The influence of an intermediate support on the stability behaviour of cantilever beams subjected to follower forces

1990 ◽  
Vol 137 (1) ◽  
pp. 107-115 ◽  
Author(s):  
M.A. De Rosa ◽  
C. Franciosi
Keyword(s):  
Cantilever Beams ◽  
Intermediate Support ◽  
Stability Behaviour ◽  
Follower Forces ◽  
The Stability

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

Effect of Intermediate Support on Instabilities of a Cantilever With Terminal Dynamic Moment

2019 ◽  
Author(s):  
Mahmoud Abdullatif ◽  
Ranjan Mukherjee
Keyword(s):  
Negative Slope ◽  
Positive Slope ◽  
Critical Stability ◽  
Flutter Instability ◽  
Intermediate Support ◽  
Instability Modes ◽  
Stability Point ◽  
The Stability ◽  
The Moment ◽  
Dynamic Moment

Abstract The stability characteristics of a cantilever beam, with and without an intermediate support, subjected to a dynamic terminal moment, is investigated. The moment is assumed to be proportional to the slope of a point along the length of the beam. The proportionally constant, which can be positive or negative, is varied to find the critical stability point. In the absence of intermediate support, stability is lost through divergence when the dynamic moment is proportional to the positive slope, and through flutter when the dynamic moment is proportional to the negative slope. In contrast, the nature of instability switches between divergence and flutter, and between different flutter instability modes while undergoing flutter, in the presence of an intermediate support.

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.

Topological Hopf bifurcation in the plane

1983 ◽  
Vol 93 (1) ◽  
pp. 113-119
Author(s):  
Dieter Erle
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Stationary Point ◽  
Parameter Family ◽  
Stability Behaviour ◽  
Closed Orbits ◽  
The Stability ◽  
Image Position ◽  
Negative System

Classical bifurcation theorems for a 1 -parameter family of plane dynamical systemsassert the presence of closed orbits clustering at some distinguished parameter value (∈ = 0, say). Here, for any ∈, the origin is the only stationary point. The topological content of the mostly analytic hypotheses imposed is some change in the stability behaviour of the origin at ∈ = 0, roughly the passing of a kind of stability to a kind of instability. Topologically speaking, e.g. some of the conditions demanded are asymptotic stability of the origin for the negative system at ∈ > 0 and asymptotic stability of the origin for at ∈ < 0 (Hopf (8), Ruelle and Takens(11)) or ∈ = 0 (Chafee(2)).

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