dimensional waveguide structures is presented. The analysis is based on a ray tracing method that considers wave propagation and scattering in the formulation, including the effects of decaying near-field wave components. The waveguide dispersion characteristics of straight and curved beams, which govern the propagation and decay of waves as they travel through the different components, are taken into account for different wave types (flexural, torsional, and axial). Separate elements are coupled using reflection and transmission coefficients, and these are derived for a general connection between several non-planar elements. A matrix formulation is used that offers an automatic and concise method for tackling free and forced vibrations problems of complex ring-beam structural systems. The general methodology is demonstrated on simple applications, and the predictions made using the proposed approach are shown to be in excellent agreement with a conventional finite element analysis, with the advantage of reduced computational costs.

Reflection Characterization of Nanoscopically Stratified Surface Structures and Optical Probing of Anisotropic Nanolayers

The reflection of linearly polarized light from a layered nanoscopic system of anisotropic dielectric films on homogeneous isotropic substrate is investigated in the long-wavelength limit. The expressions for the reflectances and ellipsometric angles of an N-layer system of anisotropic ultrathin films are derived. For absorbing substrate mathematical relationships take a relatively simple additive form. In comparison with absorbing substrate the fully transparent system is more complicated and in this case an ultrathin film in multilayer system is sensitive to the presence of other ultrathin films (an interaction between them emerges) and the contribution of each layer to the reflection coefficient is not expressed in a purely additive form. The analytical results are supported by computer-aided analysis made on the basis of general wave propagation theory for anisotropic layered media. The most useful feature of obtained approximate expressions is that they are simply invertible, allowing a direct calculation of the parameters of ultrathin layers. [DOI: 10.1380/ejssnt.2010.167]

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.

Reflection of light from nanoscopically stratified anisotropic media and optical probing of dielectric nanofilms

The reflection of linearly polarized light from a layered nanoscopic system of anisotropic dielectric films on homogeneous isotropic substrate is investigated in the long-wavelength limit. The expressions for reflection characteristics of an N-layer system of arbitrarily anisotropic ultrathin films are derived. The analytical results are supported by computer-aided analysis made on the basis of general wave propagation theory for anisotropic layered media. We show that the accuracy of the long-wavelength approximation for nanoscopic anisotropic multilayers is quite satisfactory: if the thickness of a multilayer divided by the wavelength comprises a few hundredths, then the errors of approximate formulas do not exceed a few percent. The most useful feature of obtained approximate expressions is that they are simply invertible, allowing a direct calculation of the parameters of ultrathin layers.

Early arrival waveform tomography on near-surface refraction data

We develop a waveform-tomography method for estimating the velocity distribution that minimizes the waveform misfit between the predicted and observed early arrivals in space-time seismograms. By fitting the waveforms of early arrivals, early arrival waveform tomography (EWT) naturally takes into account more general wave-propagation effects compared to the high-frequency method of traveltime tomography, meaning that EWT can estimate a wider range of slowness wavenumbers. Another benefit of EWT is more reliable convergence compared to full-waveform tomography, because an early-arrival misfit function contains fewer local minima. Synthetic test results verify that the waveform tomogram is much more accurate than the traveltime tomogram and that this algorithm has good convergence properties. For marine data from the Gulf of Mexico, the statics problem caused by shallow, gassy muds was attacked by using EWT to obtain a more accurate velocity model. Using the waveform tomogram to correct for statics, the stacked section was significantly improved compared to using the normal move-out (NMO) velocity, and moderately improved compared to using the traveltime tomogram. Inverting high-resolution land data from Mapleton, Utah, showed an EWT velocity tomogram that was more consistent with the ground truth (trench log) than the traveltime tomogram. Our results suggest that EWT can provide supplemental, shorter-wavelength information compared to the traveltime tomogram for both shallow and moderately deep seismic data.

WAVE PROPAGATION AND DISPERSION CHARACTERISTICS FOR A NONRECIPROCAL ELECTRICALLY GYROTROPIC MEDIUM

The general dispersion relation for a nonreciprocal electrically gyrotropic or a gyroelectric medium is derived in two distinct forms by using three different methods. One of them is a new method which can be used when the stratification of the layers is in the z-direction. The wave numbers corresponding to each dispersion relation are obtained in closed form. It is shown that there exist two types of waves, type I and type II, in a gyroelectric medium. The wave propagation is investigated and the polarization of the waves, resonances and cut off conditions are obtained for the principle waves. The general wave propagation regions are identified using resonances and cut off conditions. These regions are then used to construct the Clemmow-Mually-Allis (CMA) diagram. The conditions showing the frequency bands for which wave can propagate in each region are tabulated for the first time. The results presented in this paper can be used in the development of nonreciprocal devices and in ionospheric problems including radiation and scattering applications.

Directional and band‐gap behavior of periodic auxetic lattices

AbstractThe paper investigates the wave propagation characteristics of periodic two dimensional, auxetic lattice structures. Periodic structures in general feature unique wave propagation characteristics, whereby waves are allowed to propagate only within specific frequency bands. Two dimensional periodic structures complement this feature with a low frequency directional behavior. The combination of these unique characteristics makes two dimensional periodic structures ideal candidates for the design of pass‐band directional mechanical filters.Focus is here placed on honeycomb lattice configurations. A sensitivity analysis is first presented to investigate the influence of band‐gap and directional behaviors with respect to changes in the internal angle. The presented results demonstrate how re‐entrant topologies feature enhanced wave attenuation capabilities with respect to hexagonal lay‐outs. An optimization problem is then formulated by considering the internal angle as a design variable, and the width of the attenuation frequency ranges and angular range of propagation at low frequencies as objective functions. The identified optimal configurations feature combined properties which demonstrate the effectiveness of the analysis procedure. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Variable streams self-gravitating instability of radiating rotating gas cloud

The self-gravitating instability of radiating rotating gas cloud (of density ρ 0) streams with non-uniform velocity has been studied. The stability criterion of the model, for general wave propagation, is derived and the stability states are discussed. Jeans self-gravitating instability restriction has been obtained with some simplification here. The radiation effect stabilizes the gas cloud medium with critical wave length longer than that of Jeans. Normally, the streaming has a destabilizing effect. However, this effect is depressed in the presence of radiation. Neither the radiation nor the rotation stabilization influence affects the self-gravitating instability. So, the rotation and radiation do not prevent the destroying of the spiral arm of galaxy due to the influence of the self-gravitating force. However, if the wave propagation in xy-plane is normal to the direction of the rotation with angular speed Ω, the self-gravitating instability may disappear as long as Ω>( πGρ 0) 1/2 , where G is the gravitational constant.

Determination of Soundproofing of Construction Units on Basis of the General Wave Propagation Theory for a Multilayered Media

Determination of Soundproofing of Construction Units on Basis of the General Wave Propagation Theory for a Multilayered Media

Nonuniform distortionless transmission lines

Heavside's classical condition for distortionless signalling, g/c=r/l, is generalized to nonuniform transmission lines. The resulting class of nonuniform lines possesses several interesting properties, which are investigated in some detail. For instance, there exists a preferred direction for distortionless signalling, a phenomenon not observed with uniform lines. We also show that closed-form solutions to quite general wave propagation problems can be derived directly in the time domain.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.

A numerical method for general finite amplitude wave propagation in two dimensions and its application to spark pulses

The general equations of finite amplitude acoustics, including classical absorption effects and second-order nonlinear effects, are written in a form suitable for two-dimensional numerical solution. A finite difference scheme then is applied to numerically solve the equations. To demonstrate the method, examples are given of spherical free-field propagation, normal plane reflection from a hard surface, and oblique spherical reflection from a hard surface for spark pulses. This method has an advantage over Burgers’ equation methods, one-way wave equation methods, and Pestorius type algorithms in that it can predict the interaction of multiple finite amplitude acoustic waves at arbitrary propagation angles.

Wave propagation across ion cyclotron resonance harmonic layers

Wave propagation across ion cyclotron resonance layers is investigated by use of a boundary layer analysis for a perpendicularly stratified, weakly inhomogeneous plasma. Corresponding to the situation in many plasmas of interest, it is assumed that the wave frequency is much less than the ion plasma frequency, but that the ratio of ion plasma frequency to wave frequency times the ratio of ion thermal speed to the speed of light is small. Nontrivial effects of the cyclotron resonance appear in the boundary layer and modify the current density from the cold plasma limit. These corrections suggest the breakdown of the geometrical optics limit. Wave equations for the field valid within an arbitrary harmonic resonance layer are derived, as well as for the two ion hybrid resonance case. Analytical proofs of reciprocity relations are given for the general wave propagation problems.

Uncoupled Wave Systems and Dispersion in an Infinite Solid Cylinder

In this study, it is shown that there exist uncoupled wave systems for general non-axisymmetric wave propagation in an infinite isotropic cylinder. Two cylindrical surface conditions corresponding to the uncoupled wave systems are discussed. The solutions of the uncoupled wave systems are shown to provide proper bounds of Pochhammer’s equation for a free cylindrical surface. The bounds, which are easy to construct for any Fourier number in the circumferential direction, can be used to trace the branches of Pochhammer’s equation. They also give insight into the modal composition of the branches of Pochhammer’s equation at and between the intersections of the bounds. More refined dispersion relations of Pochhammer’s equation are possible through an asymptotic analysis of the itersections of the branches of Pochhammer’s equation with one family of the bounds. The asymptotic nature of wave motion corresponding to large wave numbers, imaginary or complex, for Pochhammer’s equation is studied. The wave motion is asymptotically equivoluminal for large imaginary wave numbers, and is characterized by coupled dilatation and shear for large complex wave numbers.

Gyroresonant absorption from congruent reduction of an anisotropic pressure fluid model

A system of Maxwell, multifluid momentum and anisotropic pressure equations for a weakly inhomogeneous magnetized plasma is written in a special Hermitian form. A recently developed congruent reduction technique, for extracting embedded, multidimensional, pairwise mode conversion events, is applied in studying the electron gyroresonant absorption problem. The mode conversion from an electromagnetic mode to a fluid pressure mode near the fundamental and second harmonic gyrofrequency is interpreted as gyroresonant absorption. The transmission coefficient is found in an arbitrary three-dimensional plasma and magnetic field geometry, demonstrating the potential of the approach for systematically reducing the order in general multicomponent wave propagation problems in nonuniform plasmas.