A Non-Iterative Integration Scheme Enriching the Solution to the Coupled Maglev Vehicle–Bridge System

2021 ◽  
pp. 2150052
Author(s):  
Wei Liu ◽  
Wenhua Guo
Keyword(s):  
State Space ◽  
Equation Of Motion ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Superposition Method ◽  
Coupled Equations ◽  
Maglev Vehicle ◽  
Iterative Integration ◽  
Space Equation ◽  
Bridge System

A non-iterative integration scheme is presented in this study to enrich the solutions to the coupled equations of the maglev vehicle–bridge system. The proposed integration scheme is composed of two integration methods aiming at providing the solutions to equation of motion and state-space equation. First, the equation of motion of the simply supported girder bridge is transformed by the modal superposition method. Then the state-space equation is used to describe the motions of both the vehicle and the suspension control system, with the associated matrices assembled using the fully computerized approach. By adopting this integration scheme, only pure vector calculations arise in the solution process, regardless of the existence of time-dependent displacement and velocity on the right-hand sides of the two coupled equations. The proposed integration method is of the second-order accuracy with and without damping. Being equipped with adequate numerical dissipation and dispersion, the method also possesses the characteristic of little computing errors, as can be achieved through the use of different pairs of parameters. Finally, numerical simulations have been conducted to assess the influence of different feedback gains, three types of bridges with different lengths, and guideway irregularity on the maglev vehicle–bridge system.

scholarly journals Random Vibration Analysis of Coupled Three-Dimensional Maglev Vehicle-Bridge System

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Wei Liu ◽  
Wenhua Guo
Keyword(s):  
State Space ◽  
Governing Equation ◽  
Vibration Analysis ◽  
Random Vibration ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Maglev Vehicle ◽  
Random Vibration Analysis ◽  
Space Equation ◽  
Bridge System

This paper presents a framework for the linear random vibration analysis of the coupled three-dimensional (3D) maglev vehicle-bridge system. Except for assembling the equation of motion of vehicle only via the principle of virtual work, the fully computerized approach is further expanded to assemble the governing equation of fluctuating current via the equilibrium relation. A state-space equation couples the equation of motion of the vehicle and the governing equation of fluctuating current. The equation of motion of a real three-span space continuous girder bridge is established by using finite element methods. A separated iteration method based on the precise integration method and the Newmark method is introduced to solve the state-space equation for the maglev vehicle and the equation of motion for the bridge. Moreover, a new scheme to application of the pseudoexcitation method (PEM) in random vibration analysis is proposed to maximize the computational efficiency of the random vibration analysis of the maglev vehicle-bridge system. Finally, the numerical simulation demonstrates that the proposed framework can efficiently obtain the mean value, root mean square (RMS), standard deviation (SD), and power spectral density (PSD) of dynamic response for the coupled 3D maglev vehicle-bridge system.

Dynamic Interaction Analysis of Maglev-Guideway System Based on a 3D Full Vehicle Model

2017 ◽  
Vol 17 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Dong-Ju Min ◽  
Myung-Rag Jung ◽  
Moon-Young Kim ◽  
Jong-Won Kwark
Keyword(s):  
Dynamic Equilibrium ◽  
Interaction Analysis ◽  
Equations Of Motion ◽  
Dynamic Interaction ◽  
Surface Irregularity ◽  
Superposition Method ◽  
Vehicle Model ◽  
Equilibrium Equations ◽  
Coupled Equations ◽  
Maglev Vehicle

The purpose of this paper is to develop a detailed 3D maglev vehicle and guideway model and investigate the dynamic response characteristics of the coupled system. For this, the maglev vehicle is modeled as one cabin and four bogies having eight electromagnetics, four sensors, and four secondary suspensions based on the Urban Transit Maglev (UTM) system in Korea. The 3D dynamic equilibrium equations of the cabin and bogies are derived by considering the actively controlled electromagnetic forces. Also, the equations of motion for the guideway are derived using the modal superposition method for vertical, lateral, and torsional modes. The resulting coupled equations of motion are then solved using a predictor–corrector iterative algorithm. Finally, through the numerical simulation of the developed system, the responses using the 3D maglev vehicle model are compared with those obtained by the corresponding 2D model. The effects of surface irregularity on the dynamic interaction behaviors are then evaluated for increasing vehicle speeds. Particularly, the 3D resonance conditions of the guideway girder and the maglev vehicle are presented considering the resonance conditions due to equidistant moving loads. In addition, some resonance phenomena are rigorously explored, including the lateral resonance by a series of vehicles running on a girder.

A hybrid solution for studying vibrations of coupled train–track–bridge system

2017 ◽  
Vol 20 (11) ◽  
pp. 1699-1711 ◽  
Author(s):  
Zhihui Zhu ◽  
Wei Gong ◽  
Lidong Wang ◽  
Issam E Harik ◽  
Yu Bai
Keyword(s):  
Equation Of Motion ◽  
Time Dependent ◽  
Integration Scheme ◽  
Train Track ◽  
Strongly Coupled ◽  
Coupled Method ◽  
Loosely Coupled ◽  
Hybrid Solution ◽  
Track Bridge ◽  
Bridge System

This article develops a hybrid model to analyse the dynamic interactions between a train, tracks and a bridge. The model couples the train and track subsystems to form an integrated time-dependent subsystem through a vertically interacting wheel–rail model. In turn, this time-dependent subsystem is coupled with the bridge subsystem by enforcing the compatibility of forces at the contact points between the track and the bridge. A new hybrid solution algorithm is proposed which combines the strongly coupled method and the loosely coupled method to numerically solve the equation of motion of the coupled train–track–bridge system in the time domain. The integrated time-dependent equation of motion of the train–track subsystem is solved by applying the strongly coupled method. The equilibrium equations of the train–track subsystem and bridge subsystem are then solved via the loosely coupled method using the Newmark integration scheme. Significantly faster convergence can be achieved by avoiding the iterative equilibrium calculations between the wheel and the rail, and the total computational efficiency increases significantly because of the considerably smaller size of the time-dependent equations of motion and larger integration time step. The accuracy and computational cost of the proposed method are validated and compared to the existing models using a case study on the vibration of a cable-stayed bridge.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

2018 ◽  
Author(s):  
Tuomas Kärnä ◽  
Stephan C. Kramer ◽  
Lawrence Mitchell ◽  
David A. Ham ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Unstructured Grid ◽  
Splitting Method ◽  
Time Integration ◽  
River Estuary ◽  
Coastal Ocean ◽  
Second Order ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Element Discretization

Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Akbar Gholampour ◽  
Mehdi Ghassemieh ◽  
Mahdi Karimi-Rad
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Numerical Dispersion ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Similar Time ◽  
Unconditionally Stable ◽  
Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

Concurrent Multiple-Time-Scale Simulations With Improved Numerical Dissipation for Structural Dynamics

2013 ◽  
Author(s):  
Tejas Ruparel ◽  
Azim Eskandarian ◽  
James Lee
Keyword(s):  
Time Scale ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Numerical Dissipation ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Constraint Forces ◽  
Conservation Of Energy ◽  
Coupled Equations

Work presented in this paper describes the formulation for implementation of a concurrent multiple-time-scale integration method with improved numerical dissipation capabilities. This approach generalizes the previous Multiple Grid and Multiple Time-Scale (MGMT) Method [1] implemented for the Newmark family of algorithms. The framework is largely based upon the fundamental principles of Lagrange multipliers used to enforce workless nonholonomic constraints and Domain Decomposition Methods (DDM) to obtain coupled equations of motion for distinct regions of a continuous domain. These methods when combined together systematically yield constraint forces that not only ensure conservation of energy but also enforce continuity of velocities across the interfaces. Multiple grid connections between (non-conforming) sub-domains are handled using Mortar elements whereas coupled multiple-time-scale equations are derived for the Generalized-α Method [2]. We show that MGMT Method can be easily extended to incorporate the Generalized-α family of time integration algorithms, hence allowing selective discretization in space and time along with controlled numerical dissipation for distinct grids. We also show that interface energy across connecting sub-domains is identically zero, further assuring global energy balance and continuity of velocities across connecting sub-domains.

A Precision Compensation Method for Space Manipulator Trajectory Planning Based on Particle Filter

2015 ◽  
Vol 742 ◽  
pp. 485-490
Author(s):  
Yi Fan Wang ◽  
Han Xu Sun ◽  
Gang Chen ◽  
Qing Xuan Jia
Keyword(s):  
Particle Filter ◽  
State Space ◽  
Real Time ◽  
Process Parameters ◽  
Trajectory Planning ◽  
Control Variable ◽  
Compensation Method ◽  
Statistical Process ◽  
Space Manipulator ◽  
Space Equation

A precision compensation method for space manipulator trajectory planning is presented for improving the accuracy during the execution of a task. First, the control process is described by using a state space equation. Second, process parameters are estimated in real-time using particle filter. Then, the system’s real time operational reliability is calculated based on the state space equation and process parameters. Finally, a control variable compensation strategy is given based on the theory of Statistical Process Control. Simulations show that this method effectively improves the accuracy and stability of space manipulator control system.

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