Wave Propagation in Overhead Wires with Ground Return

Power flow in distribution networks with earth return

In this paper the analysis and design of next-generation VLSI circuits using accurate electromagnetics-based models result in numerical problems of very large scale is presented. Typically, the solution of a problem with N parameters requires at least O(N) computation. With next generation VLSI circuits, however, even O(N) is prohibitively high since N is very large. The method that partially addresses this issue was developed for full-wave modeling of large-scale interconnect structures. In this method, a number of seeds (a seed has a unique cross section) are first recognized from an interconnect structure. In each seed, the original wave propagation problem is represented as a generalized eigenvalue problem. The complexity of solving 3D interconnects of O(N) is then overcome by seeking the solution of a few 2D seeds, which is then post-processed to obtain the solution of the original 3D problem through the development of an on-chip mode-matching technique. The computational bottleneck is the solution of a generalized eigenvalue problem. Efficient algorithms such as ARPACK [2] still require O(M2) storage and operations due to a dense matrix-vector multiplication. We present an algorithm that provides a solution to the generalized eigenvalue problem with O(M) complexity, thus paving the way for the full-wave simulation of next generation VLSI circuits.

Wave propagations and vibrations are associated with the removal of energy by dissipation or radiation. In mechanical systems damping forces causing dissipation are often small compared to restoring and inertia forces. However their influence can be great and is discussed in the present survey paper together with the transmission of energy away from the system by radiation. Viscoelastic constitutive equations with integer and fractional time derivatives for the description of stress relaxation and creep of strain as well as for the description of stress-strain damping hysteresis under cyclic oscillations are compared. Semi-analytical solutions of wave propagation and transient vibration problems are obtained by integral transformation and elasticviscoelastic correspondence principle. The numerical solution of boundary value problems requires discretization methods. Generalized damping descriptions are incorporated in frequency and time domain formulations for the boundary element method and the finite element method.

This work is devoted to the problem of axial shear elastic wave propagation in composites reinforced with a set of unidirected cylindrical fibers. The effective field method and quasicrystalline approximation are used for the development of the dispersion equation for the wavenumber of the mean (coherent) wave field propagating in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of the fibers. In the method, peculiarities in spatial distributions of inclusions are taken into account via a specific correlation function of the fiber set. Such a function may be constructed for random as well as for regular sets of fibers. Thus, wave propagation in random composites as well as in composites with regular fiber arrangements may be considered. In the case of a random set of fibers, different branches of the wave propagation in the composites with an epoxy matrix and glass fibers are obtained and analyzed. Such branches are constructed also for composites with regular lattices of fibers, and the position of the pass bands, where waves can propagate, and stop bands, where waves exponentially attenuate, in the frequency region are indicated. The comparison of the obtained approximate solutions with some exact solutions of the wave propagation problem for regular composites is presented.

CHAPTER 3 - ELASTODYNAMIC THEORY

Numerical solution of the two-dimensional problem of shock wave propagation in outer space

The conventional modal methods become inefficient when expanded to the high frequency region. This leads to a large number of degrees of freedom (DOF) even for one-dimension structures. Meanwhile, a short computational time is also the requirement of on-line structural health monitoring. This paper presented an application of B-spline wavelet on interval (BSWI) finite element for one-dimension elastic wave propagation problems. By using central difference method in time domain, numerical results involving wave propagations in crack free rod and beam were obtained and compared with results calculated by classical finite element method. Numerical examples validated the good performance of BSWI. BSWI could provide a accurate and efficient solution for wave propagation problems. The proposed method provides a good reference for structural health monitoring.

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.

This work presents a new method, the SOR_FEM, spurious oscillation reduction-FEM, that uses analytical solutions of simple problems to find numerical solutions of more complex problems to reduce the spurious oscillations that occur due to solution discontinuity. With the proposed method it is possible to find numerical solutions without spurious oscillations of problems submitted to impulsive point sources without using any approximation for the Dirac delta function. To validate the proposed method, linear problems of heat diffusion and wave propagation in homogeneous and heterogeneous media are solved with the Finite Element Method (FEM).

The problem of the electromagnetic wave propagation in a plane three-layer dielectric waveguide with complex values of the dielectric constant has been solved accurately. The solution of the problem, as applied to InGaAsP injection heterolasers makes it possible to explain the anomalously high temperature sensitivity of threshold current as the result of decreasing the waveguiding. It is evident that such imperfect features of the heterostructure, as the asymmetry or roughness of layers boundaries, worsen the temperature dependence of threshold current, and increase the coefficient of amplitude-phase coupling.

Axisymmetric wave propagation in a solid viscoelastic sphere

The present paper is concerned with the strong mathematical solutions of the well-known problems of hydrodynamics. An approach considered here may be used to solve more complicated problems and may help to the readers to form own point of view on the solution of problems. We tried to eliminate some methodical shortcomings met in recent books on hydrodynamics on the solution of the problems under consideration.

Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

The effect of wave propagation in nonhomogeneous elastic solid whose elastic parameters depend on one space coordinate only is considered. The stress and displacement components are assumed to depend on this same space coordinate and time alone. Taking Young’s modulus E=E0 cos αx and density ρ=ρ0 cos αx, we obtain the general solution for the problem of wave propagation in nonhomogeneous elastic rod. Particular cases in which a modified sawtooth, square, and half sine wave rectifier output as input wave, fed through one end of the rod, are studied, and the displacement u(x,t) is obtained. Graphs are drawn to study the behaviour of the input waves at time t=2 s, α=0.01, and =3.5.

The analysis of damping phenomena, that occur in many physics and engineering problems, reformulated in terms of boundary integral equations and solved via the boundary element method, is a novelty. In this context, we develop here an extension of the so-called energetic boundary element method, recently proposed in literature [1], for the numerical solution of damped waves propagation problems exterior to open arcs in the plane. Hard scattering analysis of 2D damped waves will be carried out directly in space-time domain. The presented numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions [2, 3, 4] and for the 1D damped case [5, 6, 7].