Harmonic Vibrations in Thermoelasticity of Microstretch Materials

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Marin Marin
Keyword(s):  
Steady State ◽  
Lateral Surface ◽  
Boundary Data ◽  
Heat Supply ◽  
Critical Frequency ◽  
Body Force ◽  
Decay Estimate ◽  
Angular Frequency ◽  
Plane Boundary ◽  
Harmonic Vibrations

Consider a cylinder made of a microstretch thermoelastic material for which one plane end is subjected to plane boundary data varying harmonically in time. On the lateral surface and other base, we have zero body force and heat supply. By using a Toupin type measure associated with the corresponding steady-state vibration, and by assuming that the angular frequency of oscillations is lower than a certain critical frequency, we show that the amplitude of the vibrations decays exponentially with the distance to the base. This decay estimate is similar to that of the Saint-Venant type.

Body Force Calculation of Steady-State Plasma Flow with Accurate Pressure Measurement

2019 ◽  
Vol 56 (2) ◽  
pp. 662-668
Author(s):  
Bin Wu ◽  
Chao Gao ◽  
Feng Liu ◽  
Juntao Xiong
Keyword(s):  
Steady State ◽  
Plasma Flow ◽  
Pressure Measurement ◽  
Body Force ◽  
Force Calculation ◽  
State Plasma

Two-dimensional turbulence near the viscous limit

1974 ◽  
Vol 62 (2) ◽  
pp. 273-287 ◽  
Author(s):  
J. S. A. Green
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Body Force ◽  
Reynolds Numbers ◽  
Rapid Decrease ◽  
Two Dimensional ◽  
Turbulent Stress ◽  
Viscous Limit ◽  
External Body

Two-dimensional incompressible motion is generated by a steady external body force varying sinusoidally with a transverse co-ordinate. Such flow is found to be unstable for Reynolds numbers greater than 2½, and under these conditions evolves towards a new steady state. This ‘steady-eddy’ state is itself unstable in a sense, and its breakdown suggests the catastrophic onset of a cascade of turbulence. The mechanics of this cascade can be represented by a kind of recursion system in which the turbulence dynamics of one scale is repeated in the next, and a law of turbulent stress results. The spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease (as k) towards longer wavelengths.

On Steady-State Filtration of Fluid in Strip-Like and Wedge-Shaped Porous Ground Bases

2014 ◽  
Vol 1020 ◽  
pp. 373-378
Author(s):  
Suren M. Mkhitaryan ◽  
H.V. Tokmajyan ◽  
S.A. Avetisyan ◽  
M.S. Grigoryan
Keyword(s):  
Steady State ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Vertical Velocity ◽  
Boundary Value ◽  
Integral Transforms ◽  
Plane Boundary ◽  
Filtration Theory

In statement of the steady-state filtration theory and within the framework of the Darcy`s law plane boundary value problems for the strip-like and wedge-shaped porous ground base are considered when through some system of segments on one face of the base the fluid with a certain vertical velocity or with a certain pressure is injected inside the base. These solutions are reduced to integral equations by means of integral transforms.

Optimal Thermoelastic Design for Given Deformation

1971 ◽  
Vol 38 (2) ◽  
pp. 538-540 ◽  
Author(s):  
J.-M. Chern
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Optimal Design ◽  
Lateral Surface ◽  
Total Elongation ◽  
Axial Loads ◽  
Elastic Rod ◽  
Steady State Temperature ◽  
Different Temperatures ◽  
Thermoelastic Design

Optimal design of an elastic rod for given total elongation is discussed when both the axial loads and the steady-state temperature field in the rod depend on the design. Numerical results are presented for a rod that carries a given mass at the tip and rotates about an axis through the root that is perpendicular to the axis of the rod, while tip and root are kept at different temperatures and the lateral surface of the rod is thermally insulated.

Non-Linear Diffusion - Non-linear diffusion I. Diffusion and flow of mixtures of fluids

1963 ◽  
Vol 255 (1064) ◽  
pp. 607-633 ◽  
Keyword(s):  
Mechanical Properties ◽  
Steady State ◽  
Body Force ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Viscous Fluids ◽  
Rigid Plate ◽  
Linear Diffusion ◽  
Diffusion Effects ◽  
Non Linear

A theory for the flow and non-linear diffusion effects in mixtures of fluids is formulated based upon hydrodynamical considerations. It is assumed that each point of the mixture is occupied simultaneously by all constituents in given portions. The motion of each constituent is governed by the usual equations of motion and continuity. The mechanical properties of each component are specified by means of constitutive equations for the stresses; diffusion effects are accounted for by means of a body force acting on each constituent which depends upon the composition and relative motion of the substances in the mixture. The theory is extended to deal with the diffusion of a mixture of fluids through a rigid solid. The theory is applied to a number of steady-state problems involving non-Newtonian fluids including the diffusion of a fluid through a rigid plate, the laminar flow of a mixture and the flow of a mixture between rotating cylinders. The propagation of plane waves through a homogeneous mixture of viscous fluids at rest is also examined.

REACTANTS AND OTHER PARAMETERS OF MECHANICAL SYSTEMS

2020 ◽  
pp. 4-12
Author(s):  
I. P. Popov ◽  
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Electrical Engineering ◽  
Mechanical Systems ◽  
Phase Relations ◽  
Calculation Algorithm ◽  
Steady State Mode ◽  
Harmonic Oscillations ◽  
Harmonic Vibrations ◽  
Algebraic Operations

The traditional calculation of mechanisms for forced harmonic oscillations is often a difficult task. Most often, calculators are interested in the steady-state modes of harmonic oscillations. The purpose of this paper is to significantly simplify calculations by replacing the need to solve differential equations with simpler algebraic methods. A complex representation of harmonic and related quantities is used. This approach is widely used in theoretical electrical engineering. Parallel and serial connections of mechanical power consumers are considered. The velocities of elements of mechanical systems and the forces applied to them are determined algebraically from the known parameters of systems and the disturbing harmonic effect. The use of a symbolic (complex) description of mechanical systems under forced harmonic vibrations (in steady-state mode) allowed us to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations, and replace it with simpler and more visual algebraic operations. Due to this, the time of calculations is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems under harmonic influences, have substantial methodological significance, since they show quantitative and phase relations between the parameters of systems.

A Novel Mixing Plane Method Using Nonreflecting Boundary Conditions for Multirow Analysis in Turbomachines

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Fernando Gisbert ◽  
Roque Corral
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Boundary Conditions ◽  
Reverse Flow ◽  
Plane Boundary ◽  
Normal Velocity ◽  
Nonreflecting Boundary Conditions ◽  
Plane Normal ◽  
Convergence Problems ◽  
New Formulation

A new formulation of the mixing plane boundary condition to analyze the steady-state interaction between adjacent rows of a turbomachine, used in conjunction with steady two-dimensional nonreflecting boundary conditions, is presented. Existing mixing plane formulations rely on the differences between some variables at the interface of adjacent rows to determine the boundary condition. These differences are driven to zero as the case is converged to the steady state. By contrast, the proposed approach determines the differences that result in the conservation of mass, momentum, and energy after the boundary condition is enforced, ensuring conservation at any instant during the iterative process. The reverse flow within the mixing plane boundary is naturally treated, but both inlet and outlet boundary conditions fail when the mixing plane normal velocity tends to zero, giving rise to sharp variations of the fluid variables that must be properly limited to prevent convergence problems. Some examples will be given to demonstrate the ability of the new method to resolve these cases while preserving the boundary condition robustness.

The development of concentrated vortices: a numerical study

1971 ◽  
Vol 48 (1) ◽  
pp. 1-21 ◽  
Author(s):  
L. M. Leslie
Keyword(s):  
Steady State ◽  
Numerical Experiment ◽  
Laboratory Experiments ◽  
Body Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Quasi Steady State ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Axis Of Rotation

Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.

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