Bessel Function Approach Research Articles

Inductance calculations for non‐coaxial Bitter coils with rectangular cross‐section using inverse Mellin transform

Recently, the mutual inductance between Bitter coils with rectangular cross-section has been calculated through Bessel function approach or figured out with analytical and semi-analytical formulas. In this study, using the inverse Mellin transform, relevant Bessel integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the hypergeometric functions. In addition, the results obtained by this method are compared with those by finite element method software. Also, the presented approach shows great advantages of high accuracy and very short computational time.

Calculation of mutual inductance and magnetic force between two thick coaxial Bitter coils of rectangular cross section

The mutual inductance and magnetic force between coaxial Bitter coils with rectangular cross section were recently calculated by some authors using semi-analytical expressions based on two integrations (Ren et al.) and by using the Bessel function approach (Conway). In this study, these important electrical quantities are calculated using the analytical and semi-analytical expressions based on elliptical integrals of the first and second kinds, Heuman's Lambda function, and two simple integrals with their kernel functions continuous on the whole integration interval. Simple Gaussian numerical integration is used. This method can be applied to calculate the mutual inductance and magnetic force between two thin Bitter disk coils (pancakes) as well as between two Bitter coils, where one has a rectangular cross section and the other is a thin disk (pancake). The calculations of the mutual inductances and magnetic forces are validated by comparison with values already published in the literature. The presented approach has advantages of high accuracy and low computational time.

A novel matrix method for coupled vibration and damping effect analyses of liquid-filled circular cylindrical shells with partially constrained layer damping under harmonic excitation

A novel matrix method is further developed for a liquid-filled circular cylindrical shell with partially constrained layer damping (CLD), which consists of treating liquid domain with Bessel function approach, and shell domain with transfer matrix equation based on a new set of first order matrix differential equation. In order to indicate its advantage to the finite element method (FEM), free vibration analysis on such an empty shell under clamped–clamped boundary are carried out by using the present method together with FEM. Meanwhile, coincident result is yielded for the liquid-filled shell by adopting the present method with by other transfer matrix method. Finally, a series of valuable numerical results are obtained by this method.

A connection between the double gamma model and Laplace sample mean

In this paper, we use the moment generating function of the double gamma random variable to derive the sample mean distribution of the Laplace (double exponential) model. The proposed approach simplifies the Bessel function approach in the investigation of the Laplace sample mean. The connection between double gamma and Laplace models facilitates computation for the percentile of the Laplace sample mean via percentiles of Chi-square random variables.

Studies on fluid-filled and submerged cylindrical shells with constrained viscoelastic layer

Conventional cylindrical shells (made of isotropic materials) filled with or submerged in fluid have been analysed historically by using closed-form solutions or by semi-analytical method. However, these shells suffer from a serious disadvantage of not having sufficient damping, which is crucial in controlling the response of the structure during severe vibrations. One practical way of reducing response levels is by using shells with viscoelastic treatment that would result in increased damping. Previous work in this area was mostly limited to study problems whose mathematical formulation was amenable to closed-form solution or semi-analytical method. In some cases researchers resorted to experimental studies. Further, almost all previous studies were limited to lower circumferential modes and to first axial mode only. In the present paper, the method proposed overcomes most of the limitations suffered by adopting the different approaches suggested in literature. The method consists of treating fluid domain with Bessel function approach and shell domain based on first-order shear deformation theory. The present approach obviates the discretisation of liquid domain thus reducing the computation time. A computer program is developed based on the proposed method and results are compared with previous works of various researchers. A good correlation is observed for all the case studies done. Hence, it is claimed that the present approach is more universal for analysing fluid-filled or submerged shells or both. Detailed parametric studies are carried out on both conventional and viscoelastic cylindrical shells.

Polynomial approach for calculating added mass for fluid-filled cylindrical shells

Cylindrical shells find wide applications in many engineering fields. Free vibration analysis of cylindrical shells filled with fluid has been dealt using finite element approach for both structure and fluid domain or using finite element for structure and Bessel function approach for fluid. The present paper deals with a novel method on the usage of polynomial functions for fluid domain in contrast to the usual Bessel function approach. A semi-analytical finite element approach has been used to discretise the shell structure. The fluid domain has been analysed by using polynomial functions instead of Bessel function. The study has been carried out for conventional shells as well as viscoelastic shells. The present study obviates necessity of limiting the studies to certain boundary conditions. The results of both frequency and damping corroborate well with those found in literature.

A simple formula for calculating the frequency-dependent resistance of a round wire

At high frequencies, the current distribution across a circular wire is modified by the skin effect, causing the greatest current density to be near the surface of the wire. One common method of calculating the wire resistance inoles determining complex Bessel func- tions, the solution of which is prone to approximations as the skin depth becomes less than about one tenth the wire radius. An alternatie method of determining this resistance is presented which is significantly simpler than the Bessel function approach, easier toisualize, and not reliant on approximations when determining the solution. This approach is based on determining the width of an annulus which carriers the equialent current to the full wire. Results are presented which confirm the accuracy of the equialent annulus method. Q 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 84)87, 1998.

Theoretical models for the remote field effect

The Remote Field Effect is used extensively for testing of thick tubular products where deep penetration into (primarily ferromagnetic) materials is required. The testing apparatus consists of two coils, one generating a magnetic field, the other is used as a pickup coil. The distance between the two coils is normally large (of the order of two coil diameters). The operating frequency is low, normally below 100 Hz. The method has been assumed in the past to rely on a special effect, and therefore the name Remote Field Effect. One of the most remarkable aspect of the method is its equal sensitivity to inner and outer defects in thick ferromagnetic tubes. This effect could not easily be explained by direct induction and therefore, many models have been proposed. The common model used is that of a wave propagating from the inside of the material to the outside and then back again. We proposed a theoretical model that shows the effect to be merely that of induction at large distances. The field equations are solved directly using first a Bessel function approach and then using an integral approach. Both of these models confirm the basic results associated with the remote field affect and also include the velocity of the coils.

A study of linear systems with time varying coefficients by the methods of bessel and weber functions

In this paper methods of solving linear systems with time dependent parameters by usingstraight line approximations (Bessel function approach) and by using parabolic cylinder functions (Weber function approach) are proposed. The results obtained by these two approximations are compared with those obtained by using a numerical procedure on a digital computer. The Weber function approach is comparatively simple as it uses mostly tabulated functions. It is also less time-consuming and more exact than the other approximate methods of solving linear differential equations with time varying coefficients. Examples are provided to illustrate the technique proposed.