On the construction and numerical solution of transmission-line and lumped network models of Maxwell's equations

It is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission-line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission-line network models used in the steady-state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two-dimensional example.     

A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation

This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission-line modelling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank–Nicolson routine may be expressed as the exact solution of certain transmission-line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.     

A time domain boundary element method for modeling the quasi-static viscoelastic behavior of asphalt pavements

A time domain boundary element method (BEM) is presented to model the quasi-static linear viscoelastic behavior of asphalt pavements. In the viscoelastic analysis, the fundamental solution is derived in terms of elemental displacement discontinuities (DDs) and a boundary integral equation is formulated in the time domain. The unknown DDs are assumed to vary quadratically in the spatial domain and to vary linearly in the time domain. The equation is then solved incrementally through the whole time history using an explicit time-marching approach. All the spatial and temporal integrations can be performed analytically, which guarantees the accuracy of the method and the stability of the numerical procedure. Several viscoelastic models such as Boltzmann, Burgers, and power-law models are considered to characterize the time-dependent behavior of linear viscoelastic materials. The numerical method is applied to study the load-induced stress redistribution and its effects on the cracking performance of asphalt pavements. Some benchmark problems are solved to verify the accuracy and efficiency of the approach. Numerical experiments are also carried out to demonstrate application of the method in pavement engineering.     

Comparative study of different nonconserving time integrators for wave propagation in hyperelastic waveguides

This paper addresses the formulation and numerical efficiency of various numerical models of different nonconserving time integrators for studying wave propagation in nonlinear hyperelastic waveguides. The study includes different nonlinear finite element formulations based on standard Galerkin finite element model, time domain spectral finite element model, Taylor–Galerkin finite element model, generalized Galerkin finite element model and frequency domain spectral finite element model. A comparative study on the computational efficiency of these different models is made using a hyperelastic rod model, and the optimal computational scheme is identified. The identified scheme is then used to study the propagation of transverse and longitudinal waves in a Timoshenko beam with Murnaghan material nonlinearity.     

Design and implementation of microwave multi-band/multi-level filters using equal-length transmission lines and Yule?Walker scheme

A new method to design microwave filter with multiple-band/multiple-level response is proposed. The modified Yule?Walker equation is used to define the frequency-domain response of filter in the Z domain. To implement a filter having transfer function in the Z domain, an equal-length transmission-line configuration is employed to emulate the filter. A band-pass filter a dual-band band-pass filter and a dual-level band-pass filter are implemented and their frequency responses are measured to illustrate the validity of this design method.     

Shape optimization using time evolution equations

In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original domain on which the boundary value problems of partial differential equations are defined. The variations of the domain are obtained by the time integration of the solution to derive the time evolution equations defined in the original domain. The shape gradient with respect to the domain variations are given as the Neumann boundary condition defined on the original domain boundary. When the constraints are satisfied, the decreasing property of the objective function is guaranteed by the proposed method. Furthermore, the proposed method is used to minimize the heat resistance under a total volume constraint and to solve the minimization problem of mean compliance under a total volume constraint.     

Theory of self-adjoint S-parameter sensitivities for lossless non-homogenous transmission-line modelling problems

The authors present, for the first time, a comprehensive theory for self-adjoint S-parameter sensitivities of non-homogenous transmission-line modelling problems. They show that wideband S-parameter sensitivities can be efficiently calculated without carrying out any adjoint simulations. The N_p original simulations used to calculate the S-parameters of an N_p-port electromagnetic structure supply the sensitivities as well. The authors also present their approach for two different types of nodes utilised in transmission-line modelling. The efficiency and accuracy of their algorithms are illustrated through a number of examples. Good match is obtained between their self-adjoint sensitivities and those calculated using finite differences at the response level.     

Improving the stability of time domain dual boundary element method for three dimensional fracture problems: A time weighting approach

This paper deals with the stability of time domain dual boundary element method (DBEM). A time-weighted time domain DBEM is presented in this study and used for the first time in order to improve the stability of the standard time domain dual boundary element method. In this research a time weighting function with a prediction algorithm based on constant velocity algorithm has been utilized. The present approach was tested for three-dimensional fracture problems. The computer cost for the time of the presented approach is very close to the standard form. The results of numerical experiments carried out within this study indicate that the time weighting method, which is suggested for time domain DBEM, has more stability in comparison with the conventional method.     

Calibration of time domain network analyzers

A calibration technique for a time domain reflectometry and transmission (TDR and TDT) measurement system as applied to network analysis is presented. The calibration corrects for the errors caused by the response of the measurement system. A complete physically-based model is established for the system. A set of calculable standards is developed to satisfy the time domain requirements for calibration. The calibration technique was applied to determining the model parameters of a commercial TDR and TDT system. The calibration enhanced the system bandwidth from 8 GHz to about 20 GHz. Experimental verification is given to demonstrate the validity and accuracy of the calibration technique     

结构噪声主动控制在时域声辐射模态下的仿真研究

以简支矩形板为例，提出了利用时域声辐射模态进行声辐射研究。研究表明时域声辐射模态既与时间无关，且互相独立，使得计算和控制声功率得以简化。针对瞬时声功率主要由第一阶辐射模态的声功率所决定的特点，在时域里进行结构噪声的主动控制研究，通过抵消第一阶辐射模态的声功率使得总的声功率得以有效降低。在此基础上，建立了时域声辐射模态的状态空间方程，对该方程的性能进行了分析，并利用最优控制算法的自适应反馈控制系统进行仿真计算。最后讨论了不同情况下的计算精度，并对影响仿真结果的因素进行了分析。     

Non-invasive VHF injected signal monitoring in atmospheric pressure plasma and axial DC magnetron

A universal non-invasive real-time frequency domain reflectometry plasma process measurement that is independent of impedance matching network is described. The measurement is deployed on the main power transmission line of the plasma tool to detect both hardware and reflections form plasma. An illustration for atmospheric pressure plasma and axial DC magnetron plasma is given. Power handling capability is 20 (2 A×10 V) and 100 W (250 mA×400 V), respectively. Four simple equivalent electrical models in terms of transmission-line theory and frequency dependent reflection modulus (gain) are employed to analyze the DC magnetron measurement results. It is shown that the electrical length between the directional device measurement plane and the plane at which the transmission line is termination by the hardware and plasma determines the frequency response signal. The strength of the signal (depth of the zero) is found to be inversely related to the termination resistance. Information on hardware, and dynamic process-induced changes due to physical sputtering/erosion are accessible.     

A 2.5-ns Timing Standard

The design, construction, and calibration of a passive transmission-line network that provides 2 pulses separated by 2.5 ns ± 1 ps, when excited by a single pulse, is described. The timing standard is useful for calibrating time window durations in time-domain measurement.     

非线性伺服气动弹性的时域数值模拟

运用非定常流场求解器 ,直接求解翼面作任意运动的时域非定常气动力。将拉氏域内的伺服传递函数转化成时域内的伺服状态方程。通过时域气动力、结构状态方程和伺服状态方程的耦合求解 ,实现伺服气动弹性的时域数值模拟。可以方便地模拟如跨音速、大迎角及高超音速等带有不同非线性的伺服气动弹性响应。通过数值模拟发现 ,伺服系统会降低原有气动弹性系统的稳定性 ,结构陷波器的引入可以减弱伺服系统和结构模态的耦合。应用算例给出了大迎角下翼面的极限环响应和 M=7时伺服颤振速度随迎角变化的非线性特性。     

时域有限差分法及其在室内声场模拟中的应用

时域有限差分法将声波基本方程表示为一个时间和空间的迭代方程组,实现对室内声场中低频段的模拟计算。在介绍时域肯限差分法基本原理的基础上,着重探讨采用时域有限差分法模拟室内声场时边界条件的处理方法及该方法在室内声场模拟中的应用。分析了该方法存在的一些问题及其应用前景。     

陀螺转子动力学系统的时间有限元内点法

将保辛的时间有限元法(FEM)应用于陀螺转子动力学系统,给出了陀螺转子动力学系统时间有限元法的时间单元刚度阵列式和非齐次外力的表达式,以及辛时间传递矩阵。在此基础上,提出了精度更高的时间有限元内点法(IDTFEA),该方法既继承了时间有限元保辛的优良特性,又大大提高了数值计算精度,具有非常明显的优越性。算例给出了该方法和Newmark方法的比较结果,表明该方法的优越性。     

Time and time again

In the study of human-machine systems, the need to have a model of the user is by now taken for granted. The model can be used both as support for design and analysis and as a representation of the user that resides somewhere in the machine. When it comes to the practice of modelling, two characteristic approaches can be recognized. The first focuses on the how of modelling, and is concerned mainly with the structure and contents of models. The second focuses on what is being modelled, and is concerned mainly with the functioning or performance of the model. The first approach has dominated human-machine systems research for several decades, and has led to orthodoxy in modelling by which certain structural characteristics are accepted without questioning. This unreflective attitude to modelling has been criticised several times, although with little effect. In taking the second approach and focusing on what should be modelled, two important issues are that human performance varies in level of control, i.e. in terms of how orderly it is, and that thinking and acting take time-- and occur in a context where time is limited. Although it is clearly essential that user models can account for these characteristics, very few existing models are capable of doing so because they focus on internal information processing rather than on performance in a dynamic environment. The paper describes a type of functional model, called contextual control models, which shows how it is possible to account for both different control modes and how performance is affected by time. Indeed, control and time are intimately linked and loss of one may lead to a loss of the other. The contextual control model distinguishes among four characteristic control modes (strategic, tactical, opportunistic and scrambled) and two time parameters (time to evaluate, time to select) that are seen relative to the available time. Finally, a number of applications of contextual control models are described.     

Acoustic calculations with the hybrid boundary element method in time domain

The boundary element method (BEM) is an efficient tool for the calculation of acoustic wave propagation in fluids. Transient waves can be solved by either using a formulation in frequency domain along with an inverse Fourier transformation or a time domain formulation. To increase the efficiency for the solver and allow for an efficient coupling with finite element domains the symmetry of the system matrices is advantageous. If Hamilton's principle is used, a symmetric variational formulation can be established with the velocity potential as field variable. The single field principle is generalized as multifield principle as basis of a hybrid BEM for the calculation of acoustic fields in compressible fluids in time domain. The state variables are separated into boundary variables, which are approximated by piecewise polynomials and domain variables, which are approximated by a superposition of weighted fundamental solutions. In both approximations the time and space dependency is separated. This is why static fundamental solution can be used for the field approximation. The domain integrals are eliminated, respectively, transformed into boundary integrals and an equation of motion with symmetric mass and stiffness matrix is obtained, which can be solved by a direct time integration scheme or by mode superposition. The time derivative of the equation of motion leads to a formulation with pressure and acoustic flux on the boundary for an easier interpretation of the variables.     

一种时域解调激光干涉仪调制信号的方法

针对某低频水平振动校准设备的激光干涉仪,利用NI公司的多功能采集卡,采集激光干涉仪的调制信号及与其同相位的电容式位移传感器的输出信号.根据激光干涉仪调制原理,提出一种时域解调调制信号的方法.根据调制信号条纹的时域特性和它被限幅的实际特点,利用labview软件实现了信号的解调,并将电容位移传感器信号作为参考信号,还原解调后信号的相位,从而得到振动台高精度的振动波形.实验证明,此方法对连续振动信号的解调效果良好,具有较好的重复性和稳定性,精度可达到激光干涉仪发射激光波长的四分之一.     

A new visco- and elastodynamic time domain Boundary Element formulation

The usual time domain Boundary Element Method (BEM) contains fundamental solutions which are convoluted with time-dependent boundary data and integrated over the boundary surface. If the fundamental solution is known, e.g., in Elastodynamics, the temporal convolution can be performed analytically when the boundary data are approximated by polynomial shape functions in time and in the boundary elements. This formulation is well known, but the resulting time-stepping BEM procedure produces instabilities and high numerical damping, when the time step size is chosen too small and too large, respectively. Moreover, in case of viscoelastic or poroelastic domains, the fundamental solution is known only in the frequency domain such that the time history of a response can only be obtained by an inverse transformation of the frequency domain results. Here, a new approach for the evaluation of the convolution integrals, the so-called “Operational Quadrature Methods” developed by LUBICH, is presented. In this formulation, the convolution integral is numerically approximated by a quadrature formula whose weights are determined by the Laplace transform of the fundamental solution and a linear multistep method. Hence, the frequency domain fundamental solution can be used without the need of an inverse transformation. Therefore, the extension to viscoelastic problems succeeds using the elastic-viscoelastic correspondence principle.