Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

1979 ◽  
Vol 46 (2) ◽  
pp. 454-456
Author(s):  
S. O. Onyegegbu
Keyword(s):  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Periodic Motion ◽  
Oscillation Frequency ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
The Stability ◽  
Oscillation Frequencies

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

scholarly journals New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
A. I. Ismail
Keyword(s):  
Rigid Body ◽  
Natural Frequency ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Geometric Interpretation ◽  
Parameter Method ◽  
Large Parameter ◽  
Regular Precession ◽  
New Treatment ◽  
The Stability

In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω = 0.5 . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.

Electrohydrodynamic instability in a horizontal viscoelastic fluid layer in the presence of internal heat generation

2002 ◽  
Vol 80 (6) ◽  
pp. 697-705 ◽  
Author(s):  
M IA Othman ◽  
N H Sweilam
Keyword(s):  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Linear Stability Theory ◽  
Wave Number ◽  
Power Series Method ◽  
Ac Electric Field ◽  
The Stability

Linear stability theory is applied to examine the effect of a vertical ac electric field on the stability of natural convection, which occurs in a dielectric viscoelastic fluid (Walters' liquid B' ) between two parallel horizontal plates with internal heat generation. The power-series method is used to obtain the eigenvalue equation, which is then solved numerically. Critical heat Rayleigh numbers and the critical wave number for the onset of instability are presented graphically as functions of the electric Rayleigh number for various values of the Prandtl number. PACS No.: 47.15Fe

Square-pattern convection in fluids with strongly temperature-dependent viscosity

1985 ◽  
Vol 150 ◽  
pp. 451-465 ◽  
Author(s):  
F. H. Busse ◽  
H. Frick
Keyword(s):  
Numerical Solutions ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Square Lattice ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
The Stability ◽  
Dependent Viscosity ◽  
Theoretical Results

Three-dimensional numerical solutions are obtained describing convection with a square lattice in a layer heated from below with no-slip top and bottom boundaries. The limit of infinite Prandtl number and a linear dependence of the viscosity on temperature are assumed. The stability of the three-dimensional solutions with respect to disturbances fitting the square lattice is analysed. It is shown that convection in the form of two-dimensional rolls is stable for low variations of viscosity, while square-pattern convection becomes stable when the viscosity contrast between upper and lower parts of the fluid layer is sufficiently strong. The theoretical results are in qualitative agreement with experimental observations.

scholarly journals INFLUENCE OF THE GRANULAR MIXTURE PARTICLES SIZES AND OSCILLATION FREQUENCY ON THE SEPARATION PROCESS AT THE CONICAL SIEVES WITH OSCILLATING MOVEMENT

2016 ◽  
Vol 20 (4) ◽  
Author(s):  
GHEORGHE VOICU ◽  
DOREL STOICA ◽  
GABRIEL ALEXANDRU CONSTANTIN ◽  
CRAITA CARP-CIOCÂRDIA ◽  
ELENA MĂDĂLINA ŞTEFAN
Keyword(s):  
Periodic Motion ◽  
Oscillation Frequency ◽  
Tangential Direction ◽  
Separation Process ◽  
Working Process ◽  
Axis Of Rotation ◽  
Thread Diameter ◽  
Vibratory Motion ◽  
Oscillation Frequencies ◽  
Experimental Researches

<p>The paper presents the results of experimental researches on the working process and his efficiency for a sieve with external conical surface with alternative periodic motion. The sieve is suspended at the top and bottom with three elastic threads (of silk), with thread diameter f1.5<em> </em>mm and is provided with circular apertures of f4.2<em> </em>mm. Vibratory motion was obtained with an eccentric mechanism, placed horizontally and acting on tangential direction to the sieve at adjustable distance. . Was thus obtained amplitude oscillation of 3.58, 3.74, 3.91 and 4.10 mm. The oscillation frequencies used were 250, 520 and 790 osc/min. The sieve was used for sorting of canola seeds having sizes between f1.25 mm and f2.5 mm, in percent of 95 %.</p><p>It was found that seeds are separated closer to the feeding point of sieve the more so as the oscillation frequency is smaller. Seeds of a size less than 1.5 mm is separated close to the axis of rotation. Also, the sieve orifices can properly calibrate a seeds mix for all oscillation frequencies analyzed.</p>

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

PNEUMATIC VIBROISOLATION SYSTEM OF THE BASE DESK WITH NATURAL FREQUENCY REGULATION

2021 ◽  
Vol 113 ◽  
pp. 91-100
Author(s):  
Radka JÍROVÁ ◽  
Lubomír PEŠÍK
Keyword(s):  
Natural Frequency ◽  
Automotive Industry ◽  
Natural Frequencies ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Frequency Regulation ◽  
The Stability ◽  
Short Time

Vibroisolation systems of base desks for machine and testing facilities usually cannot effect efficient changing of their own frequencies according to operating conditions. Especially in the case of the automotive industry, the possibility of changing natural frequencies is very desirable. During varying operating conditions, the vibroisolation system needs to be regulated easily and quickly regarding the minimisation of dynamical forces transmitted to the ground and to ensure the stability of the testing process. This paper describes one of the options of tuning the base desk at a relatively short time and by sufficient change of own frequencies, which decides the dynamical behaviour of the whole system.

Dynamic Instability in Quartering Seas—Part III: Nonlinear Effects on Periodic Motions

1997 ◽  
Vol 41 (03) ◽  
pp. 210-223 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Periodic Motion ◽  
Horizontal Plane ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Nonlinear Phenomena ◽  
Specific Sequence ◽  
The Stability ◽  
Two Stages

The loss of stability of the horizontal-plane periodic motion of a steered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go through the surf-riding stage. However, about this point the discussion was essentially conjectural. In order to provide substance we present here a theoretical approach that is organized in two stages: Initially, we demonstrate the existence of a mechanism of parametric instability of yaw on the basis of a rudimentary, single-degree model of maneuvering motion in waves. Then, with a more elaborate model, we identify the underlying nonlinear phenomena that govern the large-amplitude horizontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in the stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jump to resonance. Possible means for controlling the onset of such undesirable behavior are also investigated.

scholarly journals On the exact and numerical solutions to a nonlinear model arising in mathematical biology

2018 ◽  
Vol 22 ◽  
pp. 01061 ◽  
Author(s):  
Asif Yokus ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Sibel Pasali Atmaca
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Hyperbolic Function ◽  
Von Neumann ◽  
Convection Diffusion Equation ◽  
Wolfram Mathematica ◽  
Forward Difference ◽  
Von Neumann Analysis ◽  
The Stability

This study acquires the exact and numerical approximations of a reaction-convection-diffusion equation arising in mathematical bi- ology namely; Murry equation through its analytical solutions obtained by using a mathematical approach; the modified exp(-Ψ(η))-expansion function method. We successfully obtained the kink-type and singular soliton solutions with the hyperbolic function structure to this equa- tion. We performed the numerical simulations (3D and 2D) of the obtained analytical solutions under suitable values of parameters. We obtained the approximate numerical and exact solutions to this equa- tion by utilizing the finite forward difference scheme by taking one of the obtained analytical solutions into consideration. We investigate the stability of the finite forward difference method with the equation through the Fourier-Von Neumann analysis. We present the L2 and L∞ error norms of the approximations. The numerical and exact approx- imations are compared and the comparison is supported by a graphic plot. All the computations and the graphics plots in this study are car- ried out with help of the Matlab and Wolfram Mathematica softwares. Finally, we submit a comprehensive conclusion to this study.

Sign in / Sign up

Export Citation Format

Share Document