Stability of Nonconservatively Elastic Systems Using Eigenvalue Sensitivity

1994 ◽  
Vol 116 (2) ◽  
pp. 168-172 ◽  
Author(s):  
Lien-Wen Chen ◽  
Der-Ming Ku
Keyword(s):  
Critical Load ◽  
Numerical Technique ◽  
Beam Theory ◽  
Cost Effective ◽  
Element Model ◽  
Solution Technique ◽  
Concentrated Mass ◽  
Eigenvalue Sensitivity ◽  
System A ◽  
The Stability

The stability of a cantilever column, carrying a concentrated mass at the free end and resting on an elastic foundation of the Winkler-type, subjected to uniformly distributed in-plane follower forces is studied by “Timoshenko beam theory” finite elements. In order to more quickly and efficiently obtain the critical load for such a nonconservative system, a simple and cost-effective numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. The high accuracy and rapid rate of convergence through the combination of the present finite element model and the solution technique are demonstrated with the numerical example given. The influence of some system parameters on the critical load is also discussed.

Finite Element Analysis on Stability for Elastic-Jumping Membrane

2011 ◽  
Vol 287-290 ◽  
pp. 717-722 ◽  
Author(s):  
Zhen Ting Wu ◽  
Shun Jiang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Critical Load ◽  
Element Model ◽  
Structure Parameter ◽  
Element Analysis ◽  
Factors Influencing ◽  
Optimizing Design ◽  
Main Factors ◽  
The Stability

In order to increase the designing precision and study the main factors influencing the stability of metal elastic-jumping membrane, a set of experimental equipments have been designed to test the stability of metal elastic-jumping membrane. The laws of influencing the stability of elastic-jumping membrane were studies by changing the thickness, high, radius etc structure parameter. It shows that the increasing of high and thickness can enhance the distortion rigidity of metal elastic-jumping membrane, result in the increase of critical load at losing stability; the increasing of diameter can reduce the distortion rigidity of metal elastic-jumping membrane, result in the decrease of critical load at losing stability. At the same time, the correctness of finite element model was confirmed, and the basis was established for finite element method applying in optimizing design of metal elastic-jumping membrane.

Nonconservative Stability of Gyroscopic Rotor Systems

1993 ◽  
Author(s):  
Hwang-Kuen Chen ◽  
Der-Ming Ku ◽  
Lien-Wen Chen
Keyword(s):  
Direct Method ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Follower Force ◽  
The Finite Element Method ◽  
Nonconservative System ◽  
Rotor Systems ◽  
Eigenvalue Sensitivity ◽  
The Stability ◽  
Flutter Load

Abstract The stability behavior of a cantilevered shaft, rotating at a constant speed and subjected to a follower force at the free end, is studied by the finite element method. The equations of motion for such a gyroscopic system are formulated by using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformations are included. In order to determine the critical load of the present nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced. The numerical results show that for the present nonconservative system, the onset of flutter instability occurs when the first and second backward whirl speeds are coincident. And also, due to the effect of the gyroscopic moments, the critical flutter load decreases as the rotational speed increases.

Further Results on the Stability of Viscoelastic Columns

1987 ◽  
Vol 11 (3) ◽  
pp. 179-194
Author(s):  
W. Szyszkowski ◽  
P.G. Glockner
Keyword(s):  
Element Model ◽  
Static Stability ◽  
Model Material ◽  
Constitutive Law ◽  
Time Dependent ◽  
Closed Form Expression ◽  
Solution Technique ◽  
Arbitrary Boundary ◽  
Post Buckling ◽  
The Stability

Recent results published by the authors on the stability behaviour of columns made of time-dependent materials are extended in a number of ways. Firstly, the closed-form expression obtained for the safe load limit of a simply supported column made of a linear three-element model material, is generalized for an arbitrary linearly viscoelastic constitutive law. The result, obtained by means of the static stability approach, is confirmed by an asymptotic solution of the dynamic stability equations. The same solution technique is used to generalize this expression for columns with arbitrary boundary conditions. Even though columns as structural members exhibit stable post-buckling behaviour, there are structural configurations, involving compression members, the overall load deflection behaviour of which indicate unstable post-buckling characteristics. A simple example is used to alert the designer to the possibility of encountering such configurations and the danger associated with such post-buckling behaviour in the case of structures made of time-dependent materials.

Atomic disruption beam theory

2016 ◽  
pp. 3524-3528
Author(s):  
Casey Ray McMahon
Keyword(s):  
Neutron Beam ◽  
Beam Theory ◽  
Solid Material ◽  
Material Matter ◽  
Solid Matter ◽  
Plasma Generation ◽  
Resulting Effect ◽  
Drilling Operations ◽  
The Stability

In this paper, I discuss the theory behind the use of a dense, concentrated neutron particle-based beam. I look at the particle based physics behind such a beam, when it is focused against solid material matter. Although this idea is still only theoretical, it appears that such a beam may be capable of disrupting the stability of the atoms within solid matter- in some cases by passing great volumes of neutrons between the electron and nucleus thus effectively “shielding” the electron from the charge of the nucleus. In other cases, by disrupting the nucleus by firing neutrons into it, disrupting the nucleus and weakening its bond on electrons. In either case- the resulting effect would be a disruption of the atom, which in the case of material matter would cause said material matter to fail, which would appear to the observer as liquification with some plasma generation. Thus, a dense neutron particle based beam could be used to effectively liquefy material matter. Such a beam could bore through rock, metal, or even thick, military grade armour, like that used on tanks- causing such materials to rapidly liquefy. The denser and thicker the neutron beam, the more devastating the effect of the beam- thus the faster material matter will liquefy and the greater the area of liquification. Such a beam would have applications in Defence, mining and drilling operations.

NPLs — The Solution Recipe for Albania

2015 ◽  
Vol 3 (1) ◽  
pp. 48
Author(s):  
Elona Shehu ◽  
Elona Meka
Keyword(s):  
Interest Rate ◽  
Negative Relationship ◽  
Banking System ◽  
Gdp Growth ◽  
System A ◽  
Analysis Technique ◽  
Recent Financial Crisis ◽  
The Stability ◽  
Asset Quality ◽  
Macroeconomic Determinants

The quality of the loan portfolio in Albanian banking system is facing many obstacles during the last decade. In this paper we look at possible determinants of assets quality. During the recent financial crisis commercial banks were confronted with deteriorating asset quality that threatened not only the banking industry, but also the stability of the entire financial system. This study aims to examine the correlation between non-performing loans and the macroeconomic determinants in Albania during the last decade. NPLs are considered to be of a high importance as they represent the high risk exposure of banking system. A solid bank with healthy assets increases the market efficiency. Our approach is based on a panel data regression analysis technique from 2005-2015. Within this methodology this study finds robust evidence on the existing relationship between lending interest rate, real GDP growth and NPLs. We expect to find a negative relationship between lending interest rate and asset quality. Further we assume an inverse relationship between GDP growth and non-performing loans, suggesting that NPLs decrease if the economy is growing. Furthermore this study proposes a solution platform, which looks deeper into the possibility of creating a secondary active market for troubled loans, restructuring the banking system or implementing the Podgorica model. This research paper opens a new lieu of discussion in terms of academic debates and decision-making policies.

Towards a new design with generic modeling and adaptive control of a transformable quadrotor

2021 ◽  
pp. 1-31
Author(s):  
S.H. Derrouaoui ◽  
Y. Bouzid ◽  
M. Guiatni
Keyword(s):  
Adaptive Control ◽  
Control Strategy ◽  
Experimental Tests ◽  
Generic Model ◽  
System Control ◽  
System A ◽  
Viable Solution ◽  
Generic Modeling ◽  
Adaptive Control Strategy ◽  
The Stability

Abstract Recently, transformable Unmanned Aerial Vehicles (UAVs) have become a subject of great interest in the field of flying systems, due to their maneuverability, agility and morphological capacities. They can be used for specific missions and in more congested spaces. Moreover, this novel class of UAVs is considered as a viable solution for providing flying robots with specific and versatile functionalities. In this paper, we propose (i) a new design of a transformable quadrotor with (ii) generic modeling and (iii) adaptive control strategy. The proposed UAV is able to change its flight configuration by rotating its four arms independently around a central body, thanks to its adaptive geometry. To simplify and lighten the prototype, a simple mechanism with a light mechanical structure is proposed. Since the Center of Gravity (CoG) of the UAV moves according to the desired morphology of the system, a variation of the inertia and the allocation matrix occurs instantly. These dynamics parameters play an important role in the system control and its stability, representing a key difference compared with the classic quadrotor. Thus, a new generic model is developed, taking into account all these variations together with aerodynamic effects. To validate this model and ensure the stability of the designed UAV, an adaptive backstepping control strategy based on the change in the flight configuration is applied. MATLAB simulations are provided to evaluate and illustrate the performance and efficiency of the proposed controller. Finally, some experimental tests are presented.

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

2014 ◽  
Vol 756 ◽  
pp. 650-688 ◽  
Author(s):  
J. F. Torres ◽  
D. Henry ◽  
A. Komiya ◽  
S. Maruyama
Keyword(s):  
Natural Convection ◽  
Rotation Axis ◽  
Numerical Technique ◽  
Continuation Method ◽  
Rotation Vector ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Stable Solutions ◽  
The Stability ◽  
Cubical Cavity

AbstractNatural convection in an inclined cubical cavity heated from two opposite walls maintained at different temperatures and with adiabatic sidewalls is investigated numerically. The cavity is inclined by an angle $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $ around a lower horizontal edge and the isothermal wall set at the higher temperature is the lower wall in the horizontal situation ($\theta = 0^\circ $). A continuation method developed from a three-dimensional spectral finite-element code is applied to determine the bifurcation diagrams for steady flow solutions. The numerical technique is used to study the influence of ${\theta }$ on the stability of the flow for moderate Rayleigh numbers in the range $\mathit{Ra} \leq 150\, 000$, focusing on the Prandtl number $\mathit{Pr} = 5.9$. The results show that the inclination breaks the degeneracy of the stable solutions obtained at the first bifurcation point in the horizontal cubic cavity: (i) the transverse stable rolls, whose rotation vector is in the same direction as the inclination vector ${\boldsymbol{\Theta}}$, start from $\mathit{Ra} \to 0$ forming a leading branch and becoming more predominant with increasing $\theta $; (ii) a disconnected branch consisting of transverse rolls, whose rotation vector is opposite to ${\boldsymbol{\Theta}}$, develops from a saddle-node bifurcation, is stabilized at a pitchfork bifurcation, but globally disappears at a critical inclination angle; (iii) the semi-transverse stable rolls, whose rotation axis is perpendicular to ${\boldsymbol{\Theta}}$ at $\theta \to 0^\circ $, develop from another saddle-node bifurcation, but the branch also disappears at a critical angle. We also found the stability thresholds for the stable diagonal-roll and four-roll solutions, which increase with $\theta $ until they disappear at other critical angles. Finally, the families of stable solutions are presented in the $\mathit{Ra}-\theta $ parameter space by determining the locus of the primary, secondary, saddle-node, and Hopf bifurcation points as a function of $\mathit{Ra}$ and $\theta $.

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