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.

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.

On the Static Stability Analysis of Viscoelastic Perfect Columns

1985 ◽  
Vol 9 (3) ◽  
pp. 157-164
Author(s):  
W. Szyszkowski ◽  
P.G. Glockner
Keyword(s):  
Stability Analysis ◽  
Static Analysis ◽  
Element Model ◽  
Static Stability ◽  
Model Material ◽  
Zero Eigenvalue ◽  
Equilibrium Configurations ◽  
Static Approach ◽  
Elastic Column ◽  
New Interpretation

In this article the direct static equilibrium approach for stability analysis is used to study the behaviour of a perfect column made of a linear three-element model material and subjected to a concentric load. The study confirms that such a traditional static analysis admits only one non-zero eigenvalue, namely the load a the instant of application, referred to as the Euler load, PE, for the corresponding elastic column. A new interpretation of adjacent equilibrium configurations for viscoelastic structures is introduced which permits an ‘exact’ static analysis of the problem. The results from this analysis agree, in part, with those obtained from a general dynamic stability analysts. They help to clear up some misinterpretations resulting from the application of the static approach and show that time, being inherently an asymmetric parameter, generates effects typical of asymmetric influences and decreases the critical load of the structure.

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.

Stability of Isolators at Large Horizontal Displacements

1997 ◽  
Vol 13 (3) ◽  
pp. 415-430 ◽  
Author(s):  
Maura Imbimbo ◽  
James M. Kelly
Keyword(s):  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Closed Form Expression ◽  
Elastic Analysis ◽  
Form Expression ◽  
Elastomeric Bearings ◽  
Post Buckling ◽  
Link Model ◽  
The Stability ◽  
Horizontal Displacements

Elastomeric bearings used as seismic isolators are susceptible to a buckling type of instability similar to that of structural columns. The buckling load and buckling behaviour can be determined from an elastic analysis of the isolator modelled as a continuous composite column with bending and shear flexibility; this analysis cannot be used, however, to assess the post-buckling behaviour or the stability of the isolator at large horizontal displacements. By using a two-spring rigid link model that considers large angles without using linear approximations, it is possible to predict the post-buckling behaviour of an isolator. Using the simple closed form expression, this paper will model three aspects of post-buckled isolator behaviour: the dependence of horizontal stiffness on vertical load, the stability at large horizontal displacements, and the increase of horizontal displacement with respect to axial load and vertical displacement.

scholarly journals On the equilibrium bifurcation of axially deformable holonomic systems: solution of a long-standing enigma

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210327
Author(s):  
M. Fraldi ◽  
S. Palumbo ◽  
A. Cutolo ◽  
A. R. Carotenuto ◽  
F. Guarracino
Keyword(s):  
Applied Sciences ◽  
A Priori ◽  
Biological Tissues ◽  
Constitutive Law ◽  
Natural Systems ◽  
Simply Supported ◽  
Classical Stability ◽  
Post Buckling ◽  
The Stability ◽  
Physical Phenomena

The stability of equilibrium is a fundamental topic in mechanics and applied sciences. Apart from its central role in most engineering fields, it also arises in many natural systems at any scale, from folding/unfolding processes of macromolecules and growth-induced wrinkling in biological tissues to meteorology and celestial mechanics. As such, a few key models represent essential benchmarks in order to gain significant insights into more complex physical phenomena. Among these models, a cornerstone is represented by a structure made of two straight axially deformable bars, connected by an elastic hinge and simply supported at the ends, which are capable of buckling under a compressive axial force. This classical example has been proposed and analysed in some depth by Feodosyev but the attention is here focused on an apparently paradoxical result given by this model, i.e. the existence of a lower bound for the axial-to-flexural stiffness ratio in order for the bifurcation to take place. This enigma is solved theoretically by showing that, differently from other classical stability problems, constitutive and geometric nonlinearities cannot be a priori disconnected and an ideal linearized axial constitutive law cannot be employed in this case. The theory is validated with an experiment, and post-buckling and energy extrema of the proposed solution are discussed as well, highlighting possible snap-back and snap-through phenomena. Finally, the results are extended to the complementary case of tensile buckling.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals High-Speed Video Analysis of the Process Stability in Plasma Spraying

2021 ◽  
Author(s):  
K. Bobzin ◽  
M. Öte ◽  
M. A. Knoch ◽  
I. Alkhasli ◽  
H. Heinemann
Keyword(s):  
Plasma Spraying ◽  
High Speed ◽  
Plasma Jet ◽  
Plasma Jets ◽  
Time Dependent ◽  
Acquisition Time ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Dependent Signal ◽  
The Stability

AbstractIn plasma spraying, instabilities and fluctuations of the plasma jet have a significant influence on the particle in-flight temperatures and velocities, thus affecting the coating properties. This work introduces a new method to analyze the stability of plasma jets using high-speed videography. An approach is presented, which digitally examines the images to determine the size of the plasma jet core. By correlating this jet size with the acquisition time, a time-dependent signal of the plasma jet size is generated. In order to evaluate the stability of the plasma jet, this signal is analyzed by calculating its coefficient of variation cv. The method is validated by measuring the known difference in stability between a single-cathode and a cascaded multi-cathode plasma generator. For this purpose, a design of experiment, covering a variety of parameters, is conducted. To identify the cause of the plasma jet fluctuations, the frequency spectra are obtained and subsequently interpreted by means of the fast Fourier transformation. To quantify the significance of the fluctuations on the particle in-flight properties, a new single numerical parameter is introduced. This parameter is based on the fraction of the time-dependent signal of the plasma jet in the relevant frequency range.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

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