Inductance of Bitter Coil with Rectangular Cross-section

The self-inductance of Bitter coil and mutual inductance between coaxial Bitter coils with rectangular cross-section using semi-analytical expressions based on two integrations were introduced. The current density of the Bitter coil in radial direction is inversely proportional to its radius. The obtained expressions can be implemented by Gauss integration method with FORTRAN programming. We confirm the validity of inductance results by comparing them with finite filament method and finite element method. The inductance values computed by three methods are in excellent agreement. The derived expressions of inductance of Bitter coils with rectangular cross-section allow a low computational time compared with finite filament method to a specific accuracy. The derived mutual inductance expressions can be used to accurately calculate the axial force between coaxial Bitter coils with mutual inductance gradient method.     

Magnetic Force Calculation Between Thin Coaxial Circular Coils in Air

We present new and fast procedures for calculating magnetic forces between thin coaxial circular coaxial coils in air. The results are expressed in semianalytical form in terms of the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and a term that must be solved numerically. These expressions are accurate and simple to use for several practical applications. We also describe a comparative method based on the filament technique. We discuss the computational cost and the accuracy of two methods and compare them with already published data. Results obtained by our two approaches are in excellent agreement with each other. They can be used in industrial electromagnetic applications such as electrodynamic levitation systems, linear induction launchers, linear actuators, and coil guns.     

Mutual Inductance and Force Calculations Between Coaxial Bitter Coils and Superconducting Coils with Rectangular Cross Section

Mutual inductance and force calculations between coaxial Bitter coils and superconducting coils with rectangular cross section in a hybrid magnet system using derived semi-analytical expressions based on two integrations were performed. The mutual inductance and force calculations are based on the assumption of the uniform current density distribution in superconducting coils. The current density distribution of a Bitter coil in radial direction, however, is inversely proportional to the radius of the Bitter coil. The influence of the current density redistribution caused by a cooling hole and an inhomogeneous temperature distribution of Bitter coil of a water-cooled magnet was not considered. The obtained expressions can be implemented by Simpson’s integration with FORTRAN programming. We confirm the validity of mutual inductance calculation by comparing it with a filament method, and give the accuracy of two methods. The mutual inductance values computed by two methods are in excellent agreement. The derived semi-analytical expressions of mutual inductance allow a low computational time compared with filament method to a specific accuracy. The force is derived by multiplying the currents of the two coils by their mutual inductance gradient.     

Digital-to-analog (D/A) converters with nonuniformly sampledsignals

In this paper, we investigate the problem of the D/A converter with nonuniformly sampled input data. The input digital data were obtained by sampling the intended analog waveform at nonuniform time intervals, and we look into the question: “Given that the timing offset of each data sample is known, would it be beneficial, in terms of the output signal-to-noise ratio, to use this offset to adjust the playback timing of the D/A converter?” We examine two different timing strategies. The first approach simply plays out the signal at a uniform rate, while the second one uses the known timing offset to adjust the D/A converter playback timing accordingly. The closed-form expressions of the spectrum of the D/A converter output signals are derived. From these expressions, we find that the spectrum structure, for the case where the timing offsets are compensated, is the infinite sum of the weighted shift to the baseband spectrum. For the uniform playout approach, the spectrum structure is much more complicated where each shifted spectrum is modified by a different weighting function of the frequency. Although the spectrum structure may be conceptually simpler for the case where the timing offsets are compensated, it is by no means clear that either method is better than the other in terms of the output waveform quality. We then apply the results to analyze the direct digital synthesis output sine waves. The signal-to-noise ratio, SNR, for both cases is derived in simple closed form. It is found that for the case where the timing offsets are compensated, the SNR can be greatly enhanced by appropriate selection of operation parameters     

Reliability of Computational Evaluation and Indeterminacy of Fundamental Error Characteristics in Virtual Measurement Circuits

We present a methodology for conveniently obtaining analytic forms to estimate the reliability of metrological characteristics of results obtained from various virtual measurement circuits. We compare approaches to determination of reliability for metrological characteristics by using a computational method and expressions for computation of measurement indeterminacy.     

Transient modeling of multiparallel tubular linear induction motors

In this paper, we model single and multiparallel generator driven tubular linear induction motors by the current filament method, in transient and dynamic states. Using a previously written code for transient and dynamic modeling of a single motor, we simulate a sample motor noted in a reference paper and compare the results with those obtained by using our current filament method. This comparison confirms the accuracy of our method. Finally, we model a system of two or more parallel motors and show that it is feasible to achieve greater muzzle velocities by paralleling certain designs of motors.     

Analytical time integration for BEM axisymmetric acoustic modelling

In this work, a numerical time‐domain approach to model acoustic wave propagation in axisymmetric bodies is developed. The acoustic medium is modelled by the boundary element method (BEM), whose time convolution integrals are evaluated analytically, employing the concept of finite part integrals. All singularities for space integration, present in the expressions generated by time integration, are treated adequately. Some applications are presented to demonstrate the validity of the analytical expressions generated for the BEM, and the results obtained with the present approach are compared with those generated by applying numerical time integration. Copyright © 2007 John Wiley & Sons, Ltd.     

A general model-based approach to two-dimensional infrared correlation spectroscopy incorporating the global phase angle

We describe a theoretical framework for a model-based approach to two-dimensional correlation spectroscopy that is generally applicable to any arbitrary model function. The method is based on the correlation between spectral data and a set of model waveforms with a varying correlation index, the global phase angle Theta. When experimental spectral intensity variations are expressed as sinusoidal, exponential, Lorentzian, or quadratic functions, the proposed approach allows us to estimate the quantitative values of the target parameters in those expressions. In addition, this method enables us to assess the sequential order in a series of bands undergoing non-identical intensity changes in a dynamic data set. We present both simulated and experimentally obtained data that illustrate that the deviations from linearity of the absorption band intensity waveforms are clearly detected and can be quantitatively estimated using quadratic functions.     

Nonlinear estimators of probability of an event in a bernoulli scheme accounting for prior information

A general approach to estimation of probability of an event in a Bernoulli scheme is proposed. It is shown that the available estimators are particular cases of those obtained using this more general estimation approach. Basic expressions for the general estimators obtained by means of the maximum likelihood method and the minimum S-criterion are derived. Translated from Izmeritel'naya Tekhnika, No. 7, pp. 13–14, July, 1995.     

Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization

This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is radial. Such a configuration corresponds to a passive magnetic bearing. The magnetic force exerted between ring permanent magnets is determined by using the Coulombian model. The expressions obtained are semianalytical and we show that it is not possible to find an exact analytical expression of the force between two ring permanent magnets. Then, thanks to these semianalytical calculations, the ring dimensions are optimized in order to have a great force or a great stiffness. Moreover, we show that the relative position of the rings for which the force is the strongest depends on the air gap dimension. This result is new because the curvature effect is taken into account in this paper. We can say that such semianalytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite-element method. Moreover, semianalytical expressions have a low computational cost whereas the finite-element method has a high one. Thereby, as shown in this paper, such calculations allow an easy optimization of quadripolar lenses or devices using permanent magnets.      

单泡声致发光中化学反应的处理

化学反应在声致发光中扮演了重要的角色。文章比较了两种处理化学反应的方式在声致发光数值计算中的应用,即采用反应速率的方式以及利用平衡常数的方式,讨论了它们各自的优缺点。计算表明两者所得结果比较一致．初步判断这两种处理方式的计算结果是可以接受的。     

Fabrication of beam shapers in the bulk of fused silica by femtosecond laser pulses

We reported a new approach to the fabrication of three-dimensional refractive-index-modified microstructures inside transparent materials by combining two-dimensional writing by scanning the focus of the femtosecond laser pulse and by forming the long filament in the third dimension. In this way, embedded diffractive beam shapers of grid, square, and ring gratings were obtained in the bulk of fused silica by use of a femtosecond laser with a wavelength of 810 nm and a repetition rate of 1 KHz. These structures and their refractive efficiencies were optimized by selection of the appropriate fabrication parameters, including the pulse energy, grating period, scanning speed, and scanning repetition. The good performance of these devices indicates that, owing to its simple and flexible method for fabricating complex phase elements inside transparent materials, this technique has potential applications to integrated optics.     

A comprehensive study on the 2D boundary element method for anisotropic thermoelectroelastic solids with cracks and thin inhomogeneities

This paper develops Somigliana type boundary integral equations for 2D thermoelectroelasticity of anisotropic solids with cracks and thin inclusions. Two approaches for obtaining of these equations are proposed, which validate each other. Derived boundary integral equations contain domain integrals only if the body forces or distributed heat sources are present, which is advantageous comparing to the existing ones. Closed-form expressions are obtained for all kernels. A model of a thin pyroelectric inclusion is obtained, which can be also used for the analysis of solids with impermeable, permeable and semi-permeable cracks, and cracks with an imperfect thermal contact of their faces. The paper considers both finite and infinite solids. In the latter case it is proved, that in contrast with the anisotropic thermoelasticity, the uniform heat flux can produce nonzero stress and electric displacement in the unnotched pyroelectric medium due to the tertiary pyroelectric effect. Obtained boundary integral equations and inclusion models are introduced into the computational algorithm of the boundary element method. The numerical analysis of sample and new problems proved the validity of the developed approach, and allowed to obtain some new results.     

Research on the Correlation Between Oil Menitoring and Vibration Monitoring in Information Collecting and Processing Monitoring

Oil monitoring and vibration monitoring are two principal techniques for mechanical fault diagnosis and condition monitoring at present. They monitor the mechanical condition by different approaches, nevertheless, oil and vibration monitoring are related in information collecting and processing. In the same mechanical system, the information obtained from the same information source can be described with the same expression form. The expressions are constituted of a structure matrix, a relative matrix and a system matrix. For oil and vibration monitoring, the information source is correlation and the collection is independent and complementary. And oil monitoring and vibration monitoring have the same process method when they yield their information. This research has provided a reasonable and useful approach to combine oil monitoring and vibration monitoring.     

On the calculation of laser-generated ultrasound pulses

The generation of ultrasound pulses with pulsed lasers has received considerable attention in recent years. Promising applications are to nondestructive evaluation and to materials characterization, where it is convenient to have a broad-band source requiring no contact with the sample. Quantitative applications in nondestructive evaluation require theoretical calculations incorporating realistic sample and source properties. This has, until recently, dictated approaches which were very computation-intensive. After the results obtained through these approaches are reviewed, we will describe and illustrate a very recent formulation which enables such calculations to be accomplished more easily. Numerical results will be presented to demonstrate the advantages of this approach, with emphasis on the effects of finite source dimensions, and on the initial waveform. We also show that this approach may be used to investigate surface-wave generation.     

A simple approach towards fully stressed design in hyperelasticity exploiting the isoparametric finite element concept

A novel approach towards fully stressed designs in hyperelasticity is discussed leading to closed‐form expressions for the sensitivities of the objective and displacements with respect to design variations. The key idea is the modification of the classical approach coupled with a so‐called design element method offering a lot of parallelism to standard finite element methods. We bypass implicit constraints on dependent quantities and derive an explicit linearly constrained optimization problem solved by means of first‐order procedures. The results obtained with the proposed method are adequate from an engineering point of view though being computed with a simple method. Copyright © 2000 John Wiley & Sons, Ltd.     

Variational approach of displacement discontinuity method and application to crack problems

This paper deals with a variational approach of the displacement discontinuity method. This method is an indirect boundary element technique which uses the double layer potential representation of displacements and stresses. The variational approach presented here is based upon the theorem of minimum potential energy in elasticity. In the numerical procedure, the global shape function used to approximate the displacement discontinuity distribution is the continuous piecewise linear function. Regular displacements and resultant force expressions are obtained from these shape functions and these expressions are used to build the system of linear equations. The method is applied to crack problems in both infinite and finite bodies. The stress intensity factors are then calculated and high accurate numerical results are obtained.     

Deformation analysis of functionally graded beams by the direct approach

In this paper we employ the direct approach to the theory of rods and beams, which is based on the deformable curve model with a triad of rotating directors attached to each point. We show that this model (also called directed curve) is an efficient approach for analyzing the deformation of elastic beams with a complex material structure. Thus, we consider non-homogeneous, composite and functionally graded beams made of isotropic or orthotropic materials and we determine the effective stiffness properties in terms of the three-dimensional elasticity constants. We present general analytical expressions of the effective stiffness coefficients, valid for beams of arbitrary cross-section shape. Finally, we apply this method for FGM beams made of metal foams and compare our analytical results with the numerical results obtained by a finite element analysis.     

Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 1: Axial Magnetization

This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is axial. Such a configuration corresponds to a passive magnetic bearing. All the calculations are determined by using the Coulombian model. The paper also discusses the optimal ring dimensions that provide a large force or stiffness between the rings. Such properties are commonly sought in passive magnetic bearings. We propose a three-dimensional method for optimizing these parameters. An important result is established in this paper: the exact relative position of the rings for which the force is the strongest depends on the air gap dimension. As the expressions in this paper give this exact relative position, manufacturers can easily optimize their passive magnetic bearings. This result is new because the curvature effect is taken into account. Such semianalytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite-element method. In addition, semianalytical expressions have a low computational cost whereas the finite-element method is computation-intensive. Such calculations make it easy to optimize quadripolar lenses and other devices utilizing permanent magnets.