scholarly journals A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph-Catenary System

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Dongdong He ◽  
Qiang Gao ◽  
Wanxie Zhong
Keyword(s):  
Variational Principle ◽  
Dynamic Behavior ◽  
Integration Method ◽  
Time Integration ◽  
Dynamic Responses ◽  
Precise Integration ◽  
Contact Wire ◽  
Parametric Variational Principle ◽  
The Matrix ◽  
Catenary System

Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical time-integration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated.

Dynamic Responses of Supercavitating Vehicles under Non-Stationary Random Excitation

2012 ◽  
Vol 591-593 ◽  
pp. 1934-1937
Author(s):  
Xiang Hua Song ◽  
Guang Ping Zou ◽  
Wei Guang An
Keyword(s):  
High Speed ◽  
Integration Method ◽  
Random Excitation ◽  
State Equation ◽  
Dynamic Responses ◽  
State Equations ◽  
Precise Integration ◽  
Supercavitating Vehicles ◽  
Structural Responses ◽  
First Moment

When the front end of the supercavitating vehicles subjects to very large axial non-stationary random excitation at high speed motion under water, it is necessary to analyze dynamic responses of supercavitating vehicles under non-stationary random excitation. The dynamical equation of supercavitating vehicles is transformed into the form of state equations. The Simpson integration method is going to calculate the integral term of the general solution of state equation to improve the precise integration method. The explicit expression of dynamic responses of supercavitating vehicles is deduced, the means and variances of structural responses are calculated with operation laws of the first moment and second moment. Under different sailing speeds and different cone-cavitator angles dynamic responses of supercavitating vehicles are given by the examples, and the effectiveness of the method was demonstrated.

Dynamic responses of a beam with breathing cracks by precise integration method

2016 ◽  
Vol 60 (5) ◽  
pp. 891-902
Author(s):  
C.C. Cui ◽  
X.S. He ◽  
Z.R. Lu ◽  
Y.M. Chen ◽  
J.K. Liu
Keyword(s):  
Integration Method ◽  
Dynamic Responses ◽  
Precise Integration ◽  
Precise Integration Method

An Innovative Precise Integration Method in Solving Structural Dynamic Problems

2013 ◽  
Author(s):  
Chiun-lin Wu ◽  
Ching-Chiang Chuang
Keyword(s):  
Exact Solution ◽  
High Precision ◽  
Numerical Stability ◽  
Integration Method ◽  
Time Integration ◽  
Computer Hardware ◽  
Integration Algorithm ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Stability And Accuracy

An innovative time integration method that incorporates spurious high-frequency dissipation capability into the so called “high precision direct integration algorithm” is presented, and its numerical stability and accuracy is discussed. The integration algorithm is named “high precision” to emphasize its numerical capability in reaching computer hardware precision. The proposed procedure employs the well-known state space approach to solve the simultaneous ordinary differential equations, the exact solution of which contains an exponential matrix to be efficiently computed using the truncated Taylor series expansion together with the power-of-two algorithm. The proposed method, belonging to the category of explicit methods, is found to provide better accuracy than many other existing time integration methods, and the integration scheme remains numerically stable over a wide range of frequencies of engineering interest. This paper is also devoted to study numerical accuracy of the Precise Integration Method in solving forced vibration problems, particularly near resonance conditions. The numerically obtained transfer functions are then compared with the analytical exact solution to detect spurious resonance. Finally, numerical examples are used to illustrate its high performance in numerical stability and accuracy. The proposed method carries the merit that can be directly applied to solve momentum equations of motion with exactly the same procedure.

Research on Nonlinear Numerical Simulation Method of Icing Conductor on Galloping

2013 ◽  
Vol 706-708 ◽  
pp. 1799-1804
Author(s):  
Xue Ping Zhan ◽  
Kuan Jun Zhu ◽  
Bin Liu ◽  
Ya Duo Liu ◽  
Xin Min Li
Keyword(s):  
Numerical Simulation ◽  
Integration Method ◽  
Time Integration ◽  
Simulation Method ◽  
Dynamic Responses ◽  
Time Integration Method ◽  
Simulation Calculation ◽  
Numerical Simulation Methods ◽  
Nonlinear Numerical Simulation ◽  
Good Agreement

In this paper,the models of the conductors are constructed by finite element method with a three-node, isoparametric cable element. Two numerical simulation methods that include the 4th order Runge-Kutta (referred to as R-K) method and improved time integration method on galloping are studied, and the numerical results on galloping are given by using those two methods by programming. The study result shows that dynamic responses simulated on galloping by using 4th order R-K method and improved time integration method are in good agreement in this paper, but the efficiency of improved time integration method is higher. Result of this paper can provide beneficial reference for galloping simulation calculation.

A new time integration method in structural dynamics using the Taylor series

1998 ◽  
Vol 212 (7) ◽  
pp. 567-575
Author(s):  
S M Wang ◽  
R A Shenoi ◽  
L B Zhao
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Structural Response ◽  
Simultaneous Equation ◽  
Dynamic Responses ◽  
Implicit Methods ◽  
Explicit Integration ◽  
Structural Dynamic ◽  
Order Of Accuracy ◽  
Time Integration Method

The paper presents a new method of time integration for structural dynamic responses. In comparison with well-known methods, it is advantageous in several aspects. It satisfies the governing equations in continuous intervals rather than at discrete time instants (collocation, SSpj) or in average form (weighted, GNpj). It approximates the structural response with user-controllable order of accuracy. It automatically controls the convergence and accuracy so that a correct answer can be assured via auto-adjusted stepping and expansion terms. As far as the accuracy of velocity and acceleration is concerned, the method is much better since rapid convergence can be obtained with ease. Like the explicit integration method, this approach does not demand solution of simultaneous equation sets, yet it can be used with a time increment much larger than that of the implicit methods.

scholarly journals Fast Model Predictive Control Method for Large-Scale Structural Dynamic Systems: Computational Aspects

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haijun Peng ◽  
Qiang Gao ◽  
Zhigang Wu ◽  
Wanxie Zhong
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Dynamic Systems ◽  
Large Scale ◽  
Integration Method ◽  
Control Method ◽  
Matrix Exponential ◽  
Precise Integration ◽  
Structural Dynamic ◽  
The Matrix

A fast and accurate model predictive control method is presented for dynamic systems representing large-scale structures. The fast model predictive control formulation is based on highly efficient computations of the state transition matrix, that is, the matrix exponential, using an improved precise integration method. The enhanced efficiency for model predictive control is achieved by exploiting the sparse structure of the matrix exponential at each discrete time step. Accuracy is maintained using the precise integration method. Compared with the general model predictive control method, the reduced central processing unit (CPU) time required by the fast model predictive control scheme can result in a shorter control update interval and a lower online computational burden. Therefore, the proposed method is more efficient for large-scale structural dynamic systems.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

2020 ◽  
Vol 21 (1) ◽  
pp. 11-21
Author(s):  
Lin Zhao ◽  
Weihao Meng ◽  
Zhongqiang Zheng ◽  
Zongyu Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Coupling Factor ◽  
Dynamic Responses ◽  
Mooring Line ◽  
Second Law ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Runge Kutta Method ◽  
Marine Engineering

AbstractTethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

scholarly journals An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

2021 ◽  
Vol 11 (4) ◽  
pp. 1932
Author(s):  
Weixuan Wang ◽  
Qinyan Xing ◽  
Qinghao Yang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Weak Form ◽  
High Accuracy ◽  
Numerical Dissipation ◽  
Frequency Range ◽  
Time Integration Method ◽  
Numerical Damping

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

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