scholarly journals Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Abhinav Ravindra Dehadrai ◽  
Ishan Sharma ◽  
Shakti S. Gupta
Keyword(s):  
Stability Analysis ◽  
Governing Equation ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Bending Rigidity ◽  
Stable Regime ◽  
Varying Coefficients ◽  
The Stability

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

Stability of a String in Axial Flow

1985 ◽  
Vol 107 (4) ◽  
pp. 421-425 ◽  
Author(s):  
G. S. Triantafyllou ◽  
C. Chryssostomidis
Keyword(s):  
Stability Analysis ◽  
Frictional Coefficient ◽  
Axial Flow ◽  
Added Mass ◽  
Equation Of Motion ◽  
Bending Stiffness ◽  
Diameter Ratio ◽  
Constant Speed ◽  
Hamilton’S Principle ◽  
The Stability

The equation of motion of a long slender beam submerged in an infinite fluid moving with constant speed is derived using Hamilton’s principle. The upstream end of the beam is pinned and the downstream end is free to move. The resulting equation of motion is then used to perform the stability analysis of a string, i.e., a beam with negligible bending stiffness. It is found that the string is stable if (a) the external tension at the free end exceeds the value of a U2, where a is the “added mass” of the string and U the fluid speed; or (b) the length-over-diameter ratio exceeds the value 2Cf/π, where Cf is the frictional coefficient of the string.

Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid

2016 ◽  
Vol 68 (3) ◽  
pp. 386-391 ◽  
Author(s):  
Abhishek Ghosh ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
High Speed ◽  
Journal Bearing ◽  
Slenderness Ratio ◽  
Linear Perturbation ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Coupled Stress

Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

scholarly journals Flutter of Long Flexible Cylinders in Axial Flow

2006 ◽  
Author(s):  
E. de Langre ◽  
M. P. Paidoussis ◽  
Y. Modarres-Sadeghi ◽  
O. Doare´
Keyword(s):  
Stability Analysis ◽  
Axial Flow ◽  
Equation Of Motion ◽  
External Flow ◽  
Transverse Motion ◽  
Control Parameters ◽  
Limit Case ◽  
Finite Region ◽  
Flexible Cylinder ◽  
The Stability

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the up-stream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. A simple model for the behaviour of long cylinders is proposed.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

2015 ◽  
pp. 196-204
Author(s):  
Г.В. Кривовичев ◽  
С.А. Михеев
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Linear Approximation ◽  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Order Approximation ◽  
Stability Study ◽  
High Order Approximation ◽  
Spatial Variables ◽  
The Stability

Исследуется устойчивость трехслойных конечно-разностных решеточных схем Больцмана третьего и четвертого порядков аппроксимации по пространственным переменным. Проводится анализ устойчивости по начальным условиям с использованием линейного приближения. Для исследования используется метод Неймана. Показано, что устойчивость схем можно улучшить за счет аппроксимации конвективных членов во внутренних узлах сеточного шаблона. В этом случае удается получать большие по площади области устойчивости, чем при аппроксимации в граничных узлах шаблона. The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

scholarly journals On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

2021 ◽  
pp. 81-87
Author(s):  
William Atokolo ◽  
Achonu Omale Joseph ◽  
Rose Veronica Paul ◽  
Abdul Sunday ◽  
Thomas Ugbojoide Onoja
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Initial Conditions ◽  
Virus Disease ◽  
Disease Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Stability Analysis ◽  
Corona Virus ◽  
The Stability

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.

Trimming analysis of flexible aircrafts based on computational fluid dynamics/computational structural dynamics coupling methodology

2020 ◽  
pp. 095441002094194
Author(s):  
Hua Ruhao ◽  
Chen Hao ◽  
Yuan Xianxu ◽  
Tang Zhigong ◽  
Bi Lin
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Elastic Deformation ◽  
Structural Dynamics ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Stability Margin ◽  
Computational Structural Dynamics ◽  
The Stability

A numerical methodology based on the coupling of computational fluid dynamics (CFD) and computational structural dynamics is established to obtain the trimming characteristics of flexible aircrafts in this paper. Reynolds-averaged Navier–Stokes equations are solved through CFD technique. Based on the frame of unstructured mesh, techniques of dynamic chimera mesh and morphing mesh are adopted to treat the data transfer between different computational zones and structure deformation caused by aeroelasticity, respectively. When it is applied to a projectile model with large slenderness ratio constructed in this paper, convergence histories of various initial conditions demonstrate the efficiency and robustness of the algorithm. The influence of the structural rigidity and normal loads on the trimming condition of flexible projectiles is investigated, and the locations of the aerodynamic center with various rigidities present the explanation that elastic deformation can move the aerodynamic center forward and weaken the margin of the stability. Furthermore, the trimming condition of flexible projectiles with propulsion is researched, which indicates that thrust misalignment will increase the effect of elastic deformation on the trimming condition, and the stability margin will be further weakened because of thrust misalignment. The conclusion provided in this paper can provide guidance for the structural design, control system design, and stability analysis for modern aircrafts with small stability margin and low rigidity.

Stability Analysis of High-Performance Drones With Suspended Payloads

2019 ◽  
Author(s):  
Samantha Hoang ◽  
Yifeng Liu ◽  
Alberto Aliseda ◽  
I. Y. Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
High Performance ◽  
Initial Conditions ◽  
Wind Disturbance ◽  
External Disturbances ◽  
Nonlinear Simulations ◽  
Linearized System ◽  
Payload Mass ◽  
The Stability

Abstract This paper studies the stability of a system consisting of a drone with a heavy payload through both linear stability analysis and nonlinear simulations. The stability is studied with respect to two payload parameters: the length of the arm the payload is suspended from and the mass of the payload. Linearizing the drone-payload system around vertical flight results in a linearized system that is marginally stable with five negative, real eigenvalues and seven zero-eigenvalues. The presence of seven zero-eigenvalues makes it difficult to predict the stability of the nonlinear system so nonlinear simulations are completed to understand how the drone-payload system reacts to external disturbances. To directly study the severity of the nonlinear system’s instability, the system is subjected to an initial, one-second wind disturbance that induces different initial conditions on the system. The results of the nonlinear simulations indicate that the presence of a suspended payload will always cause the drone-payload system to be unstable. Both an increase in the length of the payload arm and the payload mass will individually increase the deviation of the system from the expected path.

Magnetoelastic Instability of a Long Graphene Nano-Ribbon Carrying Electric Current

2014 ◽  
Vol 6 (3) ◽  
pp. 299-306
Author(s):  
R. D. Firouz-Abadi ◽  
H. Mohammadkhani
Keyword(s):  
Electric Current ◽  
Governing Equation ◽  
Equation Of Motion ◽  
Current Strength ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

AbstractThis paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon (GNR) carrying electric current. The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton’s principle. The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws. Using Galerkin’s method, the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated.

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