On the use of the Hamiltonian for an evaluation of the stability of elastic systems subjected to follower forces

1981 ◽  
Vol 50 (6) ◽  
pp. 413-426 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Elastic Systems ◽  
Follower Forces ◽  
The Stability

Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid?

2000 ◽  
Vol 68 (2) ◽  
pp. 206-212 ◽  
Author(s):  
I. Elishakoff ◽  
N. Impollonia
Keyword(s):  
Critical Velocity ◽  
Entire Length ◽  
Velocity Versus ◽  
Winkler Foundation ◽  
Strengthening Effect ◽  
Pipe Conveying Fluid ◽  
Follower Forces ◽  
The Stability ◽  
Realistic Structure ◽  
Conveying Fluid

The effect of the elastic Winkler and rotatory foundations on the stability of a pipe conveying fluid is investigated in this paper. Both elastic foundations are partially attached to the pipe. It turns out that the single foundation, either translational or rotatory, which is attached to the pipe along its entire length, increases the critical velocity. Such an intuitively anticipated strengthening effect is surprisingly missing for the elastic column on Winkler foundation subjected to the so-called statically applied follower forces. Yet, partial foundation for the pipe conveying fluid is associated with a nonmonotonous dependence of the critical velocity versus the attachment ratio defined as the length of the partial foundation over the entire length of the pipe. It is concluded that such a paradoxical nonmonotonicity is shared by both the realistic structure (pipe conveying fluid) and in the “imagined system,” to use the terminology of Herrmann pertaining to the column under to follower forces.

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.

Stability of elastic systems under follower forces

AIAA Journal ◽  
1992 ◽  
Vol 30 (3) ◽  
pp. 767-771 ◽  
Author(s):  
Lien-Wen Chen ◽  
Der-Ming Ku
Keyword(s):  
Elastic Systems ◽  
Follower Forces
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