scholarly journals Особенности применения теоремы вириала для магнитных систем с квазибессиловыми обмотками

2022 ◽  
Vol 92 (2) ◽  
pp. 303
Author(s):  
Г.А. Шнеерсон ◽  
С.Л. Шишигин
Keyword(s):  
Boundary Conditions ◽  
Main Part ◽  
Virial Theorem ◽  
Dimensionless Parameter ◽  
Magnetic System ◽  
Local Equilibrium ◽  
Entire System ◽  
Material Density ◽  
A Value ◽  
Thin Walled

The article shows that in a magnetic system with a thin-walled balanced winding close to a force-free one, a significant increase in the parameter θ=WM γ/M σМ , is possible, which, according to the virial theorem, characterizes the ratio of the energy of the magnetic system WM to the weight of equipment with a material density γ, where under the action of electromagnetic forces there appears a mechanical stress σМ. In a quasi-force-free magnetic system, the main part of the winding is in a state of local equilibrium, and only a relatively small part of the equipment is subject to stress. This part determines the weight of the entire system, and this weight can be minimized. The configurations of balanced thin-walled windings are developed, at the boundaries two boundary conditions are fulfilled simultaneously - the absence of the induction component normal to the boundary and the constancy of the product of induction and radius. The authors consider an example of a system consisting of a main part - a sequence of balanced "transverse" modules in the form of flat discs and end parts, consisting of a combination of "transverse" modules and "longitudinal" ones, having the form of rings elongated along the axis with balanced end parts. It is shown that in the system under consideration, the characteristic dimensionless parameter θ with an unlimited increase in the number of elements of the main part can reach a value of about 24, and when the number of these elements changes within 20 - 40, it changes from 6 to 9.

scholarly journals On the theory and practice of thin-walled structures

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tamaz Vashakmadze
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Complex Analysis ◽  
Theory And Practice ◽  
Linear Case ◽  
Wide Sense ◽  
Partial Differential ◽  
Thin Walled Structures ◽  
Thin Walled

Abstract The basic problem of satisfaction of boundary conditions is considered when the generalized stress vector is given on the surfaces of elastic plates and shells. This problem has so far remained open for both refined theories in a wide sense and hierarchic type models. In the linear case, it was formulated by I. N. Vekua for hierarchic models. In the nonlinear case, bending and compression-expansion processes do not split and in this context the exact structure is presented for the system of differential equations of von Kármán–Mindlin–Reisner (KMR) type, constructed without using a variety of ad hoc assumptions since one of the two relations of this system in the classical form is the compatibility condition, but not the equilibrium equation. In this paper, a unity mathematical theory is elaborated in both linear and nonlinear cases for anisotropic inhomogeneous elastic thin-walled structures. The theory approximately satisfies the corresponding system of partial differential equations and the boundary conditions on the surfaces of such structures. The problem is investigated and solved for hierarchic models too. The obtained results broaden the sphere of applications of complex analysis methods. The classical theory of finding a general solution of partial differential equations of complex analysis, which in the linear case was thoroughly developed in the works of Goursat, Weyl, Walsh, Bergman, Kolosov, Muskhelishvili, Bers, Vekua and others, is extended to the solution of basic nonlinear differential equations containing the nonlinear summand, which is a composition of Laplace and Monge–Ampére operators.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

scholarly journals Impact of Different Components and Boundary Conditions on the Eigenfrequencies of a Magnet–Girder Assembly

Instruments ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 29
Author(s):  
Simone Andresen
Keyword(s):  
Boundary Conditions ◽  
Particle Beam ◽  
Design Development ◽  
Material Density ◽  
Electron Synchrotron ◽  
Support Points ◽  
Beam Stability ◽  
Development Processes ◽  
Large Triangle ◽  
The Impact

Synchrotron radiation facilities are very important in different areas of fundamental and applied science to investigate structures or processes at small scales. Magnet–girder assemblies play a key role for the performance of such accelerator machines. High structural eigenfrequencies of the magnet–girder assemblies are required to assure a sufficient particle beam stability. The objective of the present parametric study was to numerically investigate and quantify the impact of different boundary conditions and components on the magnet–girder eigenfrequencies. As case studies, two 3 m long girder designs following the specifications of the PETRA IV project at DESY (German Electron Synchrotron, Hamburg, Germany) were selected. High magnet–girder assembly eigenfrequencies were achieved by, e.g., positioning the magnets close to the upper girder surface, increasing the connection stiffness between the magnets and the girder and between the girder and the bases, and positioning the girder support points as high as possible in the shape of a large triangle. Comparing the E/ρ ratio (E: Young’s modulus, ρ: material density) of different materials was used as a first approach to evaluate different materials for application to the girder. Based on the findings, general principles are recommended to be considered in the future girder design development processes.

scholarly journals Buckling Of The Stiffened Flange Of The Thin-Walled Member At Longitudinal Stress Variation

2015 ◽  
Vol 61 (3) ◽  
pp. 149-168
Author(s):  
A. Szychowski
Keyword(s):  
Boundary Conditions ◽  
Free Edge ◽  
Cantilever Plate ◽  
Longitudinal Stress ◽  
Stress Variation ◽  
Buckling Modes ◽  
Load Distributions ◽  
Edge Stiffener ◽  
Thin Walled ◽  
Elastically Restrained

AbstractBuckling of the stiffened flange of a thin-walled member is reduced to the buckling analysis of the cantilever plate, elastically restrained against rotation, with the free edge stiffener, which is susceptible to deflection. Longitudinal stress variation is taken into account using a linear function and a 2nd degree parabola. Deflection functions for the plate and the stiffener, adopted in the study, made it possible to model boundary conditions and different buckling modes at the occurrence of longitudinal stress variation. Graphs of buckling coefficients are determined for different load distributions as a function of the elastic restraint coefficient and geometric details of the stiffener. Exemplary buckling modes are presented.

Reliability Comparison of Trusses Made of Thin-Walled Steel Sections

2018 ◽  
Vol 931 ◽  
pp. 280-287
Author(s):  
Sergey V. Skachkov ◽  
Ekaterina Y. Golotaystrova
Keyword(s):  
Load Capacity ◽  
Reliability Function ◽  
System Failure ◽  
Entire System ◽  
The Finite Element Method ◽  
Probabilistic Technique ◽  
Steel Sections ◽  
Internal Forces ◽  
Thin Walled ◽  
Rod Structures

The authors suggest a new truss with nodal conjugations without misalignment in the nodes. They have a greater load capacity and reliability. The results have been confirmed by the calculation of the above-mentioned trusses by the finite element method. The reliability function of trusses made of thin-walled steel sections can be determined taking into account the rods destruction probability in the system. We consider a design with the most unfavorable design model in which the destruction of any rod leads to the entire system failure. For the truss refusal it is assumed that the yield point of the material is reached at least in one of its cores. A probabilistic technique for estimating the reliability of rod structures made of thin-walled steel sections has been proposed. Other parameters being equal, including the geometric dimensions of the truss, loads, the nature of their application one can determine the most rational scheme of the truss in terms of its reliability. Differences in nodes design and internal forces direction will lead to a change in their values in trusses elements. Thus, the trusses reliability will depend on the mathematical expectation of internal efforts, camber and flexibility.

Simulation study of satisfaction rate in the mixed traffic flow with open boundary conditions

2015 ◽  
Vol 27 (02) ◽  
pp. 1650023
Author(s):  
Khalid Bentaleb ◽  
Noureddine Lakouari ◽  
Hamid Ez-Zahraouy ◽  
Abdelilah Benyoussef
Keyword(s):  
Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Mixed Traffic Flow ◽  
The Road ◽  
Satisfaction Rate ◽  
A Value ◽  
Maximal Speed ◽  
On The Road ◽  
A Chain

In this paper, we propose a single-lane cellular automata (CA) traffic model which takes into account the disorder in the length and the maximal speed of the vehicles (i.e. slow and fast) to study the satisfaction rate of the fast vehicles (i.e. the number of vehicles that run with their desired speed) with open boundary conditions in the case of a chain of one entry; where [Formula: see text] is the injecting rate of vehicles independent of their nature and [Formula: see text] is the extracting rate. The slow vehicles are injected with the conditional probability [Formula: see text], where [Formula: see text] and [Formula: see text] is the concentration of the slow vehicles. It is found that for the low value of the injecting rate [Formula: see text] and for the high extraction rate [Formula: see text], the satisfaction rate takes higher values. It also depends on the concentration of the slow vehicles injected on the road. Furthermore, we have shown that, in the case when [Formula: see text], the satisfaction rate undergoes a transition from the maximal value to the minimal one and it takes a value near to zero in the case of [Formula: see text]. We have also found that the satisfaction rate depends strongly on the probability of overtaking, also the phase diagrams ([Formula: see text]) are established for the different values of the slow vehicles concentrations [Formula: see text].

Two-Threshold Stability Loss in Magnetic System with Nonmagnetic Interlayer

2010 ◽  
Vol 168-169 ◽  
pp. 321-324
Author(s):  
Yu.V. Zakharov ◽  
A.Yu. Vlasov ◽  
R. Avakumov
Keyword(s):  
Boundary Conditions ◽  
Magnetic System ◽  
Magnetic Film ◽  
Stability Loss ◽  
Interlayer Interaction ◽  
Soft Magnetic ◽  
Effective Constant ◽  
Magnetic Layers ◽  
Magnetic Substrate

In present paper the magnetization of magnetic film consisting of two soft magnetic layers separated by a nonmagnetic interlayer is considered. The film is applied to stiff magnetic substrate. To obtain boundary conditions at the boundary between soft magnetic layers we introduce effective constant of interlayer interaction.

Modelling and vibration of composite thin-walled rotating blades featuring extension-twist elastic coupling

2005 ◽  
Vol 109 (1095) ◽  
pp. 233-246 ◽  
Author(s):  
S-Y. Oh ◽  
L. Librescu ◽  
O. Song
Keyword(s):  
Composite Material ◽  
Boundary Conditions ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Physical Characteristics ◽  
Elastic Coupling ◽  
Hamilton’S Principle ◽  
Rotating Blades ◽  
Advanced Composite ◽  
Thin Walled

Abstract The modelling and vibration of composite thin-walled pre-twisted rotating blades of non-uniform cross-sections along their span, and featuring the extension-twist elastic coupling are addressed. To this end, Hamilton’s principle is used to derive the equations of motion and the associated boundary conditions. In addition to the pretwist and warping restraint, the exotic properties of advanced composite material are used, and the efficiency of implementing the tailoring technique toward the enhancement, without weight penalties, of the vibratory behaviour of rotating blades is illustrated. Comparisons between the predictions by both Wagner’s and Washizu’s approaches are presented, and pertinent conclusions regarding the implications of the various geometrical and physical characteristics of the blade are outlined.

scholarly journals Stability of a Hot Smoluchowski Fluid

2001 ◽  
Vol 08 (01) ◽  
pp. 19-27 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Numerical Range ◽  
Nonlinear Parabolic Equations ◽  
Stationary Solutions ◽  
Small Perturbations ◽  
Material Density ◽  
Nonlinear Parabolic ◽  
The Stability ◽  
Special Case

We study coupled nonlinear parabolic equations for a fluid described by a material density ρ and a temperature Θ, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on the boundary, with no-escape boundary conditions for the material. For the special case, where the temperature on the boundary is the same at both ends, the linearized equations for small perturbations about a stationary solution at uniform temperature and density are derived; they are subject to boundary conditions, Dirichlet for Θ and no-flow conditions for the material. The spectrum of the generator L of time evolution, regarded as an operator on L2[0,1], is shown to be real, discrete and non-positive, even though L is not self-adjoint. This result is necessary for the stability of the stationary state, but might not be sufficient. The problem lies in the fact that L is not a sectorial operator, since its numerical range is ℂ.

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