Dynamic Stability of Columns Subjected to Follower Loads: A Survey

Langthjem, Mikael A.; Sugiyama, Yoshihiko

doi:10.1006/jsvi.2000.3137

Cited by 189 publications

(88 citation statements)

References 144 publications

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“…Dynamic instability, or flutter, is a general phenomenon which commonly occurs in coupled fluid-structure systems including pipes conveying fluids and airfoils [12,33,35,67,78,92,116]. Typically, the models are finite dimensional or continuous Fig.…”

Section: Infinite-dimensional Near-reversible and Near-hamiltonian Symentioning

confidence: 99%

Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?

Kirillov¹,

Verhulst

2010

Z Angew Math Mech

100

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The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation, and related bifurcations.

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Section: Infinite-dimensional Near-reversible and Near-hamiltonian Symentioning

confidence: 99%

Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?

Kirillov¹,

Verhulst

2010

Z Angew Math Mech

100

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“…Therefore, stability analysis regarding these systems is mostly based on approximate techniques, such as finite element method, Galerkin method, etc. Extensive survey of the problem involving nonconservative forces is presented in Elishakoff (2005) and Langthjem et al (2000) where the history of analysis and controversies about the Beck's column are presented in a comprehensive manner. The dynamic analysis of cantilever beam under follower force and intermediate spring support is investigated by Lee (1995) based on the Lagrange approach solved using the assumed modes.…”

Section: Latin American Journal Of Solids and Structures 13 (2016) 30mentioning

confidence: 99%

Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations

Sohrabian

Ahmadian

Fathi

2016

Lat. Am. j. solids struct.

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This paper presents effects of shear deformation on flutter instability of cantilever beam subject to a concentrated follower force. The discrete form of equation of motion is formulated based on the Lagrange. In the presented formulation, the beam is modeled using Timoshenko beam theory, and constant shear distribution through the thickness of the beam is considered. Consistent interpolation scheme is adopted to avoid the shear locking for thin beams. Consequently, convergence of the finite element simulation is enhanced. The effect of rotary inertial term is considered in the flutter study, which has significant influence on the beam behavior as the beam thickness increases. The axial degrees of freedom are taken into account in energy expressions, to improve the accuracy of the results. Results presented for different beam geometries. The numerical results show high efficiency and good convergence characteristic. The effect of concentrated mass on the flutter instability of beam is considered and results are presented for various locations and values of concentrated masses. Furthermore, the shear effects are highlighted in this study by comparing the results obtained from the Euler-Bernoulli with those obtained from the Timoshenko beam model.

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“…The linear stability of a beam under the action of a follower force exerted at one of its extremities has been the subject of intensive research, as can be seen from the extensive review in [11]. The interest in this problem lies in its potential applications and also in the large variety of fundamental topics of mechanics involved in the solution method.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Langre

Doaré

2015

J. Mech. Mater. Struct.

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The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not depend on the length. The asymptotic regime significantly differs from that of short beams: flutter prevails for all types of follower loads, and flutter is localized at the edge of the beam. An approximate solution using matched assymptotic expansion is proposed for the case of a semi-infinite beam. Using a local criterion based on the stability of waves, the characteristics of this regime as well as its range of application can be well predicted. These results are finally discussed in relation with cases of flow-induced instabilities of slender structures.

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Dynamic Stability of Columns Subjected to Follower Loads: A Survey

Cited by 189 publications

References 144 publications

Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?

Paradoxes of dissipation‐induced destabilization or who opened Whitney's umbrella?

Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations

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