Magnetoelastic buckling properties of type-II superconducting thin strip subjected to perpendicular magnetic field and parallel distributed uniform mechanical load

2020 ◽  
pp. 1-13
Author(s):  
Yuan Ma ◽  
Wen Feng ◽  
Zhen Yan
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Body Force ◽  
Mechanical Load ◽  
Plate Theory ◽  
Thin Strip ◽  
Perpendicular Magnetic Field ◽  
Type Ii ◽  
Initial Value ◽  
Classical Plate Theory

The buckling analyses of type-II superconducting strip under applied perpendicular magnetic field and/or distributed uniform mechanical load are investigated in this paper. Based on the Bean critical state model, the electromagnetic body force is firstly given. Then, based on the classical plate theory and two-point initial value method, the critical buckling states of the superconducting strip with different boundary conditions are analyzed. Numerical results show the effects of both the thickness and boundary conditions of superconducting strip on the corresponding critical buckling loads. The present work should be helpful to the research and application of superconducting thin strips.

scholarly journals Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 515
Author(s):  
Olga Mazur ◽  
Jan Awrejcewicz
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Magnetic Parameter ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Graphene Sheets ◽  
Classical Plate Theory ◽  
Foundation Parameters

Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method

2016 ◽  
Vol 23 (19) ◽  
pp. 3247-3265 ◽  
Author(s):  
Majid Ghadiri ◽  
Navvab Shafiei
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Small Scale ◽  
Quadrature Method ◽  
Bending Vibrations ◽  
Classical Plate Theory ◽  
Axial Forces

This study investigates the small-scale effect on the flapwise bending vibrations of a rotating nanoplate that can be the basis of nano-turbine design. The nanoplate is modeled as classical plate theory (CPT) with boundary conditions as the cantilever and propped cantilever. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton’s principle is used to derive the governing equation and boundary conditions for the classic plate based on Eringen’s nonlocal elasticity theory and the differential quadrature method is employed to solve the governing equations. The effect of the small-scale parameter, nondimensional angular velocity, nondimensional hub radius, setting angle and different boundary conditions in the first four nondimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nanomachines such as nanomotors and nano-turbines and other nanostructures.

Type-II-superconductor strip with current in a perpendicular magnetic field

1993 ◽  
Vol 48 (17) ◽  
pp. 12893-12906 ◽  
Author(s):  
Ernst Helmut Brandt ◽  
Mikhail Indenbom
Keyword(s):  
Magnetic Field ◽  
Perpendicular Magnetic Field ◽  
Type Ii ◽  
Type Ii Superconductor

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Type-II Superconducting Strip in Perpendicular Magnetic Field

1993 ◽  
Vol 22 (9) ◽  
pp. 735-740 ◽  
Author(s):  
E. H Brandt ◽  
M. V Indenbom ◽  
A Forkl
Keyword(s):  
Magnetic Field ◽  
Perpendicular Magnetic Field ◽  
Type Ii

Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load

2011 ◽  
Vol 261-263 ◽  
pp. 853-857
Author(s):  
Bo Yang ◽  
Xin Zhang ◽  
Han Yu Yu
Keyword(s):  
Boundary Conditions ◽  
Complex Variable ◽  
Plate Theory ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Transverse Load ◽  
Functionally Graded Plates ◽  
Uniform Load ◽  
Classical Plate Theory ◽  
Elasticity Solutions

England (2006) proposed a novel theory to study the bending problem of isotropic functionally graded plates subjected to transverse biharmonic loads. His theory is extended here to functionally graded plates of transversely isotropic materials. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of the displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solutions may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory(CPT). The elasticity solutions of an FGM annular plate under a uniform load are derived. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity and radius-to-radius ratio on the plate deflection and stresses are studied numerically.

Flexure of Polygonal Plates with Circular Holes

1985 ◽  
Vol 29 (03) ◽  
pp. 209-211
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Plate Theory ◽  
Numerical Results ◽  
Classical Plate Theory ◽  
Circular Holes ◽  
Polygonal Plate

A procedure is developed for determining the stresses in a polygonal plate with a circular hole. Classical plate theory is assumed. The boundary conditions are satisfied exactly term by term. Numerical results are given.

scholarly journals On a Degenerate Evolution System Associated with the Bean Critical-State for Type II Superconductors

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Junichi Aramaki
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Critical State ◽  
Regularity Of Solutions ◽  
Evolution System ◽  
Type Ii ◽  
Type Ii Superconductors ◽  
Limit Solution ◽  
The Magnetic Field

We study a degenerate evolution system containing thep-curl system in a bounded domain with initial and boundary conditions for the magnetic fieldHunder the influence of a system forceF. This is concerned with an approximation of Bean’s critical-state model for type II superconductors. We will show the existence, uniqueness, and regularity of solutions. Moreover we will get the properties of the limit solution asp→∞.

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