High-frequency Wave Propagation Research Articles

On the modelling of dynamic behavior of periodic lattice structures

The aim of this contribution is to propose and apply a new approach to the formulation of mathematical models for the analysis of dynamic behavior of dense periodic lattice structures (space or plane trusses) of an arbitrary form. The modelling approach is carried out on two levels. First, we formulate a discrete model, represented by the system of finite difference equations with respect to the spatial coordinates. The obtained equations describe both low- and high-frequency wave propagation problems. Second, two continuum models are derived directly from the finite difference equations and represented respectively by the second- and the fourth-order PDEs with constant coefficients. These models have a physical sense provided that the considerations are restricted to the long wave propagation phenomena. The proposed approach is applied to the vibration analysis for a certain plane lattice structure. Special attention is given to the determination of the range of applicability of the continuum models.

Kinetic Theory of Plasma Waves - Part III: Inhomogeneous Plasma

Given the extent of the subject, the present text merely provides a list of topics, striking features and references relevant to the kinetic theory of high-frequency wave propagation and absorption in inhomogeneous plasmas. The discussion focuses on tokamak geometry.

Energy Dissipated Across Shocks in Weak Solutions of Conservation Laws

Manipulation of conservation laws through multiplication by mappings of the unknown function result in singular terms that are densities supported on the discontinuity locus. We derive an expression for these singular terms which have been interpreted as the energy dissipated at the shocks. As an application, the expression for these singular terms is obtained from the transport equation governing the propagation of small amplitude high frequency waves in hyperbolic conservation laws. Analogous formulas are obtained for rich systems in several space dimensions.

Time splitting for the Lioville equation in a random medium

We consider the Liouville equations with highly heterogeneous Hamiltonians and their numerical solution by a time splitting algorithm. Such equations model the density of particles evolving according to the corresponding Hamiltonian dynamics as well as the propagation of high frequency waves with a wavelength much smaller than the correlation length of the random Hamiltonian. Our main results are on the relation between the time step used in the time splitting algorithm and the correlation length of the Hamiltonian. In order to fully resolve the Liouville equation, the time step must be chosen much smaller than the correlation length. However, we show that the time step can be chosen of the same order as the correlation length of the Hamiltonian when one is only interested in suitable statistical properties of the solution to the Liouville equation. We also present a more involved time splitting algorithm that allows us to take a time step independent of the correlation length.

Perfectly matched layers for radio wave propagation in inhomogeneous magnetized plasmas

We present 1D and 2D numerical models of the propagation of high-frequency (HF) radio waves in inhomogeneous magnetized plasmas. The simulations allow one to describe the process of linear conversion of HF electromagnetic waves into electrostatic waves. The waves, launched from the lower boundary normally or at a specified angle on a layer of a magnetostrictive plasma, can undergo linear conversion of the incident O-mode into a Z-mode at appropriate locations in an inhomogeneous prescribed plasma density. The numerical scheme for solving 2D HF wave propagation equations is described. The model employed the Maxwellian perfectly matched layers (PML) technique for approximating nonreflecting boundary conditions. Our numerical studies demonstrate the effectiveness of the PML technique for transparent boundary conditions for an open-domain problem.

Perfectly matched layers for radio wave propagation in inhomogeneous magnetized plasmas

We present 1D and 2D numerical models of the propagation of high-frequency (HF) radio waves in inhomogeneous magnetized plasmas. The simulations allow one to describe the process of linear conversion of HF electromagnetic waves into electrostatic waves. The waves, launched from the lower boundary normally or at a specified angle on a layer of a magnetoactive plasma, can undergo linear conversion of the incident O-mode into a Z-mode at appropriate locations in an inhomogeneous prescribed plasma density. The numerical scheme for solving 2D HF wave propagation equations is described. The model employed the Maxwellian perfectly matched layers (PML) technique for approximating nonreflecting boundary conditions. Our numerical studies demonstrate the effectiveness of the PML technique for transparent boundary conditions for an open-domain problem.

Measuring high-frequency wave propagation in railroad tracks by joint time–frequency analysis

The behavior of high-frequency elastic waves propagating in railroad tracks is relevant to the field of rail noise generation and long-range rail inspection. While a large amount of theoretical and numerical work exists to predict transient vibrations propagating in rails, obtaining experimental data has been particularly challenging due to the multimode and dispersive behavior of the waves. In this work a joint time–frequency analysis based on the Gabor wavelet transform is employed for characterizing longitudinal, lateral and vertical vibrational modes propagating in rails in the 1000– 7000 Hz range. The Gabor transform optimizes the time–frequency resolution of the measurements and theoretically requires a single excitation point and a single measurement point. These features make the analysis well-suited for the study of wave propagation in rails. The theory of the wavelet transform is reviewed in the context of dispersive measurements. Accelerometer data were taken from a section of rail subject to impulse dynamic testing in the laboratory. The group (energy) velocity dispersion curves and the frequency-dependent attenuation of the waves were successfully extracted from the wavelet scalograms of the accelerometer signals.

Computational high frequency wave propagation

Numerical simulation of high frequency acoustic, elastic or electro-magnetic wave propagation is important in many applications. Recently the traditional techniques of ray tracing based on geometrical optics have been augmented by numerical procedures based on partial differential equations. Direct simulations of solutions to the eikonal equation have been used in seismology, and lately approximations of the Liouville or Vlasov equation formulations of geometrical optics have generated impressive results. There are basically two techniques that follow from this latter approach: one is wave front methods and the other moment methods. We shall develop these methods in some detail after a brief review of more traditional algorithms for simulating high frequency wave propagation.

Propagation of High Frequency Waves in Slender Engineering Structures

High-frequency vibration in complex engineering structures is challenging problem. Attempts to describe all of the details of real structures fail for many reasons. First, the existence of many inherently uncontrolled factors plays an essential role. In structural dynamics, uncertainties arise from stiffness, mass and damping fluctuations caused by variations in material properties as well as by variations resulting from manufacturing and assembly. The boundary conditions for each structural member also are not known precisely since the high frequency dynamic properties of joints between structural members are especially uncertain. Second, the essential heterogeneity and presence of secondary systems have to be taken into account. Third, the interpretation of the solution of an “exact” boundary-value problem presents great difficulty. The field of vibration of a complex structure (for instance, under a broad-band excitation) is a very complicated function of time and spatial coordinates because a great many modes are excited in the structure. Hence, new approaches are needed for an adequate modelling of structures at high frequencies since with the conventional methods, results become unreliable and can hardly be interpreted. There exist a great number of approaches, among which the Statistical Energy Analysis is the more celebrated one. However, it belongs to a class of discrete approaches, in which field is averaged within each structural member. Thus this approach is not applicable to problems of wave propagation. An alternative is the so-called continuous approach, the approach of high-frequency structural dynamics being utilised in the present paper. The basic substantiation for this approach is that the structures at high frequencies behave like a mechanical system with a continuous spectrum of natural frequencies. This result naturally leads to the representation of complex structures in the form of an elastic carrier structure, in which the primary structure is modelled with oscillators attached to it. The oscillators are introduced into the model to describe numerous secondary systems which comprise the major portion of the structural members of a unit. A number of investigations have been concerned with such a representation. One pioneering work dealt with a one-dimensional representation, whilst other papers were devoted to the three-dimensional analysis of isotropic and anisotropic carrier media, respectively. The present paper is devoted to the problem of propagation of high frequency vibration in such structures, which allows the application of one-dimensional models. It is shown that closed-form solutions are obtained for a rather general case of a structure with varying cross-sectional area, nonlinear energy absorption and secondary systems. The vibration field is shown to have an upper limit which does not depend on the intensity of external excitation.

Computational high-frequency wave propogation using the level-set method with applications to the semi-classical limit of the Schrödinger equations

We introduce a level set method for computational high frequency wave propagation in dispersive media and consider the application to linear Schrodinger equation with high frequency initial data. High frequency asymptotics of dispersive equations often lead to the well-known WKB system where the phase of the plane wave evolves according to a nonlinear Hamilton-Jacobi equation and the intensity is governed by a linear conservation law. From the Hamilton-Jacobi equation, wave fronts with multiple phases are constructed by solving a linear Liouville equation of a vector valued level set function in the phase space. The multi-valued phase itself can be constructed either from an additional linear hyperbolic equation in phase space or an additional linear homogeneous equation and component to the level set function in an augmented phase space. This phase is in fact valid in the entire physical domain, but one of the components of the level set function can be used to restrict it to a wave front of interest. The use of the level set method in this numerical approach provides an Eulerian framework that automatically resolves the multi-valued wave fronts and phase from the superposition of solutions of the equations in phase space.

Influence of ballistics to diffusion transition in primary wave propagation on parametric antenna operation in granular media.

A model of parametric transmitting antenna in granular media is developed, which takes into account velocity dispersion, frequency-dependent absorption, and frequency-dependent scattering of acoustic waves in granular media. The latter process may induce a transition from the ballistics to the diffusion regime of pump (primary) high-frequency wave propagation with increasing frequency. The conditions under which the transition from ballistics to diffusion manifests itself in the change of the demodulated (rectified) low-frequency acoustic pulse profile are established. It is demonstrated that parametric low-frequency radiation contains information on both absorption and scattering of high-frequency acoustic waves.

High-frequency (whispering-gallery mode)-to-beam conversion on a perfectly conducting concave-convex boundary

When a well-confined high-frequency (HF) whispering-gallery (WG) mode launched from the concave side of a concave-convex perfectly conducting boundary propagates toward the convex side, it becomes successively less confined and eventually detaches completely to form a radiated beam field. Detailed characterization of the intricate WG mode-to-beam conversion (here considered for the two-dimensional case) poses a challenging problem in HF wave propagation and asymptotics. This paper begins with a review of the accomplishments and shortcomings in previous investigations that dealt with the analytic-asymptotic aspects as well as the construction of numerical reference solutions to validate the HF approximations. We then develop algorithms based upon the earlier results, but with inclusion of new refinements. These yield a comprehensive asymptotic theory for the induced surface currents on the boundary as well as the near and far fields generated by them, well-matched to the WG mode detachment phenomenology and numerically accurate when compared with reference data obtained from a new hybrid analytic-numerical code. The asymptotic analysis makes use of Kirchhoff, physical optics, and spectral integral representations, WG modes on the concave side, modal ray tracing, replacing modal and/or ray caustics by equivalent induced source distributions, creeping waves on the convex side, etc., with self-consistent blending of nonuniform and locally uniform asymptotics through transition regions where transformations of the affected wavefields occur.

High-Frequency Wave Propagation by the Segment Projection Method

Geometrical optics is a standard technique used for the approximation of high-frequency wave propagation. Computational methods based on partial differential equations instead of the traditional ray tracing have recently been applied to geometrical optics. These new methods have a number of advantages but typically exhibit difficulties with linear superposition of waves. In this paper we introduce a new partial differential technique based on the segment projection method in phase space. The superposition problem is perfectly resolved and so is the problem of computing amplitudes in the neighborhood of caustics. The computational complexity is of the same order as that of ray tracing. The new algorithm is described and a number of computational examples are given, including a simulation of waveguides.

Kinetic Theory of Plasma Waves - Part III: Inhomogeneous Plasma

Given the extent of the subject, the present text merely provides a list of topics, striking features and references relevant to the kinetic theory of high-frequency wave propagation and absorption in inhomogeneous plasmas. The discussion focuses on tokamak geometry.

Propagation of waves in a multicomponent plasma having charged dust particles

Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of that obtained by previous authors. It is found that nonlinear localization of high frequency electromagnetic field in such a plasma generates magnetic field. This magnetic field is seen to depend on the temperatures of electrons and positrons and also on their equilibrium density ratio. It is suggested that the present model would be applicable to find the magnetic field generation in space plasma.

A Continuous Sensor to Measure Acoustic Waves in Plates

An active fiber composite tape with segmented electrodes was modeled for use as a continuous sensor for structural health monitoring of plate structures. The material has unidirectional piezoceramic fibers with interdigital electrodes on the top and bottom surfaces and is poled in the fiber direction. The elastic response of a plate with the modeled sensor was computed in closed form at small time steps, and the coupled piezoceramic constitutive equations were solved. Wave propagation responses and the corresponding sensor voltages were computed in the simulations. The simulations indicate that the continuous sensor can detect damage to the plate based upon high frequency wave propagation characteristics. A continuous sensor comprised of monolithic piezoceramic patches was built and tested to measure simulated acoustic emissions on panel structures. The monolithic patches were used to simplify fabrication of the sensor. The sensor detected simulated acoustic emissions in a fiberglass panel using only one channel of data acquisition. The continuous sensor can potentially reduce the cost, complexity, number of channels of data acquisition, and the weight of monitoring instrumentation to a level where it becomes practical to perform health monitoring on large structures.

Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensional scattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction.

Kinetic Theory of Plasma Waves - Part III: Inhomogeneous Plasma

Given the extent of the subject, the present text merely provides a list of topics, striking features and references relevant to the kinetic theory of high-frequency wave propagation and absorption in inhomogeneous plasmas. The discussion focuses on tokamak geometry.

Use of Gaussian ray basis functions in ray tracing methods for applications to high frequency wave propagation problems

Traditional ray tracing approaches require a large number of geometrical optical (GO) ray tubes, and can become inefficient in many practical applications. The pulse-type basis functions of GO ray tubes cannot provide a good representation in the field expansion if the field to be expanded is not locally planar or the size of the GO ray tubes is too large. A previously developed Gaussian ray basis function (GRBF) has a Gaussian-type amplitude distribution and is suitable to replace a GO ray tube in the ray tracing approaches because the Gaussian-type distribution tends to yield a more efficient field expansion. The GRBFs are incorporated into existing computer programs of generalised ray expansion (GRE). Numerical results validate its accuracy and efficiency in comparison with GO-based GRE for the prediction of EM scattering from open cavities.

High-frequency radars: physical limitations and recent developments

High-frequency (HF) radars based on ground-wave propagation are used for remotely sensing ocean surface currents and gravity waves. For some 20 years a number of systems have been developed taking advantage of improved electronics and computer techniques. However, the performance of these systems are limited by physical constraints, which are due to HF wave propagation and scattering as well as to the technical design of the measuring system. Attenuation of the HF ground-wave is strongly dependent on the radio frequency and sea-water conductivity. Experimental data confirm the predicted decrease of propagation range with decreasing conductivity. HF radar systems use different methods of spatial resolution both in range and azimuth. Range resolution by means of short pulses and frequency-modulated chirps is compared, as well as azimuthal resolution by means of beam forming and direction finding (phase comparison). The emphasis is placed on recent developments.