A Time-Harmonic Three-Dimensional Vector Boundary Element Model for Electromechanical Devices

2010 ◽  
Vol 25 (3) ◽  
pp. 606-618 ◽  
Author(s):  
Tim C. O'Connell ◽  
Philip T. Krein
Keyword(s):  
Boundary Element ◽  
Three Dimensional ◽  
Element Model ◽  
Dimensional Vector ◽  
Time Harmonic ◽  
Electromechanical Devices

Modelling ground vibration from railways using wavenumber finite- and boundary-element methods

2005 ◽  
Vol 461 (2059) ◽  
pp. 2043-2070 ◽  
Author(s):  
X Sheng ◽  
C.J.C Jones ◽  
D.J Thompson
Keyword(s):  
Boundary Element ◽  
Singular Integrals ◽  
Moving Load ◽  
Three Dimensional ◽  
Ground Surface ◽  
Ground Vibration ◽  
Element Model ◽  
Boundary Element Methods ◽  
Element Discretization ◽  
Environmental Vibration

A mathematical model is presented for ground vibration induced by trains, which uses wavenumber finite- and boundary-element methods. The track, tunnel and ground are assumed homogeneous and infinitely long in the track direction ( x -direction). The models are formulated in terms of the wavenumber in the x -direction and discretization in the yz -plane. The effect of load motion in the x -direction is included. Compared with a conventional, three-dimensional finite- or boundary-element model, this is computationally faster and requires far less memory, even though calculations must be performed for a series of discrete wavenumbers. Thus it becomes practicable to carry out investigative study of train-induced ground vibration. The boundary-element implementation uses a variable transformation to solve the well-known problem of strongly singular integrals in the formulation. A ‘boundary truncation element’ greatly improves accuracy where the infinite surface of the ground is truncated in the boundary-element discretization. Predictions of vibration response on the ground surface due to a unit force applied at the track are performed for two railway tunnels. The results show a substantial difference in the environmental vibration that could be expected from the alternative designs. The effect of a moving load is demonstrated in a surface vibration example in which vibration propagates from an embankment into layered ground.

SIX BOUNDARY ELEMENTS PER WAVELENGTH: IS THAT ENOUGH?

2002 ◽  
Vol 10 (01) ◽  
pp. 25-51 ◽  
Author(s):  
STEFFEN MARBURG
Keyword(s):  
Boundary Element ◽  
Linear Time ◽  
Three Dimensional ◽  
Quadrilateral Elements ◽  
Time Harmonic ◽  
Linear Elements ◽  
Numeric Solution ◽  
Interpolation Polynomials ◽  
Detailed Presentation ◽  
Interpolation Functions

The commonly applied rule of thumb to use six (linear) elements per wavelength in linear time-harmonic acoustics is discussed in this paper. In a survey of related work, rules of element design in computational acoustics are collected. This is followed by a brief review of the boundary element method and a more detailed presentation of boundary element interpolation functions. Constant, bilinear and biquadratic interpolation polynomials are used on triangular and quadrilateral elements. In the investigation of a long duct, the numeric solution of the three dimensional problem is compared with the analytic solution. The performance of triangular and quadrilateral, constant, bilinear and biquadratic elements is compared. The error of the numeric solution is calculated in the maximum norm and the Euclidean norm on the surface and at internal points. It is estimated how many elements per wavelength are required to remain below certain error bounds of the sound pressure magnitude. Finally, a sedan cabin compartment is analyzed using different meshes. Again, performance of constant, bilinear and biquadratic elements is discussed.

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