Axisymmetric magnetoelastic deformation of a flexible orthotropic ring plate with orthotropic conductivity

Mol’chenko, L. V.; Loos, I. I.; Fedorchenko, L. M.

doi:10.1007/s10778-013-0570-1

Cited by 7 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the results of [8][9][10][11][12][13][14][15][16][17], and considering the geometry of the shell, a complete system of equations in a curvilinear orthogonal coordinate system is derived; it allows mathematical description of a nonlinear two-dimensional model of…”

Section: Nonlinear Model Of Magneto-elasticity Of the Current-carmentioning

confidence: 99%

Nonlinear Vibrations of a Current-Carrying Anisotropic Cylindrical Shell in a Magnetic Field.

Indiaminov¹,

Kholjigitov²,

Narkulov³

2020

Theoretical & Applied Science

View full text Add to dashboard Cite

Impact Factor: ISRA (India) = 4.971 ISI (Dubai, UAE) = 0.829 GIF (Australia) = 0.564 JIF = 1.500 SIS (USA) = 0.912 РИНЦ (Russia) = 0.126 ESJI (KZ) = 8.716 SJIF (Morocco) = 5.667 ICV (Poland) = 6.630 PIF (India) = 1.940 IBI (India) = 4.260 OAJI (USA) = 0.350 Philadelphia, USA 205 QR -Issue QR -ArticleAbstract: A nonlinear two-dimensional model of magnetoelasticity of a current-carrying cylindrical shell is constructed in the paper with account for anisotropy of conductive properties. It is assumed that the main directions of the anisotropy of shell material properties coincide with the directions of the corresponding coordinate axes, and it is believed that an anisotropic body is linear with respect to magnetic and electrical properties. A coupled system of nonlinear differential equations is obtained that describes the stress-strain state of flexible current-carrying cylindrical shells with anisotropy of conductive properties, under unsteady-state power and electromagnetic loads; a boundary-value problem is formulated.

show abstract

Section: Nonlinear Model Of Magneto-elasticity Of the Current-carmentioning

confidence: 99%

Nonlinear Vibrations of a Current-Carrying Anisotropic Cylindrical Shell in a Magnetic Field.

Indiaminov¹,

Kholjigitov²,

Narkulov³

2020

Theoretical & Applied Science

View full text Add to dashboard Cite

show abstract

“…Following [1,[7][8][9][10][11], taking into account the diagonality of the tensors s ij , m ij , e ij , and performing appropriate transformations, we obtain a coupled system of nonlinear differential equations in Lagrangian coordinates in normal form: …”

mentioning

confidence: 99%

“…Procedure for Solution of Nonlinear Problem. The problem of magnetoelasticity for an orthotropic ring plate of radially varying stiffness is solved by sequentially using the Newmark scheme, the quasilinearization method, and the discrete-orthogonalization method [1,[7][8][9][10][11]. To separate variables dependent on the time coordinate, we integrate the magnetoelastic equations using the implicit Newmark scheme [14].…”

mentioning

confidence: 99%

Influence of Extraneous Current on the Stress State of an Orthotropic Ring Plate with Orthotropic Conductivity

2014

Self Cite

View full text Add to dashboard Cite

A nonlinear problem of magnetoelasticity for an orthotropic ring plate with orthotropic electric conductivity is solved. A governing system of nonlinear differential equations describing the stress-strain state of flexible orthotropic plates is solved. A numerical example is considered. The effect of extraneous current on the stress state of a flexible ring plate is analyzed Keywords: orthotropic ring plate, magnetic field, magnetoelasticity Introduction. The great interest in problems of the mechanics of coupled fields, primarily electro-and magnetoelasticity, stems from the demands of the technological progress in various industries and the development of new technologies. However, the effects of interaction between mechanical and electromagnetic fields have been studied inadequately. These are, primarily, effects observed in thin-walled elements undergoing large-displacement deformation in a strong magnetic field and in current-carrying thin-walled elements [4-6, 12, 13, 16, 17]. The interaction of extraneous and induced currents in magnetoelastic systems and strong magnetic fields results in electromagnetic body forces that induce high or even ultimate mechanical stresses. Therefore, a nonlinear theory has to be used to study the effects of coupling of fields and to determine the stress-strain state in problems of such class.Problems of magnetoelasticity for thin shells and plates made of real (with finite conductivity) materials are very challenging to treat theoretically. Note also that the advanced technology employs structural materials that are anisotropic or, in specific cases, orthotropic even in undeformed state.Magnetoelasticity in the presence of extraneous current is of particular interest. Problems involving extraneous currents are very complicated, but become simpler for thin bodies.1. Problem Formulation. Basic Equations. Consider an orthotropic ring plate with varying thickness h h r = ( ) and orthotropic conductivity; its mid-surface is described by polar coordinates r, q.Let all the components of the strain and induced electromagnetic fields that appear in the magnetoelastic equations be independent of the coordinate q.A variable electric current from an extraneous source is applied to the edge of the plate. Polarization, magnetization, and thermal stresses are neglected.The material of the plate is orthotropic; the coordinate axes are aligned with its principal axes of elastic symmetry. The electromagnetic properties of the material are characterized by the tensors of conductivity s ij , permeability m ij , and permittivity e ij i j ( , , , ) = 1 2 3 .To analyze the electromagnetic effects, we will use the system of equations consisting of Maxwell's equations in Lagrangian form, constitutive equations, and equations of motion. The constitutive equations relate the magnetic-flux density r B, electric-flux density r D, magnetic-field strength r H, electric-field strength r E, and current density r J. In the case of anisotropic conductivity, these quantities are related as

show abstract

Stress–Strain State of a Two-Layer Circular Orthotropic Plate with Low Shear Stiffness

Kirakosyan

Stepanyan

2014

Int Appl Mech

View full text Add to dashboard Cite

Axisymmetric magnetoelastic deformation of a flexible orthotropic ring plate with orthotropic conductivity

Cited by 7 publications

References 5 publications

Nonlinear Vibrations of a Current-Carrying Anisotropic Cylindrical Shell in a Magnetic Field.

Nonlinear Vibrations of a Current-Carrying Anisotropic Cylindrical Shell in a Magnetic Field.

Influence of Extraneous Current on the Stress State of an Orthotropic Ring Plate with Orthotropic Conductivity

Stress–Strain State of a Two-Layer Circular Orthotropic Plate with Low Shear Stiffness

Contact Info

Product

Resources

About