Influence of a bow of finite width on bowed string motion: numerical modelling and experimental evidence

An enhanced physical model of the bowed string presented previously [1] is explored. It takes into account: the width of the bow, the angular motion of the string, bow-hair elasticity and string bending stiffness. The results of an analytical investigation of a model system - an infinite string sticking to a bow of finite width and driven on one side of the bow - are compared with experimental results published by Cremer [2] and reinterpreted here. Comparison shows that both the width of the bow and the bow-hair elasticity have a large impact on the reflection and transmission behaviour. In general, bending stiffness plays a minor role. Furthermore, a method of numerical simulation of the stiff string bowed with a bow of finite width is presented along with some preliminary results.

On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis

This paper demonstrates how a finite element model which exploits domain decomposition is applied to the analysis of three-phase induction motors. It is shown that a significant gain in cpu time results when compared with standard finite element analysis. Aspects of the application of the method which are particular to induction motors are considered: the means of improving the convergence of the nonlinear finite element equations; the choice of symmetrical sub-domains; the modelling of relative movement; and the inclusion of periodic boundary conditions. © 1999 IEEE.

Application of domain decomposition and transmission line modelling techniques to 2D, time-domain, finite element problems

In this paper a recently published finite element method, which combines domain decomposition with a novel technique for solving nonlinear magnetostatic finite element problems is described. It is then shown how the method can be extended to, and optimised for, the solution of time-domain problems. © 1999 IEEE.

Finite volume distance field solution applied to medial axis transform

Accurate and efficient computation of the nearest wall distance d (or level set) is important for many areas of computational science/engineering. Differential equation-based distance/ level set algorithms, such as the hyperbolic-natured Eikonal equation, have demonstrated valuable computational efficiency. Here, in the context, as an 'auxiliary' equation to the main flow equations, the Eikonal equation is solved efficiently with two different finite volume approaches (the cell vertex and cell-centered). Application of the distance solution is studied for various geometries. Moreover, a procedure using the differential field to obtain the medial axis transform (MAT) for different geometries is presented. The latter provides a skeleton representation of geometric models that has many useful analysis properties. As an alternative approach to the pure geometric methods (e.g. the Voronoi approach), the current d-MAT procedure bypasses many difficulties that are usually encountered by pure geometric methods, especially in three dimensional space. It is also shown that the d-MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.