Dynamics of a Tubular Cantilever Simultaneously Subjected to Internal and Partially-Confined External Axial Flows

2018 ◽  
Author(s):  
Ahmed R. Abdelbaki ◽  
Arun K. Misra ◽  
Michael P. Païdoussis
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Dynamical Behaviour ◽  
External Flow ◽  
Annular Region ◽  
Heaviside Step Function ◽  
Cantilever Length ◽  
Theoretical Predictions ◽  
External Flows ◽  
The Stability

In this paper the dynamics of a tubular cantilever, simultaneously subjected to internal and external axial flows, is examined theoretically. The tube is discharging fluid downwards which then flows upwards through an annular region surrounding the tube. Thus, the internal and external flows are interdependent and in opposite directions. Also, the external flow is confined over a certain range of the cantilever length and unconfined over the rest. The Heaviside step function has been used in the literature, for such a system, to model the discontinuity in the external flow velocity occurring when the flow enters the annular region. A more accurate way to model this discontinuity is introduced in this study, in which the logistic function is used instead of the Heaviside step function. The stability of the system is investigated by analysis of the system eigenfrequencies, and the effects of varying the length of the confined region are theoretically studied. The obtained results are compared to theoretical predictions and experimental data from the literature having the same system parameters. The proposed theory captures the same dynamical behaviour as observed experimentally, and has a better estimation for the onset of instability and the frequency of oscillations compared to the theory in the literature.

A family of recurrence generated sigmoidal functions based on the Verhulst logistic function. Some approximation and modelling aspects

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Nikolay V. Kyurkchiev
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation ◽  
Logistic Functions

  In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

scholarly journals A family of recurrence generated sigmoidal functions based on the Verhulst logistic function. Some approximation and modelling aspects

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Nikolay Kyurkchiev
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation ◽  
Logistic Functions

In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

scholarly journals A family of recurrence generated sigmoidal functions based on the Log-logistic function. Some approximation aspects

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Nikolay Kyurkchiev ◽  
Svetoslav Markov
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Biochemical Reactions ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation

In this note we construct a family of recurrence generated sigmoidal functions based on the Log--logistic function. The study of some biochemical reactions is linked to a precise Log--logistic function analysis.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given. The plots are prepared using CAS Mathematica.

scholarly journals A new transmuted cumulative distribution function based on the Verhulst logistic function with application in population dynamics

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Nikolay Kyurkchiev
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Logistic Function ◽  
Step Function ◽  
Cumulative Distribution ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
New Class ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation

In this note we find application of a new class cumulative distribution function transformations to construct a family of sigmoidal functions based on the Verhulst logistic function. We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

Polydomain Structure of Epitaxial PbTiO3 films on MgO

1997 ◽  
Vol 493 ◽  
Author(s):  
S. P. Alpay ◽  
A. S. Prakash ◽  
S. Aggarwal ◽  
R. Ramesh ◽  
A. L. Roytburd ◽  
...  
Keyword(s):  
Domain Structure ◽  
Pulsed Laser ◽  
Laser Deposition ◽  
X Ray Diffraction ◽  
X Ray ◽  
Theoretical Predictions ◽  
The Stability ◽  
Increasing Temperature ◽  
Stable Domains ◽  
Domain Stability

ABSTRACTA PbTiO3(001) film grown on MgO(001) by pulsed laser deposition is examined as an example to demonstrate the applications of the domain stability map for epitaxial perovskite films which shows regions of stable domains and fractions of domains in a polydomain structure. X-ray diffraction studies indicate that the film has a …c/a/c/a… domain structure in a temperature range of °C to 400°C with the fraction of c-domains decreasing with increasing temperature. These experimental results are in excellent agreement with theoretical predictions based on the stability map.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

A Meshless Local Petrov-Garlerkin Method for Solving the Biharmonic Equation

2014 ◽  
Vol 931-932 ◽  
pp. 1488-1494
Author(s):  
Supanut Kaewumpai ◽  
Suwon Tangmanee ◽  
Anirut Luadsong
Keyword(s):  
Relative Error ◽  
Biharmonic Equation ◽  
Interpolation Method ◽  
Step Function ◽  
Special Treatment ◽  
Maximum Relative Error ◽  
Heaviside Step Function ◽  
Treatment Techniques ◽  
Point Interpolation Method ◽  
Point Interpolation

A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numerical examples using conventional nodal arrangement as well as polynomial basis choices are considered to demonstrate the applicability, the easiness, and the accuracy of the proposed method. This robust method gives quite accurate numerical results, implementing by maximum relative error and root mean square relative error.

Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

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.

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