Dynamic stability of viscoelastic columns loaded by a follower force

2004 ◽  
Vol 218 (10) ◽  
pp. 1091-1101 ◽  
Author(s):  
T T Darabseh ◽  
J Genin
Keyword(s):  
Boundary Value Problems ◽  
Dynamic Instability ◽  
Element Model ◽  
Follower Load ◽  
Dynamic Approach ◽  
Stability Analyses ◽  
Damping Coefficients ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
The Stability

This paper analyses the motion of a linear viscoelastic column using the dynamic approach. The viscoelastic material is mathematically represented by the four-element model. Using this model as a recursion equation, the elastic, one-, two-, three- and four-element models are solved and their results compared. The stability analyses of these systems are investigated by studying the eigenvalues of the characteristic equations for the solution to the boundary value problems. The stability analyses determined the smallest value of the follower load beyond which the system, under a suitable disturbance, will perform oscillations with increasing amplitudes. The dynamic instability is found to occur in the form of flutter. The effect of damping on the critical follower load is also examined. Three damping parameters are considered that affect the results. They are the damping coefficients related to a Maxwell unit, to a Kelvin unit and one appropriate to a combination of the two. The destabilization effects of viscosity are discussed.

Transverse Vibration of a Viscoelastic Column With Initial Curvature Under Periodic Axial Load

1969 ◽  
Vol 36 (4) ◽  
pp. 814-818 ◽  
Author(s):  
K. K. Stevens
Keyword(s):  
Polymethyl Methacrylate ◽  
Transverse Vibration ◽  
Axial Load ◽  
Dynamic Instability ◽  
Complex Modulus ◽  
Lateral Vibrations ◽  
Lateral Response ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
Frequency Curves

The lateral response of a slightly curved viscoelastic column subjected to a periodic axial load P0 + P1 cos ωt is investigated. The analysis makes use of the complex modulus representation for linear viscoelastic materials. It is shown that the lateral vibrations stemming from imperfections can be of significant amplitude. Experimentally determined amplitude-frequency curves for a polymethyl methacrylate (Plexiglas) column are presented, and are found to be in excellent agreement with the theory. It is shown that there is an analogy between the dynamic instability and the static buckling of imperfect columns.

scholarly journals ABOUT THE STABILITY OF NONCONSERVATIVE UNDAMPED ELASTIC SYSTEMS: SOME NEW ELEMENTS

2009 ◽  
Vol 09 (02) ◽  
pp. 357-367 ◽  
Author(s):  
JEAN LERBET ◽  
ELIE ABSI ◽  
ALAIN RIGOLOT
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Static Stability ◽  
Stability Domain ◽  
Dynamic Approach ◽  
Linear Approach ◽  
Elastic Systems ◽  
The Common ◽  
The Stability ◽  
New Criterion

It is well-known that the domains of static stability and dynamic stability (even for a linear approach) do not match each other when the system is no more conservative and the dynamic approach is usually privileged, meaning that the dynamic stability domain is included in the static one. Following previous works proposing a new criterion of static stability of nonconservative systems and prolonging a paper of Gallina devoted to linear dynamic instability (flutter), we show in this paper some remarkable relations between the two approaches: contrary to the common thought, the new static stability criterion implies partially the dynamic one.

Separating the Contributions in Localization Methods: A Technique to Enhance Identification of Damping Related Parameters

1999 ◽  
Author(s):  
Hervé Algrain ◽  
Calogero Conti ◽  
Pierre Dehombreux
Keyword(s):  
Finite Element ◽  
Model Updating ◽  
Element Model ◽  
Dynamic Responses ◽  
Finite Element Model Updating ◽  
Global Localization ◽  
Localization Method ◽  
The Family ◽  
Family Based ◽  
The Stability

Abstract Finite Element Model Updating has for objective to increase the correlation between the experimental dynamic responses of a structure and the predictions from a model. Among different initial choices, these procedures need to establish a set of representative parameters to be updated in which some are in real error and some are not. It is therefore important to select the correct properties that have to be updated to ensure that no marginal corrections are introduced. In this paper the standard localization criteria are presented and a technique to separate the global localization criteria in family-based criteria for damped structures is introduced. The methods are analyzed and applied to both numerical and experimental examples; a clear enhancement of the results is noticed using the family-based criteria. A simple way to qualify the stability of a localization method to noise is presented.

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.

Parameter Sensitivity in Numerical Modelling of Ice-Structure Interaction With Cohesive Element Method

2016 ◽  
Author(s):  
Dianshi Feng ◽  
Sze Dai Pang ◽  
Jin Zhang
Keyword(s):  
Element Model ◽  
Offshore Structures ◽  
Parameter Sensitivity ◽  
The Arctic ◽  
Cohesive Element ◽  
Structure Interaction ◽  
Marine Structure ◽  
Ice Loads ◽  
The Stability ◽  
Element Method

The increasing marine activities in the Arctic has resulted in a growing demand for reliable structural designs in this region. Ice loads are a major concern to the designer of a marine structure in the arctic, and are often the principal factor that governs the structural design [Palmer and Croasdale, 2013]. With the rapid advancement in computational power, numerical method is becoming a useful tool for design of offshore structures subjected to ice actions. Cohesive element method (CEM), a method which has been widely utilized to simulate fracture in various materials ranging from metals to ceramics and composites as well as bi-material systems, has been recently applied to predict ice-structure interactions. Although it shows promising future for further applications, there are also some challenging issues like high mesh dependency, large variation in cohesive properties etc., yet to be resolved. In this study, a 3D finite element model with the use of CEM was developed in LS-DYNA for simulating ice-structure interaction. The stability of the model was investigated and a parameter sensitivity analysis was carried out for a better understanding of how each material parameter affects the simulation results.

scholarly journals The Stability Analyses of the Mathematical Models of Hepatitis C Virus Infection

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Maureen Siew Fang Chong ◽  
Masitah Shahrill ◽  
Laurie Crossley ◽  
Anotida Madzvamuse
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Virus Infection ◽  
Mathematical Models ◽  
Hepatitis C Virus Infection ◽  
Stability Analyses ◽  
The Stability

scholarly journals EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON THE STABILITY OF CYLINDRICAL SHELLS

2021 ◽  
Vol 26 (4) ◽  
pp. 34-39
Author(s):  
ATTILA BAKSA ◽  
DAVID GONCZI ◽  
LASZLA PETER KISS ◽  
PETER ZOLTAN KOVACS ◽  
ZSOLT LUKACS
Keyword(s):  
Cylindrical Shells ◽  
Element Model ◽  
Tolerance Range ◽  
Axial Pressure ◽  
Geometric Imperfections ◽  
Numerical Investigations ◽  
Negative Effect ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
The Stability

The stability of thin-walled cylindrical shells under axial pressure is investigated. The results of both experiments and numerical simulations are presented. An appropriate finite element model is introduced that accounts not only for geometric imperfections but also for non-linearities. It is found that small geometrical imperfections within a given tolerance range have considerable negative effect on the buckling load compared to perfect geometry. Various post buckling shell shapes are possible, which depend on these imperfections. The experiments and simulations show a very good correlation.

Étude de la réouverture de la lagune du Havre aux Basques. I. Modélisation numérique des conditions d'écoulement

1995 ◽  
Vol 22 (1) ◽  
pp. 55-71
Author(s):  
Y. Ouellet ◽  
A. Khelifa ◽  
J.-F. Bellemare
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Element Model ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Modélisation Numérique ◽  
Tidal Flows ◽  
Dimensional Finite Element ◽  
The Stability ◽  
La Madeleine

A numerical study based on a two-dimensional finite element model has been conducted to analyze flow conditions associated with different possible designs for the reopening of Havre aux Basques lagoon, located in Îles de la Madeleine, in the middle of the Gulf of St. Lawrence. More specifically, the study has been done to better define the depth and geometry of the future channel as well as its orientation with regard to tidal flows within the inlet and the lagoon. Results obtained from the model have been compared and analyzed to put forward some recommendations about choice of a design insuring the stability of the inlet with tidal flows. Key words: numerical model, finite element, lagoon, reopening, Havre aux Basques, Îles de la Madeleine.

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