Numerical Solution of Some Three-State Random Vibration Problems

1995 ◽  
Author(s):  
S. F. Wojtkiewicz ◽  
L. A. Bergman ◽  
B. F. Spencer
Keyword(s):  
Finite Element ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Planck Equation ◽  
Iterative Solution ◽  
Response Characteristics ◽  
Solution Strategies ◽  
Gaussian White Noise Process ◽  
Vibration Problems

Abstract This paper reports some of the recent efforts by the authors to examine the random vibration of mechanical systems of large dimension. A finite element solution method for the stationary three-dimensional Fokker-Planck equation, employing sparse storage and iterative solution strategies, is outlined and then applied to several representative systems. The first of these is a linear oscillator subjected to a first order linearly filtered Gaussian white noise process. This problem is used to verify and assess the accuracy of the method. After verification, two Duffing systems are analyzed, one exhibiting unimodal and the other bimodal response characteristics. Finally, some comparisons of the finite element results with those from Monte Carlo simulation are made for the two nonlinear systems.

Electromagnetic induction by a finite electric dipole source over a 2-D earth

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Martyn J. Unsworth ◽  
Bryan J. Travis ◽  
Alan D. Chave
Keyword(s):  
Finite Element ◽  
Electromagnetic Fields ◽  
Electric Dipole ◽  
Numerical Solutions ◽  
Current Source ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Horizontal Electric Dipole

A numerical solution for the frequency domain electromagnetic response of a two‐dimensional (2-D) conductivity structure to excitation by a three‐dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite‐element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far‐field. In combination with an iterative solution for the along‐strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air‐earth interface are presented to illustrate the usefulness of the code.

A Parallel Computational Model for Three-Dimensional, Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

2014 ◽  
Vol 16 (4) ◽  
pp. 1056-1080 ◽  
Author(s):  
Wei Leng ◽  
Lili Ju ◽  
Max Gunzburger ◽  
Stephen Price
Keyword(s):  
Finite Element ◽  
Computational Model ◽  
Stokes Flow ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Iterative Solution ◽  
Element Model ◽  
High Order

AbstractThis paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the “cold spoke” instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.

scholarly journals A Quasi-Three-Dimensional Finite Element Solution for Steady Compressible Flow Through Turbomachines

1982 ◽  
Author(s):  
A. S. Ücer ◽  
İ. Yeġen ◽  
T. Durmaz
Keyword(s):  
Finite Element ◽  
Solution Method ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Field Variable ◽  
Dimensional Solution ◽  
Subsonic Flows ◽  
Dimensional Finite Element ◽  
Flow Through ◽  
Three Dimensional Finite Element

A quasi-three-dimensional solution method is presented for subsonic flows through turbomachines of arbitrary geometry. Principal equations are based on Wu’s formulation of flow on blade-to-blade and hub-to-shroud surfaces, modified such that the same hub-to-shroud principal equation is used for all types of stream surfaces. Blade-to-blade surfaces are assumed to be surfaces of revolution. A stream function is used as the field variable. The problem is solved by finite element method. An iterative solution is used to find the quasi-three-dimensional solution. Solutions at hub, tip and mid height blade-to-blade surfaces are used to construct a mean hub-to-shroud surface and vice versa, until convergence is obtained. Results indicate that the developed technique is satisfactory for predicting the flow through turbomachine blades.

Application of the Dang Van Fatigue Criterion to the Rail/Wheel Contact Problem

2010 ◽  
Vol 636-637 ◽  
pp. 1178-1185 ◽  
Author(s):  
D.F.C. Peixoto ◽  
L.A.A. Ferreira ◽  
Paulo Manuel Salgado Tavares de Castro
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Three Dimensional ◽  
Element Analysis ◽  
Solution Strategies ◽  
Dimensional Finite Element ◽  
Preliminary Study ◽  
Rigid Plane ◽  
Three Dimensional Finite Element ◽  
Fatigue Criterion

Great interest is dedicated to the wheel/rail contact problem, in particular as a result of some accidents worldwide and also in Portugal. In the present work a three dimensional finite element analysis of the wheel/ rail contact problem was performed using the software ABAQUS. A preliminary study on simpler geometries was carried out, in order to identify the solution strategies giving more accurate solutions. The influence of mesh refinement, friction coefficient, and numerical techniques as Lagrange and penalty functions were analysed in the simpler cases of contact of two cylinders along a generatrix, and the contact of a cylinder and a rigid plane. The corresponding Hertz solutions were programmed using MATLAB in order to compare with the finite element analyses. The numerical procedures giving better results were later applied to the wheel/rail contact problem, using standard rail and wheels profiles used by the Portuguese Railways company (CP). The influence of small geometry variations on the stress analysis results was then studied, and the study of initiation of defects using the Dang Van fatigue criterion was performed.

Finite Element Analysis of Ballastless Track Rail-Floating Slab’s Dynamic Characteristics

2010 ◽  
Vol 44-47 ◽  
pp. 3907-3911
Author(s):  
Lin Ya Liu ◽  
Jin Wang ◽  
Rui Lv
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Response ◽  
Three Dimensional ◽  
Element Model ◽  
Maximum Response ◽  
Vertical Force ◽  
Element Analysis ◽  
Response Characteristics ◽  
Ballastless Track

By using the finite element analysis software ANSYS, a three-dimensional dynamic finite element model of ballastless track rail –floating slab was established. The model takes into account of the track irregularity case, the analysis the dynamic response characteristics of the rail and floating slab under the vertical force in the track structure. The results showed that: when the train load goes through the line, the dynamic response of the rails and floating slabs gradually increases to maximum and then decreases; the maximum response displacement of rail is at 0.625mm ~ 0.75mm and the maximum response acceleration values is in between 5000m/s2~6000 m/s2; the maximum response displacement value of floating slab is about 0.25mm, the maximum response acceleration value is between 0.8 m/s2~1.2m/s2.

Vibration and Noise Analysis for a Motor of Pure Electric Vehicle

2014 ◽  
Vol 915-916 ◽  
pp. 98-102 ◽  
Author(s):  
Meng Bao ◽  
En Wei Chen ◽  
Yi Min Lu ◽  
Zheng Shi Liu ◽  
Shuai Liu
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Electric Vehicle ◽  
Natural Frequency ◽  
Noise Analysis ◽  
Three Dimensional ◽  
Time Signal ◽  
Element Analysis ◽  
Response Characteristics ◽  
Coil Winding

To control the pure electric vehicle motors vibration and noise, the dynamic characteristics of the motor are analyzed. Dynamic characteristic include the natural frequency and response characteristics of different parts of the motors structural member. This paper uses three-dimensional software Pro/E modeling of the motor: By making appropriate assumptions and equivalent treatment of the motors stator, rotor core and coil winding, establish the finite element simulation model of the various components .Using the finite element analysis software Workbench analyzes the windings and motor model modal analysis, to get natural frequency of each mode. To make a modal analysis test, we can use hammering method done on the motor. By using real-time signal analyzer AWA6291 make spectral analysis of the motor online, comprehensive comparative analysis of the results and used to guide motor design.

A Quasi-Three-Dimensional Finite Element Solution for Steady Compressible Flow Through Turbomachines

1983 ◽  
Vol 105 (3) ◽  
pp. 536-542 ◽  
Author(s):  
A. S. U¨cer ◽  
I˙. Yeg˙en ◽  
T. Durmaz
Keyword(s):  
Finite Element ◽  
Solution Method ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Field Variable ◽  
Dimensional Solution ◽  
Subsonic Flows ◽  
Dimensional Finite Element ◽  
Flow Through ◽  
Three Dimensional Finite Element

A quasi-three-dimensional solution method is presented for subsonic flows through turbomachines of arbitrary geometry. Principal equations are based on Wu’s formulation of flow on blade-to-blade and hub-to-shroud surfaces, modified such that the same hub-to-shroud principal equation is used for all types of stream surfaces. Blade-to-blade surfaces are assumed to be surfaces of revolution. A stream function is used as the field variable. The problem is solved by finite element method. An iterative solution is used to find the quasi-three-dimensional solution. Solutions at hub, tip, and midheight blade-to-blade surfaces are used to construct a mean hub-to-shroud surface and vice versa, until convergence is obtained. Results indicate that the developed technique is satisfactory for predicting the flow through turbomachine blades.

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