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1

The regions of divergence and flutter instability of a column subjected to beck’s generalized load taking into account an elastic support at the loaded end

Tomski L., Uzny S.

Vibrations in Physical Systems

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2012

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Vol. 25

423--428

EN

The boundary value problem concerning the free vibrations of a slender system subjected to Beck’s generalized load was formulated and solved in the work. The considered column was elastically supported by a spring with linear characteristic at the loaded end. The critical load of the system, both divergence and flutter, and the regions of presence of divergence and flutter instability were determined on the basis of the boundary problem concerning the free vibrations (the kinetic criterion of stability). Numerical calculations have been assigned to different values of the parameters of the considered system for which the follower factor, the rigidity parameter of a spring supporting column, the parameter of the translational inertia of the body mounted at the loaded end of the column are ranked.

2

Stability of Composite Rotors with Massive Discs and Follower Load

Weronko J., Kurnik W.

Machine Dynamics Problems

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2006

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Vol. 30, No. 1

113-124

EN

The paper is concerned with a new approach to the stability behaviour of a rotating composite shaft with two supports and massive disc at the end using dynamic eigenvalues and eigenform for bifurcation analysis. The shaft subjected to tip-concentrated axial follower load and discussion is focused on the influence of gyroscopic effect on the critical rotation speed and post-critical behaviour of the system. Dynamic base functions are applied in Galerkin's discretization procedure. Two mechanisms of flutter instability exhibited by the system are studied and explained for prospective applications in industrial machinery like compressors, pumps and turbines.

3

Gyroscopic Effect in the Stability Problem of a Slender Rotating Shaft with Follower Load

Kurnik W., Przybyłowicz P. M., Weronko J., Wiatr P.

Machine Dynamics Problems

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2003

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Vol. 27, No. 2

55-70

EN

The paper is concerned with stability analysis of a flexible rotating shaft supported as a cantilever beam and subjected to tip-concentrated follower load. Such systems exhibit two mechanisms of instability of flutter type, different in physical nature and, what is most important, interacting to produce complicated stability regions in the space of rotation speed and follower load. In such systems even for high-speed working conditions, the rotary inertia as well as the gyroscopic effect is usually neglected like in slender beams. However, in some regions of parameters, especially in slightly internally dissipative shafts the gyroscopic effect can considerably change the boundaries of the stability domain. Moreover, an interesting phenomenon can be observed when two pairs of eigenvalues with different speeds at the same time intersect the imaginary axis of the complex plane. This leads to bifurcation with four critical eigenvalues similar to that studied by Iooss in the Navier-Stokes equations.

4

Instability regions of a prestressed compound column subjected to a follower force

Przybylski J.

Journal of Theoretical and Applied Mechanics

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1999

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nr 1

147-162

EN

The influence of prestressing and bending rigidity distribution between rods of a non-linear column on its natural vibrations and stability is studied. The perturbation method is used for solving the problem. Regions of divergence and flutter instabilities for a column have been determined on the basis of courses of eigencurves as a function of bending rigidity ratio and prestress rate. Discontinuities of the critical force have been observed for certain values of the investigated parameters leading to instability of the column, even for small values of the external load. Although each prestress reduces the critical force, it can be applied to passive vibration control.

PL

W pracy zbadano wpływ wstępnego sprężania i asymetrii rozkładu sztywności na zginanie między prętami geometrycznie nieliniowej kolumny dwuprętowej na drgania takiego układu. Do rozwiązania zagadnienia zastosowano metodę małego parametru. Wyznaczono obszary niestateczności dywergencyjnej i fluterowej na podstawie przebiegów krzywych wartości własnych w odniesieniu do relacjimiędzy sztywnościami i stopniem sprężenia. Zaobserwowano skokowe zmiany wartości siły krytycznej dla pewnych wartości obu parametrów prowadzące do niestateczności układu przy niewielkiej sile zewnętrznej. Mimo tego, że każde wstępne sprężenie obniża wartość siły krytycznej, może być wprowadzane w celu pasywnej kontroli częstości drgań.