Problem In Time Domain Research Articles

A boundary element formulation to solve transient dynamic elastoplastic problems

Transient dynamic elastoplastic analysis is performed with the alternative use of the standard simple elastostatic fundamental solution. The explicit presence of the inertial domain integral (arising from the use of the elastostatic fundamental solution) and the option for its maintenance in the formulation leads to the discretization of the entire domain of the problem in the numerical implementation. The time domain problem is solved by the direct integration method, with the Houbolt integration scheme, whereas the initial stress problem is solved, for each time step, by employing efficient implicit procedures. An illustrative example is presented in the end of the paper to verify the accuracy of the results produced by this formulation.

A shutter design for time domain studies using synchrotron radiation at the Advanced Photon Source

In general, a variable repetition rate of the x-ray bunches is needed to explore time domain problems using x-rays. In some instances, the results of several hundreds or thousands of x-ray pulses must be averaged requiring the sample to be in the same time-dependent state each time the monitoring pulse strikes. The important point is that before a second x-ray pulse hits the sample, the system must return to its initial relaxed ground state prior to another spectrum pulse in order to prepare the same excited state again. Our key design principle employs a subsonic, rotating mirror whose period is slaved to the synchrotron intrapulse period. The synchrotron x-ray bunches will be reflected a distance of about 2 m to a narrow 0.5-mm slit just in front of the sample. A mirror rotating at a low 7500 rpm (125 Hz) is sufficient to select a single synchrotron pulse for the Advanced Photon Source. The very precise phase stability required by this method is currently available in rotating mirror devices for laser scanning.

Shape functions for mixed p-version finite elements in the time domain

The advantages of mixed formulations are well known in that they simplify the form of the governing equations and can lead to potentially significant savings in computational effort for given accuracy. Likewise, the p-version of the finite element method is known to offer savings in computational effort for some problems. In this paper, shape functions for a mixed p-version finite element formulation in the time domain are developed. These shape functions produce a high percentage of zeros in certain coefficient matrices. The mixed formulation in time used here is based on a weak form of Hamilton's extended principle. The present formulation allows for accurate and efficient solution of time-domain problems. The accuracy and power of this formulation are shown for initial value problems (such as time marching) and for directly obtaining the periodic response of linear systems. The method is shown to yield a family of accurate, unconditionally stable algorithms for initial-value problems based on a simple linear oscillator.

Time-Domain Green Function Corresponding to a Time-Harmonic Point Source in Complex Space

ABSTRACT The time-domain counterpart of the scalar field arising from a time-harmonic point source in the complex space is derived. The solution corresponds to the complex-space source Green function, which has grown very important in various electromagnetic problems, because it can be applied to approximate the narrow radiation of the Gaussian beam type. The time-domain counterpart presented in the present paper is seen to be real and causal. The solution is demonstrated to an asymptotic case of the Sommerfeld half-space problem in time domain.

The discrete time domain Green's function or Johns matrix — A new powerful concept in transmission line modelling (TLM)

AbstractA new TLM‐based concept analogous to the Green's function approach in classical electromagnetic theory is presented. It employs the procedure known as time domain diakoptics. The response of a TLM mesh to a unit impulse excitation at selected input points is interpreted as a discrete Green's function in the time domain, and the term ‘Johns matrix’ is proposed for this characteristic response. As in classical theory, the response of the mesh to an arbitrary excitation is found by convolving the excitation with its Johns matrix. This concept extends the generalized scattering parameter concept into the time dimension, opens unprecedented possibilities for partioning time domain problems at the field level, and permits large‐scale preprocessing of substructures for computer‐aided design. It also represents and elegant way of modelling broadband absorbing boundary conditions, imperfectly conducting walls and general frequency dispersive boundaries in the time domain.

Mooring Line Damping for Slow Drift Oscillation of Semi-Submersibles

Dynamic tensions of mooring lines may be ignored in the estimation of wave frequency motions of a floating structure, but for slow drift oscillations hydrodynamic forces acting on mooring lines are important, because drag forces acting on mooring lines act as the damping force and have a great effect on the slow drift oscillation. When dynamic tension of mooring lines are calculated in full consideration of added mass forces and drag forces acting on mooring lines, a numerical calculation such as Lumped Mass Method is usually used. The numerical calculation needs prohibitively long computer time and it is not practical in the early stage of the design of a floating structure. The authors have developed an Approximate Method for calculating the dynamic tension taking the added mass force and drag force into consideration. The method has a short computation time and the accuracy has been confirmed by comparing calculated results with experiments. In this paper a Modified Approximate Method extended to the time domain problem is presented. The calculated results are compared with the experimental ones and they are found to be in good agreement.

Rise and fall of directed transient: Use of Mellin transformation in time domain problems

The Mellin transform is utilized in the study of the time domain radiation from a circular disk. In the Mellin transformed space, the integrals over the source distribution for the frequency domain fields and the Fourier transform of the fields to the time domain can be carried out in closed form. The source is a uniform distribution of current which is switched on at t = 0 and varies as (t/T)2δ for some positive T. It is found that δ must be positive when the source is assumed to be switched on at t = 0. Furthermore, in some finite volume of space, the transient pulse is plane wave‐like and propagates along the axis of the disk. Its E and H field strengths decrease as R−2δ. Its energy decreases as R−1–4δ. A measure of the effectiveness of the current source in generating such a directed transient pulse is also provided.

Time-domain solution of the parabolic equation including nonlinearity

This paper develops a two-dimensional (range and depth) formulation for small-angle propagation of nonlinear acoustic pulses and weak shocks in a refracting medium which can be range dependent. The formulation readily extends to three dimensions. The nonlinearity is most efficiently treated in the time domain, so the signal is not Fourier decomposed into component frequencies. Beginning with a second-order wave equation which includes the lowest-order nonlinearity, an approximate first-order nonlinear progressive wave equation (NPE) is derived. The NPE is the nonlinear time-domain counterpart of the linear frequency-domain parabolic equation (PE). The derivation is accomplished by transforming the wave equation to a pulse-following frame and perturbing about a unidirectional plane-wave signal. The NPE manifests a natural separation of terms governing refraction, diffraction, spreading and nonlinear steepening. Numerical methods are outlined for the solution of the time-domain problem. Calculations using the formulation developed here successfully follow the development of initially smooth pulses into N waves and the reflection of weak shocks from a caustic.

3-D DYNAMIC ANALYSIS OF GROUND MOTION BY FEM WITH NON-REFLECTING BOUNDARY

Dynamic Finite Element Method is frequently used in analyzing wave propagation problems. In the case of infinite or infinite half media, the presence of artificial boundaries introduces wave reflections from boundaries. Authors tried to solve the problem applying Smith-Cundall's method and extended the method to three dimensional problem. Smith-Cundall's method is to solve the problem by superposing two types of reflected wave from Dirichlet's and Neumann's boundaries. This method is theoretically complete. Authors made clear the weak point of the method, however, the influence of the weak point on the computed results is small, therefore, the results by this method is reliable. This method treats problems in time domain, so nonlinear problem such as liquefaction can be solved by this method in near future.

A comparative study on three boundary element method approaches to problems in elastodynamics

AbstractIn this study, three boundary element method approaches are compared by solving a typical problem in linear elastodynamics. The first approach formulates and solves the problem in the real time domain in conjunction with a time‐stepping algorithm. The other two approaches formulate and solve the problem in the Laplace and the Fourier transformed domains, which necessitates a numerical inversion of the results to the time domain. The results obtained compare favourably with available analytic solutions. A detailed tabulation of the computer time and memory requirements of each approach is presented.

Adaptive frequency sampling filters

We present two new structures for adaptive filters based on the idea of frequency sampling filters and gradient based estimation algorithms. These filters have a finite impulse response (FIR) and can be thought of as attempting to approximate a desired frequency response at given points on the unit circle. The filters operate in real time with no batch processing of signals as is the case when using the discrete Fourier transform. They result in a marked reduction in dimension of the time-domain problem of fitting an Nth-order FIR transversal filter to a collection of length 2 transversal filters and further to a collection of N scalar filters. The advantages of this are then discussed.

Adaptive frequency sampling filters

We present two new structures for adaptive filters based on the idea of frequency sampling filters and gradient based estimation algorithms. These filters have a finite impulse response (FIR) and can be thought of as attempting to approximate a desired frequency response at given points on the unit circle. The filters operate in real time with no batch processing of signals as is the case when using the discrete Fourier transform. They result in a marked reduction in dimension of the timedomain problem of fitting an Nth-order FIR transversal filter to a collection of length 2 transversal filters and further to a collection of N scalar filters. The advantages of this are then discussed.

Application of the Hybrid Technique to Time Domain Problems

A hybrid technique which formally combines the method of moments with the geometrical theory of diffraction is used to efficiently generate sufficient frequency domain data so that accurate transformation to the time domain can be accomplished via the fast fourier transform. The advantage of the hybrid technique is that it permits one to solve problems that cannot readily be solved by either method alone. For example, the problem of a monopole at the center of a circular disk is considered. The monopole is characterized by the method of moments, and the finite size of the disk is accounted for by geometrical theory of diffraction techniques. The technique applies equally well, however, to antennas on other bodies such as satellites and aircraft and could be used to investigate the electromagnetic pulse (EMP) response of antennas on such bodies.

Application of the hybrid technique to time domain problems

A hybrid technique which formally combines the method of moments with the geometrical theory of diffraction is used to efficiently generate sufficient frequency domain data so that accurate transformation to the time domain can be accomplished via the fast fourier transform. The advantage of the hybrid technique is that it permits one to solve problems that cannot readily be solved by either method alone. For example, the problem of a monopole at the center of a circular disk is considered. The monopole is characterized by the method of moments, and the finite size of the disk is accounted for by geometrical theory of diffraction techniques. The technique applies equally well, however, to antennas on other bodies such as satellites and aircraft and could be used to investigate the electromagnetic pulse (EMP) response of antennas on such bodies.

Time-domain approximation and system modelling using a damped least-squares algorithm

The method of damped least-squares is proposed for the solution of time-domain approximation problems, system-modelling problems and data-fitting problems. The method is based on the Levenberg-Marquardt damping technique together with the recent Massara—Fidler algorithm. The method is very efficient and it can be applied to a variety of problems. A number of examples illustrate the method.

Time domain approximation using digital methods

Abstract Two digital methods are proposed for the solution of the time-domain approximation problem. Tho first method, based on a reeursivo algorithm for tho matrix pseudo-iriverso, determines the pulse transfer function of a discrete-timo system of a prescribed order providing the best fit in tho least squares sense at tho samplo points. Tho continuous-time system transfer function is then derived by using a simple transformation provided that tho sampling frequence oxeeeds tho Nyquist rate. Tho method is direct and computationally efficient. The second method is based on using an offieiont gradient search algorithm providing the best fit in the least pti sense at tho samplo points. A number of examples illustrato the methods

An Interactive Computer Approach to Tolerance Analysis

An interactive technique for statistical tolerance analysis has been developed for a computer with graphic display. The computer program called TAP provides for random perturbation of parameter values, repeated evaluation of system performance, and display of distribution histograms. The interactive capability of the program enables the designer to introduce modifications to the system so that the relative effects of these changes can be quickly evaluated with the graphic display. The program has been implemented on a computer facility consisting of a CDC 3300 digital computer, an ITT digital display scope, and an EAI 8800 analog computer. Two applications are discussed to illustrate the adaptability of the technique to either linear or nonlinear problems. The digital simulation of an active circuit is used to show how the interaction with graphic display saves time in evaluating alternative designs. A hybrid simulation of an equalizer for a digital transmission system illustrates that complex time domain problems can be economically analyzed using TAP. In addition, it is shown how TAP is used to measure the reproducibility of an analog simulation.

A general theory of finite elements. II. Applications

AbstractIn Part I of the this paper, topological properties of finite element models of functions defined on spaces of finite dimension were examined. In this part, a number of applications of the general theory are presented. These include the generation of finite element models in the time domain and certain problems in wave propagation, kinetic theory of gases, non‐linear partial differential equations, non‐linear continuum mechanics, and fluid dynamics.