Influence of End Supports on the Stability of Nonconservative Elastic Systems

1974 ◽  
Vol 41 (1) ◽  
pp. 313-315 ◽  
Author(s):  
C. Sundararajan
Keyword(s):  
Elastic Systems ◽  
The Stability

On the Stability of Elastic Systems Subjected to Nonconservative Forces

1964 ◽  
Vol 31 (3) ◽  
pp. 435-440 ◽  
Author(s):  
G. Herrmann ◽  
R. W. Bungay
Keyword(s):  
Critical Loads ◽  
Kinetic Method ◽  
Euler Method ◽  
Parameter Instability ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Nonconservative Loading ◽  
The Stability ◽  
Two Degree Of Freedom ◽  
Increasing Load

Free motions of a linear elastic, nondissipative, two-degree-of-freedom system, subjected to a static nonconservative loading, are analyzed with the aim of studying the connection between the two instability mechanisms (termed divergence and flutter by analogy to aeroelastic phenomena) known to be possible for such systems. An independent parameter is introduced to reflect the ratio of the conservative and nonconservative components of the loading. Depending on the value of this parameter, instability is found to occur for compressive loadings by divergence (static buckling), flutter, or by both (at different loads) with multiple stable and unstable ranges of the load. In the latter case either type of instability may be the first to occur with increasing load. For a range of the parameter, divergence (only) is found to occur for tensile loads. Regardless of the non-conservativeness of the system, the critical loads for divergence can always be determined by the (static) Euler method. The critical loads for flutter (occurring only in nonconservative systems) can be determined, of course, by the kinetic method alone.

A New Method for Predicting the Critical Taylor Number in Rotating Cylindrical Flows

1987 ◽  
Vol 54 (3) ◽  
pp. 713-719 ◽  
Author(s):  
J. O. Cruickshank
Keyword(s):  
Dynamic Stability ◽  
Critical Stress ◽  
Stress Condition ◽  
Flow Instability ◽  
Fluid System ◽  
Fluid Systems ◽  
Concentric Cylinders ◽  
Elastic Systems ◽  
Subsequent Motion ◽  
The Stability

A method for determining the boundaries of dynamic stability of a fluid system, as distinct from the prediction of the subsequent motion, is presented. The method is based on well-known approaches to the problem of instability in elastic systems. The extension of these methods to fluid systems, specifically, to the stability of flow between concentric cylinders, confirms that it may be possible in some cases to determine the boundaries of stability of fluid systems without recourse to an Orr-Sommerfeld type treatment. The results also suggest that the concept of apparent (virtual) viscosity may have implications for fluid stability outside the current realm of turbulence modelling. Finally, it is also shown that flow instability may be preceded by the onset of a critical stress condition in analogy with elastic systems.

scholarly journals RESTABILIZATION OF THE POSTCRITICAL EQUILIBRIUM OF ELASTIC SYSTEMS

2019 ◽  
Vol 15 (1) ◽  
pp. 98-109
Author(s):  
Gaik Manuylov ◽  
Sergey Kosytsyn ◽  
Maxim Begichev
Keyword(s):  
Bifurcation Diagram ◽  
Elastic System ◽  
Critical Force ◽  
Load Parameter ◽  
First Eigenvalue ◽  
Bifurcation Points ◽  
The First Eigenvalue ◽  
Elastic Systems ◽  
Hesse Matrix ◽  
The Stability

The application of the Appel-Vozlinsky theorem on the stability or instability conditions for bifurcation points of conservative elastic systems with a symmetric bifurcation diagram to evaluate restabilization possibility of structures under loads substantially larger than the first critical force. It is shown that restabilization is possible if the first eigenvalue of the Hesse matrix is a continuous alternating function of the load parameter, and the remaining eigenvalues are sign-definite quantities. The examples of the systems with restabilization are given: a high Mises girder and an elastic system composed of compressible rods.

scholarly journals On the stability of non-conservative elastic systems under mixed perturbations

2009 ◽  
Vol 13 (3) ◽  
pp. 347-367 ◽  
Author(s):  
Noël Challamel ◽  
François Nicot ◽  
Jean Lerbet ◽  
Félix Darve
Keyword(s):  
Elastic Systems ◽  
The Stability

Some Observations on Nonconservative Problems of Elastic Stability

1970 ◽  
Vol 37 (3) ◽  
pp. 671-676 ◽  
Author(s):  
C. Oran
Keyword(s):  
Elastic System ◽  
Elastic Stability ◽  
Stability Behavior ◽  
Elastic Systems ◽  
Concentrated Masses ◽  
The Stability ◽  
The Masses ◽  
Special Case ◽  
Infinitesimal Mass

With reference to undamped elastic systems subjected to nonconservative forces, the possibility of a transition from stability to divergence through infinitely large values of the frequency is considered. Examined in detail is the special case of a cantilever column with two concentrated masses and subjected to a follower end force. It is shown that either flutter or divergence may first set in, depending on the relative magnitudes and locations of the masses. The results obtained by letting one of the masses tend to zero are not necessarily consistent with those obtained directly by setting that mass equal to zero; alternately, it may be stated that an additional infinitesimal mass may lead to drastic changes in the stability behavior of a given elastic system subjected to nonconservative forces.

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