Problem In Time Domain Research Articles

A fully discrete Calderón calculus for the two-dimensional elastic wave equation

In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov–Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.

A Fractional Step Method for the Dynamic Electro-Thermal Modelling of Device Structures

Device design in nano-electronics typically leads to large multi-physics problems in time-domain that are characterised by strong feedback coupling. The classical monolithic method results in huge linear systems that must be solved for all time steps. In this contribution a fractional time-stepping scheme is employed in the context of electro-thermal problems in nano-electronics that solves the system without sacrificing the convergence order in time.

Reliable engineering computations of large infrastructures

Engineering computational power and improved mathematical platforms have advanced exponentially in recent years. The presence of uncertainty must also be considered in such formulation. Simulation-based algorithms have been routinely used to address uncertainty-related problems. However, they have limited application to study the realistic behaviour of large infrastructure, and the computations could be very tedious. Incorporation of uncertainties in the context of reliable computations, applied to three different classes of problems, is discussed in this paper. The first part of the paper presents the incorporation of uncertainty in a finite element based computational formulation, denoted as the stochastic finite element method. However, it becomes very inefficient when applied to time-domain dynamic problems. The concept can be improved further by different mathematical schemes. They are discussed in the second part. In the third part, sophisticated computational schemes are integrated with noise-contaminated measured response information to extract features of practical interest in the context of structural health assessment.

A novel solution algorithm for nonlinearly loaded transmission lines inside resonating enclosures

Abstract. Nonlinearly loaded lossless transmission lines inside a rectangular cavity are studied using the left- and right-hand Green's functions of the problem in time domain. These Green's functions are developed for a transmission line with quasi-matched loads. This ensures Green's functions of a short duration. Therefore, the amount of frequency data necessary to obtain time-domain Green's functions is quite limited. The time-domain Green's functions are finally convolved with the left- and right-hand line voltages. With this technique it is possible to treat arbitrarily loaded transmission lines in resonators. An example is presented to demonstrate the applicability of this technique to a transmission line with a simple diode as nonlinear load.

A Hybrid PEEC–SPICE Method for Time-Domain Simulation of Mixed Nonlinear Circuits and Electromagnetic Problems

The simulation of mixed circuit and electromagnetic (EM) structures is of major interest in most EM applications. Many of the developed methods involve modifying a SPICE-like solver to incorporate an EM numerical method, or to extend the EM numerical method to handle the circuit components (e.g., diodes, transistors, etc.) by reimplementing their model definitions. A novel technique has been developed to simulate combined linear/nonlinear circuit and EM problems in time domain. This technique utilizes the partial element equivalent circuit method as the EM solver and employs OrCAD as the circuit solver. The link between the two solvers is established by defining the circuits connected to the EM structure as ports and approximating each port's current-voltage relations at each time point by a system of linear equations. To demonstrate the capability of the developed method, four structures are examined. Good agreement of the results shows the feasibility of the developed method to solve this type of mixed problems. Since OrCAD is used for the circuit simulations, the need to modify a SPICE-like solver or to reimplement the definitions of the circuit devices has been removed. On the other hand, by manipulating the system of equations and proper optimization techniques, an optimal solver can be achieved.

Equating Heteroclinic Orbits in Chen System by Using Scaling Logarithm Change Series (SLS) Method

In this paper, we have used the Scale Logarithm Change Series (SLS) method to reduce the boundary value problem in an infinite time domain to the initial value problem. In this method, we transformed time scale to logarithmic scale by using power series method for each governing point. These points are for each unknown functions and then equate with the corresponding coefficients. This paper demonstrates how the Scale Logarithm Change Series (SLS) method allows to obtain heteroclinic and monoclinic orbits in Chen system.The simulation results obtianed gives the reliability of newly developed algorithm which is extended to prolonged application of Chen system.

Calculation of Dynamic Stress Intensity Factor by the Boundary Element - Laplace Transform Method

Using the Laplace transform and freezing time variable, the problem in the time domain into the frequency domain to solve the problem. The establishment of a crack unit model in the frequency domain, and the boundary integral equation and discrete form containing the crack unit has been deduced. While using Durbin algorithm suitable for transient dynamic response of the inverse Laplace transform, the amount of stress intensity factor of a set of transformation parameters corresponding to the frequency domain into a time domain to obtain the dynamic stress intensity factor of time curve, and calculate the stress intensity factor compared to the boundary finite element method has a Laplace transform high precision, easy to save CPU time and data preparation features, we recommend using this method to calculate the dynamic stress intensity factor.

Time Domain Inverse Problems in Nonlinear Systems Using Collocation & Radial Basis Functions

In this study, we consider ill-posed time-domain inverse problems for dynamical systems with various boundary conditions and unknown controllers. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables. Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is de- veloped in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points. The duffing optimal control problem with var- ious prescribed initial and final conditions, as well as the orbital transfer Lambert's problem are solved by the proposed RBF collocation method as examples. It is shown that this method is very simple, efficient and very accurate in obtaining the solutions, with an arbitrary solution as the initial guess. Since methods such as the Shooting Method and the Pseudo-spectral Method can be unstable and require an accurate initial guess, the proposed method is advantageous and has promising ap- plications in optimal control and celestial mechanics. The extension of the present study to other optimal control problems, and other orbital transfer problems with perturbations, will be pursued in our future studies.

Approximation of the inverse of the Hodge matrix via sparsity pattern

AbstractThe solution of electromagnetic wave propagation problems in time domain using an explicit method requires the inversion of Hodge matrices. This paper proposes an approximation to obtain a sparse inverse via the sparsity pattern of the original matrix. It is also shown the application of the algorithm Cuthill–McKee on Hodge matrices in order to reduce their bandwidth and thus speed up the method of recursive sparsification. Copyright © 2014 John Wiley & Sons, Ltd.

Transient thermal stresses in functionally graded thick truncated cones by graded finite element method

In this paper, an axisymmetric thick truncated cone made of functionally graded materials under transient thermal loads based on classical theory of linear thermoelasticity is considered. The cone is made of a combined ceramic–metal material, and its material is graded through the thickness direction according to a power law distribution. Graded finite element method based on Rayleigh–Ritz energy formulation and Crank–Nicolson algorithm is used to solve the problem in time and space domain. Distributions of temperature, displacements and stresses for different power law exponent and semi-vertex angle of the cone are investigated. Results denote that the distributions of radial displacement are qualitatively similar for the cones and cylinders but the stresses are not and due to increasing the semi-vertex angle, the nature of radial, axial and tangential stresses near the small or large bases of the cone changes. The proposed method is verified by an example which is extracted from published literature and it shows very good agreement.

주파수와 시간영역에서의 강인제어에 관한 연구동향조사

This survey paper reviews robust control problems in both frequency domain and time domain. Robust control is focused on model uncertainties such as modeling error, system parameter variations, and disturbances. Robust control design problems are discussed according to parameter uncertainty, polytopic uncertainty, and norm-bounded uncertainty. Nowadays, robust control theory is combined with various control theory such as model predictive control, adaptive control, intelligent control, and time delay control.

Linear Subspace Reduction for Quasistatic Field Simulations to Accelerate Repeated Computations

The design of electrical machines and high-voltage devices requires the simulation of non-linear low frequency electromagnetic problems in time domain. Typically magneto- and electro-quasistatic problems in magnetic vector/electric scalar potential formulation lead after space discretization to differential-algebraic or ordinary differential equations, respectively. Therefore, huge systems of equations have to be solved in both cases. Typically a large number of degrees of freedom (DoF) is in domains with constant material parameters, i.e., linear subdomains, e.g., air or vacuum in exterior domains. In this paper, we present a method for low frequency simulations based on the proper orthogonal decomposition to reduce the DoF in these linear subspaces. The application of the method will be shown for a simple transformer model and within a global sensitivity analysis (uncertainty quantification) of the switching point in a non-linear resistive material used in a 11 kV standard insulator model.

Inference of weighted $V$-statistics for nonstationary time series and its applications

We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle of Fourier analysis. The established theory for $V$-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference of periodograms and spectral densities.

A Fast Frequency-Domain Parameter Extraction Method Using Time-Domain FEM

In the design of electric devices, the designers are usually required to extract the equivalent circuit parameters of electromagnetic fields at different frequencies. A traditional method is to solve a frequency-domain problem of eddy-current fields using FEM and to calculate the parameters in postprocessing. To obtain the parameters at different frequencies, frequency-sweeping is required. However, it is time consuming and inefficient. In this paper, a novel method for impedance extraction is presented. The proposed method only needs to solve a time-domain problem using FEM a few times, then the impedances at all frequencies can be directly obtained. The numerical experiment, as reported in this paper, shows that it can reduce the computing time by about 95% when compared with traditional methods.

Seismic Response Characteristics of Tunnel Entrance during the Propagation of Rayleigh Wave

During the seismic damage investigation of Wenchuan earthquake, it is found that some of the entrance lining structures, such as that of the Longxi Tunnel, suffered significant pavement blowup, which can be attributed to the effect of Rayleigh wave. Unlike the conventional analysis under shear wave propagating upwards, numerical dynamic analysis under the effect of Rayleigh wave in time domain is much more complicated in practice. In this paper, a practical wave motion input method for three-dimensional Rayleigh wave propagation problems in time domain is proposed and consequently applied in a numerical model to analysis the dynamic response characteristics of tunnel entrance. Desirable simulation result and sufficient accuracy is accomplished with the proposed approach. The particular seismic damage of tunnel entrance that was observed in Longxi tunnel is reproduced successfully in the simulation.

Fault detection observer design using time and frequency domain specifications

This paper deals with a multi-objective fault detection observer design problem in time and frequency domain for time invariant systems. Firstly, to improve the abilities of designed observer, different design criteria are proposed, which are evaluated by some suitable performance indices in time and frequency domain. Details about the relationships among different criteria are analyzed for two cases when the fault appears and disappears. With selected residual evaluation function and threshold, a formula with an envelope in time domain to realize fast fault detection is proposed for some typical faults. The designed observer considers the trade-off between fast transients of the residual for specified faults and the traditional criterion H–/H∞ for general faults and disturbances. Compared with H–/H∞ frequency design method, the effectiveness of the proposed method is demonstrated by the numerical simulation with a vehicle lateral dynamics system.

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Purpose– In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues.Design/methodology/approach– In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-βtechniques, are proposed.Findings– Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods.Originality/value– The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.

An iterative Rankine BEM for wave-making analysis of submerged and surface-piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method (BEM) for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.

Nonlinear Vibration Analysis of Microscale Functionally Graded Timoshenko Beams using the Most General form of Strain Gradient Elasticity

ABSTRACTBased on the Timoshenko beam model, the nonlinear vibration of microbeams made of functionally graded (FG) materials is investigated under different boundary conditions. To consider small scale effects, the model is developed based on the most general form of strain gradient elasticity. The nonlinear governing equations and boundary conditions are derived via Hamilton's principle and then discretized using the generalized differential quadrature technique. A pseudo-Galerkin approach is used to reduce the set of discretized governing equations into a time-varying set of ordinary differential equations of Duffing-type. The harmonic balance method in conjunction with the Newton-Raphson method is also applied so as to solve the problem in time domain. The effects of boundary conditions, length scale parameters, material gradient index and geometrical parameters are studied. It is found that the importance of the small length scale is affected by the type of boundary conditions and vibration mode. Also, it is revealed that the classical theory tends to underestimate the vibration amplitude and linear frequency of FG microbeams.

A Bayesian approach for impact load identification of stiffened composite panel

This paper proposes a statistical approach for identifying impact location and impact force history on a stiffened composite panel using Bayesian inference, in which uncertainties from modelling error and measurement noise are explicitly included. The impact load identification problem in both space domain (impact location) and time domain (impact force history) is first transformed to a parameter identification problem by representing the impact load using a set of parameters. A forward impact model characterising the dynamic responses of a stiffened composite panel subject to a known impact load is incorporated in the identification procedure. By combining the measured data and the prior information, Bayes’ theorem is used to update the probability distributions of the parameters of impact load. In particular, Markov chain Monte Carlo method is employed for sampling the posterior distributions to estimate the impact parameters. Numerical simulation studies using noisy finite element data are conducted to demonstrate the effectiveness of the proposed method.