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Article
Publication date: 4 November 2014

Palaniyandi Ponnusamy

The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle…

Abstract

Purpose

The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle, square, pentagon and hexagon) cross-section immersed in fluid is using Fourier expansion collocation method, with in the frame work of linearized, three-dimensional theory of thermo-piezoelectricity.

Design/methodology/approach

A mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid is studied using the three-dimensional theory of elasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional bar immersed in fluid. Since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the curved surface of the polygonal bar directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.

Findings

From the literature survey, it is clear that the free vibration of an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

Research limitations/implications

Wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes of piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

Originality/value

The researchers have discussed the wave propagation in thermo-piezoelectric circular cylinders using three-dimensional theory of thermo-piezoelectricity, but, the researchers did not analyzed the wave propagation in an arbitrary/polygonal cross-sectional bar immersed in fluid. So, the author has studied the free vibration analysis of thermo-piezoelectric polygonal (triangle, square, pentagon and hexagon) cross-sectional bar immersed in fluid using three-dimensional theory elasticity. The problem may be extended to any kinds of cross-sections by using the proper geometrical relations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 March 2006

Baodong Shao and Zhaowei Sun

To give a new method to calculate the thermal conductivity of thin films which thickness is less than micro‐nanometer when non‐Fourier effect will appear in heat conduction and…

Abstract

Purpose

To give a new method to calculate the thermal conductivity of thin films which thickness is less than micro‐nanometer when non‐Fourier effect will appear in heat conduction and Fourier law is not applicable for calculating the thermal conductivity.

Design/methodology/approach

The Cattaneo equation based on the heat flow relaxation time approximation is used to calculate the thermal conductivity.

Findings

The results show that the thermal conductivity is not the thermophysical properties of material, but is the non‐linear function of temperature and film thickness when the dimension of film is less than micro‐nanometer.

Research limitations/implications

The application of this method is limited by little experimental data of heat flow relaxation time for materials other than Ar crystals.

Originality/value

The paper demonstrates how the thermal conductivity of Ar crystals film can be calculated by NEMD algorithm and considers the non‐Fourier effect in the simulation.

Details

Aircraft Engineering and Aerospace Technology, vol. 78 no. 2
Type: Research Article
ISSN: 0002-2667

Keywords

Article
Publication date: 2 October 2017

S. Saha Ray

The purpose of this paper is to consider the time-splitting Fourier spectral (TSFS) method to solve the fractional coupled Klein–Gordon–Schrödinger (K-G-S) equations. A…

Abstract

Purpose

The purpose of this paper is to consider the time-splitting Fourier spectral (TSFS) method to solve the fractional coupled Klein–Gordon–Schrödinger (K-G-S) equations. A time-splitting spectral approach is applied for discretizing the Schrödinger-like equation and along with that, a pseudospectral discretization has been accurately utilized for the temporal derivatives in the Klein–Gordon-like equation. Furthermore, the time-splitting scheme is proved to be unconditionally stable. Numerical experiments guarantee high accuracy of the TSFS scheme for the K-G-S equations. Here, the derivative of fractional order is taken in the Riesz sense.

Design/methodology/approach

The focus of this paper is to study the Riesz fractional coupled K-G-S equations using the TSFS method. This method is dependent on evaluating the solution to the given problem in small steps, and treating the nonlinear and linear steps separately. The nonlinear step is made in the time domain, while the linear step is made in the frequency domain, which necessitates the use of Fourier transform back and forth. It is a very effective, powerful and efficient method to solve the nonlinear differential equations, as in previous works (Bao et al., 2002; Bao and Yang, 2007; Muslu and Erbay, 2003; Borluk et al., 2007), the initial and boundary-value problem is decomposed into linear and nonlinear subproblems. Summarizing the technique of the TSFS method, it can be stated that first the Schrödinger-like equation is solved in two splitting steps. Then, the Klein–Gordon-like equation is solved by discretizing the spatial derivatives by means of the pseudospectral method.

Findings

The utilized method is found to be very efficient and accurate. Moreover, the time-splitting spectral scheme is found to be unconditionally stable. By means of thorough study, it is found that the spectral method is time-reversible, is gauge-invariant and also conserves the total charge. Moreover, the results have been graphically presented to exhibit the accuracy of the proposed methods. Apart from that, the numerical solutions have been also compared with the exact solutions. Numerical experiments establish that the proposed technique manifests high accuracy and efficiency.

Originality/value

To the authors’ best knowledge, the Riesz fractional coupled K-G-S equations have been for the first time solved by using the TSFS method.

Details

Engineering Computations, vol. 34 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 2 January 2018

Norman Borchardt and Roland Kasper

This study aims to present a parametric model of a novel electrical machine, based on a slotless air gap winding, allowing for fast and precise magnetic circuit calculations.

Abstract

Purpose

This study aims to present a parametric model of a novel electrical machine, based on a slotless air gap winding, allowing for fast and precise magnetic circuit calculations.

Design/methodology/approach

Approximations of Fourier coefficients through an exponential function deliver the required nonlinear air gap flux density and inductance. Accordingly, major machine characteristics, such as back-EMF and torque, can be calculated analytically with high speed and precision. A physical model of the electrical machine with air gap windings is given. It is based on a finite element analysis of the air gap magnetic flux density and inductance. The air gap height and the permanent magnetic height are considered as magnetic circuit parameters.

Findings

In total, 11 Fourier coefficient matrixes with 65 sampling points each were generated. From each, matrix a two-dimensional surface function was approximated by using exponentials. Optimal parameters were calculated by the least-squares method. Comparison with the finite element model demonstrates a very low error of the analytical approximation for all Fourier coefficients considered. Finally, the dynamics of an electrical machine, modeled using the preceding magnetic flux density approximation, are analyzed in MATLAB Simulink. Required approximations of the phase self-inductance and mutual inductance were given. Accordingly, the effects of the two magnetic circuit parameters on the dynamics of electrical machine current as well as the electrical machine torque are explained.

Originality/value

The presented model offers high accuracy comparable to FE-models, needing only very limited computational complexity.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 June 2003

K. Darowicki and A. Krakowiak

A new method of spectral analysis has been proposed for non‐stationary harmonic analysis of corrosion processes. The current of a model circuit has been considered which would…

Abstract

A new method of spectral analysis has been proposed for non‐stationary harmonic analysis of corrosion processes. The current of a model circuit has been considered which would simulate a first‐order electrode reaction proceeding in conditions of a linearly changing electrode potential with a superimposed sinusoid signal. It has been shown that the Fourier transformation approach does not reflect the amplitude changes of harmonic components as a function of constant potential. In addition, it has been shown mathematically that application of Gabor transformation in spectral analysis is a means of obtaining the correct frequency components. The Gabor transform correctly reflects amplitude changes of harmonic components as a function of potential. Digital analysis of current changes by Gabor transformation unequivocally confirmed the usability of this method for harmonic analysis of corrosion processes.

Details

Anti-Corrosion Methods and Materials, vol. 50 no. 3
Type: Research Article
ISSN: 0003-5599

Keywords

Article
Publication date: 1 January 2006

Tadeusz Sobczyk, Konrad Weinreb, Maciej Sułowicz, Tomasz Węgiel and Adam Warzecha

To study effects in the Fourier spectra of cage motor phase currents due to saturation of the main magnetic circuit by the fundamental MMF harmonic.

Abstract

Purpose

To study effects in the Fourier spectra of cage motor phase currents due to saturation of the main magnetic circuit by the fundamental MMF harmonic.

Design/methodology/approach

An idea of an equivalent magnetizing current is applied, which allows to consider an influence of all currents of stator and rotor windings on the main magnetic circuit permeability. The energy base approach is used to write machine equations and the harmonic balance method is used to determine the Fourier spectra of currents.

Findings

It has been shown that the saturation generate additional harmonics in phase currents, which are shifted by 100 Hz from the so called slot harmonics.

Research limitations/implications

A model and a solving method allows to predict all slot harmonics quantitatively, but qualitative difference of the Fourier spectra to measurement still exist.

Practical implications

More precise prediction of the Fourier spectra of stator phase currents for on‐line diagnostic systems.

Originality/value

A circuit model of a cage motor accounting for saturation by slot harmonics and an algorithm for determination of additional components in the phase current Fourier spectra.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 28 September 2010

David A. Sanders, Gareth Lambert, Jasper Graham‐Jones, Giles E. Tewkesbury, Spencer Onuh, David Ndzi and Carl Ross

The paper aims to propose a system that uses a combination of techniques to suggest weld requirements for ships parts. These suggestions are evaluated, decisions are made and then…

Abstract

Purpose

The paper aims to propose a system that uses a combination of techniques to suggest weld requirements for ships parts. These suggestions are evaluated, decisions are made and then weld parameters are sent to a program generator.

Design/methodology/approach

A pattern recognition system recognizes shipbuilding parts using shape contour information. Fourier‐descriptors provide information and neural networks make decisions about shapes.

Findings

The system has distinguished between various parts and programs have been generated so that the methods have proved to be valid approaches.

Practical implications

The new system used a rudimentary curvature metric that measured Euclidean distance between two points in a window but the improved accuracy and ease of implementation can benefit other applications concerning curve approximation, node tracing, and image processing, but especially in identifying images of manufactured parts with distinct corners.

Originality/value

A new proposed system has been presented that uses image processing techniques in combination with a computer‐aided design model to provide information to a multi‐intelligent decision module. This module will use different criteria to determine a best weld path. Once the weld path has been determined then the program generator and post‐processor can be used to send a compatible program to the robot controller. The progress so far is described.

Details

Assembly Automation, vol. 30 no. 4
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 10 July 2009

M. van der Giet, R. Rothe and K. Hameyer

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses…

Abstract

Purpose

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses numerical field simulation to obtain the magnetic air gap field of electrical machines and an analytical‐based post‐processing approach to reveal the relationship between air gap field harmonics and the resulting force wave.

Design/methodology/approach

The simulated air gap field is sampled in space and time and a two‐dimensional Fourier transform is performed. The convolution of the Fourier transformed air gap field by itself represents a multiplication in space time domain. During the convolution process, all relevant combinations of field waves are stored and displayed using space vectors.

Findings

The effectiveness of the proposed approach is shown on an example machine. Particular examples of individual force waves demonstrate how the approach can be used for practical application in analysis of noise and vibration problems in electrical machines. The proposed method is compared to the result of a Maxwell stress tensor calculation. It shows that the deviation is small enough to justify the approach for analysis purposes.

Originality/value

The combination of analytically understood force waves and the use of numerical simulation by means of air gap field convolution has not been proposed before.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 8 August 2016

Vladimir Kobelev

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length…

Abstract

Purpose

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

Design/methodology/approach

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

Findings

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Research limitations/implications

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

Practical implications

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

Originality/value

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 26 September 2018

C.H.H.M. Custers, J.W. Jansen, M.C. van Beurden and E.A. Lomonova

The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions…

Abstract

Purpose

The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.

Design/methodology/approach

In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.

Findings

The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.

Research limitations/implications

Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.

Practical implications

Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.

Originality/value

With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

21 – 30 of over 4000