Raphson Iteration Research Articles

MCB-DPO: Multiport Constrained Barrier Method-Based Decoupling Capacitor Placement Optimization on Irregularly Shaped Planes

A multi-port constrained optimization methodology is presented for the optimal placement of decoupling capacitors in power distribution networks (PDNs) of printed circuit boards (PCBs). The proposed method is based on barrier methods and can simultaneously handle multiple ball grid array (BGA) devices and capacitor ports on practical power/ground plane pairs of polygonal shapes without restriction in the problem geometry. Semi-analytical expressions are developed for the magnitude of device port impedance that is set as the objective function. The placement optimization problem including constraints of planar boundaries and impedance specifications is cast into a matrix expression that meets Karush–Kuhn Tucker (KKT) conditions and solved through Newton–Raphson (N–R) iterations. The convergence of iterations is ensured by guaranteeing the positive definiteness of the system matrix through the Levenberg–Marquardt algorithm. Mutual coupling among multiple ports and discrete components of the problem domain is accounted for via matrix calculus techniques applied to the partial derivatives of optimization variables. The derivatives are evaluated accurately exploiting the semi-analytical relations developed for the distributed planar impedance. The proposed method is tested with several examples, and the results are observed to be in good agreement with those obtained from a numerical electromagnetic (EM) simulator while yielding significant speed-up.

Impact and contact problems of explosives by ‘Mixed’ meshless local Petrov-Galerkin finite volume method

The ‘Mixed’ Meshless Local Petrov-Galerkin Finite Volume method (MLPG5) is developed for solving low-velocity impact problems of plastic bonded explosives (PBX). Due to the ductility and plasticity of PBX, there is large deformation instead of pulverization or fragmentation. In this paper, the impact dynamics equations are solved by the meshless approach (MLPG5), both stress as well as displacements are interpolated, through the moving least squares (MLS) interpolation schemes, which eliminates the expensive process of domain integrals and differentiating the shape function. The collocation method is applied to enforce strain-displacement relationships only at each nodal point, instead of the subdomain. In the present mixed method, the independent interpolation of stress improves accuracies of both the plastic stress and contact stress. The contact force is obtained by penalty function method via iteration scheme. Due to the non-linear constitutive relation, the incremental stress is obtained via radial return schemes through Newton Raphson iteration. Finally, several numerical examples are given to demonstrate the feasibility and the accuracy of the present numerical approach compared with the finite element method. Numerical examples also demonstrate the advantages of the present methods: (i) smaller support sizes can be used; (ii) higher accuracies of stress are obtained.

Rigid-Flexible Coupling Dynamics Modeling of Spatial Crank-Slider Mechanism Based on Absolute Node Coordinate Formulation

In order to study the influence of compliance parts on spatial multibody systems, a rigid-flexible coupling dynamic equation of a spatial crank-slider mechanism is established based on the finite element method. Specifically, absolute node coordinate formulation (ANCF) is used to formulate a three-dimensional, two-node flexible cable element. The rigid-flexible coupling dynamic equation of the mechanism is derived by the Lagrange multiplier method and solved by the generalized α method and Newton–Raphson iteration method combined. Comparison of the kinematics and dynamics response between rigid-flexible coupling system and pure rigid system implies that the flexible part causes a certain degree of nonlinearity and reduces the reaction forces of joints. The elastic modulus of the flexible part is also important to the dynamics of the rigid-flexible multibody system. With smaller elastic modulus, the motion accuracy and reaction forces become lower.

Estimation of Distribution Function Parameters for Cases of Risk of Mortality Rate due to Malnutrition and Unhealthy Sanitation in Indonesia

Child undernutrition is a significant problem in Indonesia; persistently high rates of stunting, underweight and wasting. Data about malnutrition and sanitation that taken for this research is data of age-standardized death rate, measured per 100,000 individuals from unsafe sanitation and malnutrition in Indonesia. The purpose of this research is to determine the distribution function and estimate the parameter distribution, so the values can provide identification of risk events. The method used for this research is Maximum Likelihood Estimation (MLE) and Newton Raphson iterations. The distribution function formed is gamma and Generalized Pareto Distribution (GPD), respectively for sanitation and malnutrition problems in Indonesia. The projected probability of occurrence of the risk of death due to malnutrition tends to be low in the future. So that the risk classification of the mortality rate due to malnutrition is considered low based on the results of the probability distribution approach on the GPD function. While, the projected probability of occurrence of the risk of death due to sanitation tends to decrease in the future. Based on the graph, the risk value with a high probability is around 20. So, the risk classification of the mortality rate due to malnutrition is considered moderate based on the results of the probability distribution approach on this gamma function.

Finite-element modeling of partially prestressed concrete beams with unbonded tendon under monotonic loadings

Purpose The partially prestressed concrete beam with unbonded tendon is still an active field of research because of the difficulty in analyzing and understanding its behavior. The finite-element (FE) simulation of such beams using numerical software is very scarce in the literature and therefore this study is taken to demonstrate the modeling aspects of unbonded partially prestressed concrete (UPPSC) beams. This study aims to present the three-dimensional (3-D) nonlinear FE simulations of UPPSC beams subjected to monotonic static loadings using the numerical analysis package ANSYS. Design/methodology/approach The sensitivity study is carried out with three different mesh densities to obtain the optimum elements that reflect on the load–deflection behavior of numerical models, and the model with optimum element density is used further to model all the UPPSC beams in this study. Three half-symmetry FE model is constructed in ANSYS parametric design language domain with proper boundary conditions at the symmetry plane and support to achieve the same response as that of the full-scale experimental beam available in the literature. The linear and nonlinear material behavior of prestressing tendon and conventional steel reinforcements, concrete and anchorage and loading plates are modeled using link180, solid65 and solid185 elements, respectively. The Newton–Raphson iteration method is used to solve the nonlinear solution of the FE models. Findings The evolution of concrete cracking at critical loadings, yielding of nonprestressed steel reinforcements, stress increment in the prestressing tendon, stresses in concrete elements and the complete load–deflection behavior of the UPPSC beams are well predicted by the proposed FE model. The maximum discrepancy of ultimate moments and deflections of the validated FE models exhibit 13% and −5%, respectively, in comparison with the experimental results. Practical implications The FE analysis of UPPSC beams is done using ANSYS software, which is a versatile tool in contrast to the experimental testing to study the stress increments in the unbonded tendons and assess the complete nonlinear response of partially prestressed concrete beams. The validated numerical model and the techniques presented in this study can be readily used to explore the parametric analysis of UPPSC beams. Originality/value The developed model is capable of predicting the strength and nonlinear behavior of UPPSC beams with reasonable accuracy. The load–deflection plot captured by the FE model is corroborated with the experimental data existing in the literature and the FE results exhibit good agreement against the experimentally tested beams, which expresses the practicability of using FE analysis for the nonlinear response of UPPSC beams using ANSYS software.

Monitoring and Evaluation of The Reliability of Distribution Network with Distributed Generation

With the growing population of Ezenei 11KV feeder radiating from the Asaba mains Injection Substation and overstretched distribution network, monitoring and evaluation of the reliability and improvement of distribution network feeder is essential. Failure of some of the equipment at supply restoration is frequent due to weakness of some of the line conductors and long usage of the equipment. In this research work, simulation, analysis and evaluation of the reliability and improvement of Ezenei 11kV feeder was investigated. Load data used were collected from Benin Electricity Distribution Company (BEDC) Asaba between February and April 2018 and this was used to model the sixty – seven (67) buses on the network using Electrical Transient and Analysis Program (ETAP). Load flow analysis was carried out on the modelled network using Newton – Raphson (N-R) iteration method to determine the various bus power (active and reactive) and voltage magnitude using the base and distributed generation injected power. Reliability study was carried out on the network and result showed that the load point indices were increasing as distance of load point increased from feeder. The Seventeen load buses which was Okeke bus to Starcom bus forms the location A. and St. Rebecca bus to Chief Ofili bus forms location B. while Odogu bus to Old Deputy Govt. bus forms location, Iyabi bus to MTN III bus forms location D. Okeke and Jimok water which are the closest load buses to the feeder have an Average Interruption Rate (f/yr) and Annual Output Interruption Rate (hr/yr) of 8.9264f/yr, 417.1507hr/yr while Victor Odogu and Auditor General has an Average Interruption Rate (f/yr) and Annual Output Interruption Rate (hr/yr) of 8.9318f/yr, 417.2857hr/yr and 8.9264 f/yr, 417.1507hr/yr. It was also observed that Chief Osita, Anacho and Estate buses had the highest Average Interruption Rate (f/yr) and Annual Output Interruption Rate (hr/yr).

Dynamic thermal buckling of spherical porous shells

The aim of present work is to address nonlinear dynamic thermal buckling of shallow spherical functionally graded porous shells subjected to transient thermal loading using the first order shear deformation theory (FSDT). A power-law distribution as well as cosine-type porosity distribution are used to model the variation of constituents through the shell thickness. Thermomechanical properties are assumed to be temperature dependent. Using Crank–Nicolson time marching scheme, an iterative procedure is employed to solve nonlinear transient heat conduction equation. For thermal boundary conditions, the outer surface of shells is kept at a reference temperature, while the inner surface experiences a sudden temperature rise. Geometrical type of nonlinearity in the sense of von-Karman is taken into account. The highly coupled nonlinear governing equations of motion are extracted by constructing the appropriate weak form and also using multi-term Ritz–Chebyshev method. The resulting ODEs are then reduced to a system of nonlinear algebraic equations by employing the well-known Newmark family of time integration schemes. The latter equations are solved by means of Newton–Raphson iteration procedure. Budiansky criterion is used to recognize critical parameters of dynamic instability of shells due to applied thermal shocks. Some comparison studies are conducted in order to verify the accuracy of results of the present work. Moreover, various parametric studies are performed to assess the influence of involved parameters.

TUBING SYSTEM PERFORMANCE PROFILING OF DRY GAS WELLS USING NEWTON RAPHSON ITERATION METHOD

This paper focusses on the use of Newton Raphson iteration in determining gas compressibility factor (z) while performing tubing system performance for dry gas wells through the development of a computer model (TBG_SPARK). However, tubing performance analysis performed on the case study (Well-A and Well-B) revealed that the production system of Well-B performed better – since its tubing size and wellhead pressure was lower than that of Well-A. Also, investigations made using modified data revealed that, lower tubing sizes and higher wellhead pressures yield higher gas rates. Conversely, reverse was the case when wellhead pressures were not varied.

Estimating the Catenary Parameter for Catenary Shape Using the Newton Raphson Iterative Method as a Tool for Extended Reach Well Buildup Section Design

The catenary well profile was first used to design extended reach well buildup section in 1985, ever since then a number of wells have been constructed using this profile. It towers over the constant build (circular arc) profile in terms of advantages. Prominent of which is the reduction of torque and drag. This advantage was restrained by the catenary parameter “a”, as “a” determines the shape or trajectory of a catenary shape in any given circumstance. We proffered a solution to estimating the catenary parameter “a” using the Newton-Raphson iteration method for linear equations. This method makes it easy to calculate “a” for almost every desired catenary shape. Also after estimating the values for “a” we went ahead to calculate tensions that will produce that calculated catenary parameter “a” as the parameter is the product of tension at the end of the string and inverse of unit weight. This method of catenary parameter prediction has been used to design overhead electrical cables and predict the extent of sagging of this cables. We used it here to design the path or trajectory of an extended reach well with satisfactory success. Results from the study shows that the use of the Newton-Raphson iterative method for the estimation of catenary parameter “a” for buildup section design of extended reach wells makes it easy for engineers to plan catenary trajectories with available materials and also removes the uncertainties that are inherent in predicting the shape of the trajectory. Keywords : Caternary, String, well, Newton-Raphson, Extended Reach well DOI: 10.7176/JETP/11-5-04 Publication date: October 31 st 2021

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

Linear and nonlinear solvers for simulating multiphase flow within large-scale engineered subsurface systems

Multiphase flow simulation is well-known to be computationally demanding, and modeling large-scale engineered subsurface systems entails significant additional numerical challenges. These challenges arise from: (a) the presence of small-scale discrete features like shafts, tunnels, waste packages, and barriers; (b) the need to accurately represent both the waste form processes at the small spatial scale of the repository and the large-scale transport processes throughout heterogeneous geological formations; (c) the strong contrast in material properties such as porosity and permeability, as well as the nonlinear constitutive relations for multiphase flow. Numerical solution entails discretization of the coupled system of nonlinear governing equations and solving a linear system of equations at each Newton–Raphson iteration. Practical problems require a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. The unique challenges noted above can lead to an ill-conditioned Jacobian matrix and non-convergence with Newton’s method due to discontinuous nonlinearity in constitutive models. Moreover, practical applications can require numerous Monte-Carlo simulations to explore uncertainly in material properties, geological heterogeneity, failure scenarios, or other factors; governmental regulatory agencies can mandate these as part of Performance Assessments. Hence there is a need for flexible, robust, and computationally efficient methods for multiphase flow in large-scale engineered subsurface systems.We apply the open-source simulator PFLOTRAN to the practical problem of performance assessment of the US DOE Waste Isolation Pilot Plant (WIPP) site. The simulator employs a finite volume discretization and uses the PETSc parallel framework. We evaluate the performance of several preconditioners for the iterative solution of the linearized Jacobian system; these range from stabilized-biconjugate-gradient with block-Jacobi preconditioning (BCGS) to methods adopted from reservoir modeling, such as the constrained pressure residual (CPR) two-stage preconditioner and flexible generalized residual solver (FGMRES). We also implement within PETSc the general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), which truncates the Newton update or modifies the update with a Cauchy solution that is within the quadratic model trust-region of the objective function. We demonstrate the effectiveness of each method for a series of test problems with increasing difficulty. We find that the NTRDC and FGMRES-CPR-ABF (FCA) preconditioners generally perform best for the test problem having the extreme nonlinear processes, achieving a 50x speed-up compared with BCGS. The most ill-conditioned and extreme nonlinear simulations do not converge with BCGS (as one may expect), but they do complete the simulation with NTRDC and FCA. We also investigate the strong scalability of each method and demonstrate the impact of node-packing upon parallel performance on modern processor architectures.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

Willingness to Pay of Fishermen Insurance Using Logistic Regression with Parameter Estimated by Maximum Likelihood Estimation Based on Newton Raphson Iteration

The high risk of losing fishermen's life while at sea is inversely proportional to their low welfare. Fishermen are also unable to meet their daily needs when they are not going to sea. Fishermen welfare insurance can be a solution for them to meet their daily needs. Willingness to Pay (WTP) of fishermen to participate in fishermen welfare insurance can be analyzed using Logistic Regression with Newton Raphson and Genetic Algorithm approximations. Some of the main factors that can support their WTP to participate in fishermen welfare insurance, are fishermen education, membership in the fishing community, membership in fisherman business cards, and knowledge about the existence of fishermen insurance. From these four factors, Logistic Regression Model is generated which is expected to help the increase of fishermen’s WTP on fishermen insurance in Indonesia.

Elastic Wave Propagation in Strongly Nonlinear Lattices and Its Active Control

Abstract This work studies elastic wave propagation in strongly nonlinear periodic systems and its active control with specific attention to an infinite mass-in-mass lattice. Piezoelectric materials are applied to it to provide active control loads to manipulate band structures of the lattice. Governing equations of the active mass-in-mass lattice with cubic nonlinearities are established. The control loads are modeled by using linear piezoelectric springs. Due to phase differences among vibrations of different cells during wave propagation, a series of delay functions with different delays are used to represent the steady-state of a traveling wave. The incremental harmonic balance method for delay dynamic systems is employed in this case to calculate periodic solutions of the lattice. The fast Fourier transform is employed to construct the Jacobian matrix of the Newton–Raphson iteration to avoid a large number of Galerkin integrations, and thus, the efficiency is significantly improved. Amplitude-dependent dispersion curves are calculated using results of the linearized system as an initial guess for the iteration. The results are compared with existing results in the literature, which demonstrates that the present method is efficient for wave propagation analysis of strongly nonlinear structures. Effects of nonlinearities, the mass ratio, and different control actions on band structures of the mass-in-mass lattice are investigated through a comprehensive parametric study. Numerical results show that the band structures can be influenced by nonlinearities of the lattice. New stopbands and critical wave numbers can be created by the control actions.

Finite element modelling of fully-coupled flow/fiber-orientation effects in polymer composite deposition additive manufacturing nozzle-extrudate flow

This paper presents a Finite Element Method (FEM) based algorithm to simulate the mutually dependent effects between non-Newtonian polymer melt flow and fiber orientation in Polymer Composite Deposition Additive Manufacturing (PCDAM). The computational approach is employed to analyze an axisymmetric flow with a free surface that defines the melt extrudate. The non-Newtonian power law model is applied to quantify the shear thinning rheological behavior of the polymer flow. The fiber orientation state of the composite melt is simulated using the Advani-Tucker orientation tensor approach, and a streamline-based remeshing technique is applied to compute die swell of the free extrudate. The non-linear FEM system is solved with the Newton Raphson iteration method. Computed results are compared to those obtained using a flow-fiber one way coupling simulation, where it is shown that the magnitude of flow field along the direction of extrusion, as well as the fiber alignment in the flow direction, both increase when full coupling is used. In addition, the extrudate swell ratio solved by the fully-coupled scheme reduces by roughly a factor of ~2× as compared to the weakly-coupled flow solution.

Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme.

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

The parameter estimation of logistic regression with maximum likelihood method and score function modification

The maximum likelihood parameter estimation method with Newton Raphson iteration is used in general to estimate the parameters of the logistic regression model. Parameter estimation using the maximum likelihood method cannot be used if the sample size and proportion of successful events are small, since the iteration process will not yield a convergent result. Therefore, the maximum likelihood method cannot be used to estimate the parameters. One way to resolve this un-convergence problem is using the score function modification. This modification is used to obtain the parameters estimate of logistic regression model. An example of parameter estimation, using maximum likelihood method with small sample size and proportion of successful events equals 0.1, showed that the iteration process is not convergent. This non-convergence can be solved with modifications on a score function. Modification on score function is to change a score function, a matrix of the first derivative of the log likelihood function, to the first derivative matrix itself minus multiplication of information matrix and biased vector. The modification of the score function can quickly yield values of parameter estimates, especially when the sample sizes are larger, and convergence was reached before the 10th iteration.

Conversion of explicit microplane model with boundaries to a constitutive subroutine for implicit finite element programs

AbstractWhereas various simplistic microplane models of limited applicability, defined by stress–strain curves on the microplane, can function as either explicit or implicit, the explicit‐to‐implicit conversion of realistic versatile microplane models for plain or fiber‐reinforced concrete, shale and composites has remained a challenge for quarter century. The reason is that these realistic models use microplane stress–strain boundaries defined by inequalities. Here, we show how the conversion can be easily achieved on the microplane level and then transferred to a tangent stiffness tensor or an inelastic stiffness tensor to be used in Newton–Raphson iterations within a loading step. To ensure convergence, a minor adjustment in the M7 algorithm is introduced to achieve continuity. Power‐law convergence, almost quadratic in most cases, is also demonstrated. Seven examples of crack‐band finite element simulations of challenging laboratory tests document nearly identical implicit and explicit results, as well as good match of test data. Three of them, including the vertex effect in compression‐torsion tests, pure Mode II shear fracture, and the “gap test” of the crack‐parallel compression effect on Mode I load‐deflection curve, have not been reproduced by other models before. The coding of implicit M7 subroutine, usable in, for example, UMAT of ABAQUS, is posted for a free download.

Moving Element Analysis of High-Speed Train-Slab Track System Considering Discrete Rail Pads

This paper presents a study of the dynamic behavior of a coupled train-slab track system considering discrete rail pads. The slab track is modeled as a three-layer Timoshenko beam. The study is carried out using the moving element method (MEM). By introducing a convected coordinate system moving at the same speed as the vehicle, the governing equations of motion of the slab track are formulated in a moving frame-of-reference. By adopting Galerkin’s method, the element stiffness, mass and damping matrices of a truncated slab track in the moving coordinate system are derived. The vehicle is modeled as a multi-body with 10 degrees of freedom. The nonlinear Hertz contact model is used to account for the wheel–rail interaction. The Newmark integration method, in conjunction with a global Newton–Raphson iteration algorithm, is employed to solve the nonlinear dynamic equations of motion of the vehicle–track coupled system. The proposed MEM model of the system is validated through comparison with available results in the literature. Further study is then made to investigate the vehicle–track system accounting for track irregularities modeled as short harmonic wave forms. Results showed that irregularities with short wavelengths have a significant effect on wheel–rail contact force and rail acceleration, and the dynamic response of the track structure does not increase monotonously with the increase of the vehicle speed.