scholarly journals Stability of a nonlinear thermoelastic plate

2021 ◽  
Vol 2131 (2) ◽  
pp. 022023
Author(s):  
G I Volokitin ◽  
D V Moiseev
Keyword(s):  
Temperature Field ◽  
Circular Plate ◽  
Small Deformation ◽  
Loss Of Stability ◽  
Lateral Compression ◽  
Thermoelastic Plate ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field

Abstract The problem of loss of stability of a circular plate under lateral compression in an inhomogeneous temperature field is considered. The theory of superposition of a small deformation on a finite one is used. A similar approach to the study of the equilibrium bifurcation of nonlinear thermoelastic bodies was used in the following works.

scholarly journals STABILITY OF A VISCOUS INCOMPRESSIBLE CONDUCTING LIQUID LAYER OF A CYLINDRICAL SHAPE IN AN INHOMOGENEOUS TEMPERATURE FIELD AND A MAGNETIC FIELD OF A VACUUM ARC CURRENT THROUGH IT

2021 ◽  
pp. 91-97
Author(s):  
O.L. Andrieieva ◽  
B.V. Borts ◽  
А.F. Vanzha ◽  
I.М. Korotkova ◽  
V.I. Tkachenko
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
External Magnetic Field ◽  
Fluid Layer ◽  
Vacuum Arc ◽  
Cylindrical Shape ◽  
Conducting Liquid ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Arc Current

Convective mass transfer in a cylindrical viscous incompressible conductive fluid layer in an inhomogeneous temperature field and in the external magnetic field of the vacuum arc current through it is theoretically investigated in this work. For a horizontal layer of a viscous, incompressible, conducting liquid of a cylindrical shape, located in a temperature field inhomogeneous in height and in an external magnetic field of a vacuum arc current flowing through it, the original equations are written. These equations consist of linearized equations for small velocity perturbations, small deviations from the equilibrium values of temperature, pressure, and magnetic field strength. The considered boundary value problem is solved for the case of free boundaries. Comparison of the experimental data with theoretical calculations made it possible to determine the rotation velocity of the steel melt during vacuum arc melting.

scholarly journals Development of unsteady boundary layers on the generatrices of a vertical silicon rod heated by electric current in the mode of conjugate radiation-convective heat transfer

2021 ◽  
Vol 2119 (1) ◽  
pp. 012163
Author(s):  
A. V. Mitina ◽  
V. S. Berdnikov ◽  
K. A. Mitin
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Convective Heat Transfer ◽  
Electric Current ◽  
Convective Heat ◽  
Longitudinal Direction ◽  
Longitudinal Distribution ◽  
Grashof Number ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field

Abstract The nonstationary conjugate radiation-convective heat transfer of a single silicon rod heated by an electric current with the surrounding gas medium is studied numerically in the axisymmetric formulation by the finite element method. The calculations were carried out at the Prandtl number Pr = 0.68, and the range of the Grashof number, determined by the temperature difference and the radius of the rod 9 703 ≤ Gr ≤ 261 977. It is shown that after a short incubation period, a circulation flow is formed. As a result, a significantly inhomogeneous temperature field in the longitudinal direction is formed in a silicon rod heated by an electric current. As the Grashof number increases, the inhomogeneity of the longitudinal distribution of the temperature field increases.

Assessment of the Fluctuations in the Microstructural Parameters of Cellulose in Wood in an Inhomogeneous Temperature Field

2018 ◽  
Vol 45 (6) ◽  
pp. 275-278
Author(s):  
N.N. Matveev ◽  
N.S. Kamalova ◽  
N.Yu. Evsikova ◽  
A.S. Chernykh
Keyword(s):  
Temperature Field ◽  
Crystallite Size ◽  
Wood Specimen ◽  
Average Crystallite Size ◽  
Potential Difference ◽  
Microstructural Parameters ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Homogeneous Temperature

The possibility of assessing the average crystallite size of cellulose in wood by formalised modelling from the magnitude of the potential difference arising in the wood specimen owing to polarisation in a non-homogeneous temperature field is considered.

scholarly journals Thermoelastic Response of Closed Cylindrical Shells in a Supersonic Gas Flow

Aerospace ◽  
2020 ◽  
Vol 7 (8) ◽  
pp. 103
Author(s):  
Marine Mikilyan
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Gas Flow ◽  
Nonlinear Oscillations ◽  
Supersonic Velocity ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Supersonic Gas Flow ◽  
The Stability ◽  
The Galerkin Method

The work is devoted to the investigation of flutter oscillations and the stability of the closed cylindrical shell in supersonic gas flow in an inhomogeneous temperature field. It is assumed that supersonic gas flows on the outside of the shell with an unperturbed velocity U, directed parallel to the cylinder generatrix. Under the action of an inhomogeneous temperature field the shell bulges out, this deformed state is accepted as unperturbed, and the stability of this state is studied. The main nonlinear equations and relationships describing the behavior of the examined system are derived. The formulated boundary value problem is solved using the Galerkin method. The joint influence of the flow and the temperature field on the relationship between the amplitude of nonlinear oscillations of a cylindrical shell and the speed of the flowing stream is studied. The critical velocity values are calculated from the corresponding linear system and are given in tables. The numerical results show that: (a) the surrounding flow significantly affects the nature of the investigated relationship; (b) a certain interval of supersonic velocity exists where it is impossible to excite steady-state flutter oscillations (the silence zone); (c) the dependence of amplitude on the supersonic velocity can be either multivalued or single-valued.

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