scholarly journals Optimal Gyrodine Rotor Shape in the Class of Conical Bodies

2021 ◽  
pp. 69-81
Author(s):  
Andrey Biryuk ◽  
Mikhail Drobotenko ◽  
Igor Ryadchikov ◽  
Alexander Svidlov
Keyword(s):  
Angular Momentum ◽  
Numerical Solution ◽  
Poisson Ratio ◽  
Stress Fields ◽  
Constant Thickness ◽  
Calculation Error ◽  
Angular Rotation ◽  
Axis Of Rotation ◽  
Rotor Shape ◽  
Two Parameters

The problem is to find the optimal shape of the gyrodine rotor and its angular rotation speed that maximizes the angular momentum relative to the axis of rotation at a fixed radius, mass and material of the rotor, taking into account the final strength of the material. The gyrodine rotor is a body of revolution, the thickness of which depends only on the distance r to the axis of rotation, r ∈ [0,R], where R is the radius of the rotor. The rotor surface is defined by rotating the curves z = ±z(r) around the axis. When the rotor is spinning, it undergoes deformation due to centrifugal forces. Normal stress fields appear: radial and annular. Assuming the rotor to be thin, deformations can be described by the functions of the radial displacement of the rotor points u(r). Stress fields can be expressed in terms of this function. The functions u(r) and z(r) are related by the equation of the elastically deformed state. This equation is supplied with the boundary conditions for the absence of radial stresses at r = R and the condition for the absence of displacement on the axis of rotation u(0) = 0. Using the numerical solution of the equation, the problem is solved for the class of conical rotors z(r) = a + br with two parameters a and b. The numerical method is used due to the fact that even in this relatively simple case the problem cannot be solved analytically. Several integrable cases are used to analyze the calculation error in the numerical solution of the problem. The dependence of the problem on the Poisson ratio μ ∈ (−1.1) is investigated, with the remaining parameters fixed. The gain in the angular momentum relative to a rotor of constant thickness is compared. The optimal steel conical rotor (μ = 0.3) is 2.068 times thicker at the center than at the edge. Its advantage in the angular momentum over the rotor of constant thickness is 3.2 %.

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

Analysis and numerical solution of dynamic Jiles–Atherton model applied to hysteresis modeling for giant magnetostrictive materials

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ce Rong ◽  
Zhongbo He ◽  
Guangming Xue ◽  
Guoping Liu ◽  
Bowen Dai ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Numerical Computation ◽  
Model Parameters ◽  
Calculation Error ◽  
Rational Form ◽  
Modified Model ◽  
Content Type ◽  
Magnetostrictive Materials ◽  
Giant Magnetostrictive Materials ◽  
Computation Scheme

PurposeOwing to the excellent performance, giant magnetostrictive materials (GMMs) are widely used in many engineering fields. The dynamic Jiles–Atherton (J-A) model, derived from physical mechanism, is often used to describe the hysteresis characteristics of GMM. However, this model, despite cited by many different literature studies, seems not to possess unique expressions, which may cause great trouble to the subsequent application. This paper aims to provide the rational expressions of the dynamic J-A model and propose a numerical computation scheme to obtain the model results with high accuracy and fast speed.Design/methodology/approachThis paper analyzes different published papers and provides a reasonable form of the dynamic J-A model based on functional properties and physical explanations. Then, a numerical computation scheme, combining the Newton method and the explicit Adams method, is designed to solve the modified model. In addition, the error source and transmission path of the numerical solution are investigated, and the influence of model parameters on the calculation error is explored. Finally, some attempts are made to study the influence of numerical scheme parameters on the accuracy and time of the computation process. Subsequently, an optimization procedure is proposed.FindingsA rational form of the dynamic J-A model is concluded in this paper. Using the proposed numerical calculation scheme, the maximum calculation error, while computing the modified model, can remain below 2 A/m under different model parameter combinations, and the computation time is always less than 0.5 s. After optimization, the calculation speed can be enhanced with the computation accuracy guaranteed.Originality/valueTo the best of the authors’ knowledge, this paper is the first one trying to provide a rational form of the dynamic J-A model among different citations. No other research studies focus on designing a detailed computation scheme targeting the fast and accurate calculation of this model as well. And the performance of the proposed calculation method is validated in different conditions.

scholarly journals A Global Analysis of The Generalized Sitnikov Problem

1999 ◽  
Vol 172 ◽  
pp. 291-302
Author(s):  
Steven R. Chesley
Keyword(s):  
Angular Momentum ◽  
Global Analysis ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Bounded Motion ◽  
Type Symmetry ◽  
The Stability ◽  
Two Parameters ◽  
Three Body ◽  
Area Preserving

AbstractThe isosceles three-body problem with Sitnikov-type symmetry has been reduced to a two-dimensional area-preserving Poincaré map depending on two parameters: the mass ratio, and the total angular momentum. The entire parameter space is explored, contrasting new results with ones obtained previously in the planar (zero angular momentum) case. The region of allowable motion is divided into subregions according to a symbolic dynamics representation. This enables a geometric description of the system based on the intersection of the images of the subregions with the preimages. The paper also describes the regions of allowable motion and bounded motion, and discusses the stability of the dominant periodic orbit.

The Constant Stress Hanging String with Bottom Load — An Exact Solution

2021 ◽  
pp. 2171005
Author(s):  
C. Y. Wang
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Unique Solution ◽  
Characteristic Equation ◽  
Maximum Stress ◽  
Cross Sectional Area ◽  
Vibration Frequencies ◽  
Sectional Area ◽  
Cross Sectional ◽  
Two Parameters

The unique solution for the fully stressed hanging string with a bottom load is found. For a given length of string, the problem depends on two parameters, representing the ratio of string density to maximum stress, and the ratio of bottom mass to maximum stress. The cross-sectional area of the string decays exponentially downward. Vibration frequencies are found from the exact characteristic equation. Results from analytic perturbation formulas compare well with those of numerical solution.

NUMERICAL REALIZATION OF THE ALGORITHM FOR SOLVING THE TASKS OF HYDROPHYSICS IN THE AREA WITH COMPLEX GEOMETRY

2019 ◽  
pp. 3-12
Author(s):  
A. I. Sukhinov ◽  
A. E. Chistyakov ◽  
V. N. Litvinov ◽  
A. V. Nikitina
Keyword(s):  
Numerical Solution ◽  
Hydrodynamic Model ◽  
Complex Shape ◽  
Complex Geometry ◽  
Model Problem ◽  
Computational Grids ◽  
Calculation Error ◽  
Physical Processes ◽  
Hydrodynamic Processes ◽  
Rectangular Grids

The work is devoted to the development and numerical implementation of an algorithm for solving the problem of modeling the process of hydrophysics, describing the transport of polluting biogenic substances in a complex shape. The velocity field of the water flow, calculated according to the hydrodynamic model of the Sea of Azov, is used in the model of transport of polluting nutrients as input data. To test the accuracy of the numerical solution of the hydrodynamic model problem, a test problem of viscous fluid flow between two coaxial semicylinders is used. To solve the interrelated problems of hydrophysics, including a model of hydrodynamic processes and a model of transport of polluting nutrients, rectangular grids are used, taking into account the “fullness” of the cells. The approximation of the problem in time is made on the basis of splitting schemes for physical processes. To assess the accuracy of the numerical solution of hydrodynamic problems, an analytical solution describing the Couette–Taylor flow is used as a reference. The simulation was carried out on a sequence of thickening computational grids with dimensions: 11×21, 21×41, 41×81 and 81×161 nodes in the cases of a smooth and stepped border. To increase the smoothness of the solution, grids were used that take into account the “fullness” of the cells. In the case of a stepwise approximation of the interface between two media, the calculation error reaches 70 % of the error solution of the problem. When using grids that take into account the “fullness” of cells, the error in the numerical solution of model problems of hydrodynamics, caused by the approximation of the boundary, does not exceed 6 % of the error solution of the problem. The example shows that the fragmentation of the grid by 8 times for each of the spatial directions does not lead to an increase in the accuracy that solutions obtained on the grids, which take into account the “fullness” of the cells, possess.

scholarly journals Analysis of Power Spinning of Cones

1960 ◽  
Vol 82 (3) ◽  
pp. 231-244 ◽  
Author(s):  
B. Avitzur ◽  
C. T. Yang
Keyword(s):  
Strain Rate ◽  
Numerical Solution ◽  
Experimental Evidence ◽  
Force Measurement ◽  
Tangential Force ◽  
Experimental Tests ◽  
Stress Fields ◽  
Process Variables ◽  
Power Spinning ◽  
Shear Type

The geometry of the cone, the roller, and the spinning operation are described mathematically. A shear type of deformation is postulated, based on experimental evidence. The displacement, velocity, strain rate, and stress fields are computed for “Mises’ material,” and hence with Mises’ stress-strain rate law. The power consumed in the operation is computed from the strain rate and stress fields. The expression for the power is in a form that can scarcely be solved analytically. A numerical solution is therefore employed and results are presented in graphical forms, where the power and tangential force are plotted for a variety of the process variables. The numerical solution is compared with actual power and force measurement in experimental tests and the agreement is reasonably good.

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