Włodzimierz Kurnik

Active stabilisation of a piezoelectric fiber composite shaft subject to follower load

Abstract The paper is concerned with active stabilisation of self-excited vibration of slender rotating columns subject to tangential follower forces. Such systems exhibit flutter-type instability as a result of energy transfer from rotation and to transverse motion of the shaft. There are two reasons for the instability to occur in rotating slender shafts––rotation in the presence of internal friction in the shaft material, and the follower load. The study reveals an interesting coupled effect of these parameters on the system stability as they create a concave set in which the system remains stable, and this means that one parameter neutralises influence of the other. The paper also takes up the problem of near-critical behaviour of the system. Non-linear bifurcation analysis is carried out to predict type of the self-excitation (either soft or hard), near-critical vibration amplitude and jump phenomena. In the second part of the paper a method of active stabilisation based on making use of piezoelectric fibre composites (PFC) is presented. The composites containing active fibres made of piezoceramics constitute the state-of-the-art structural materials capable of adjusting their mechanical state according to dynamic loading conditions. Some fundamentals concerning the operation of PFCs as rotating columns are given in the paper.

Bifurcating self-excited vibrations of a horizontally rotating viscoelastic shaft

SummarySelf-excited postcritical vibrations of a rotating geometrically non-linear shaft caused by internal friction are analysed in this paper using the Hopf bifurcation theory. Stable periodic vibrations bifurcate from the non-trivial equilibrium which becomes unstable itself. Ordinary differential equations of motion are obtained by means of Galerkins method. Bifurcating periodic solution is constructed in a parametric form due to Iooss and Joseph.ÜbersichtDie von der inneren Reibung abhängigen selbsterregten Schwingungen einer drehenden geometrisch nichtlinearen Welle werden in dieser Arbeit mit Hilfe der Hopfschen Bifurkationstheorie analysiert. Die stabilen periodischen Schwingungen verzweigen sich ausgehend von der Gleichgewichtslage, die selbst instabil wird. Die Bewegungsgleichungen werden mit Hilfe der Galerkinschen Methode ausgewertet. Verzweigungslösungen werden in parametrischer Form nach Iooss und Joseph konstruiert.

THERMOACTIVE STABILIZATION OF A COMPOSITE LEIPHOLZ COLUMN

A model of the Leipholz column made of orthotropic layers is analyzed. Apart from reinforcing fibers, the layers contain thermoactive shape memory alloy fibers. A nonlinear equation of motion that takes into account moderate deflections of the column, as well as Braziers cross-section flattening effect, is examined. The effect of the martensite transformation due to external cooling and heating on the system stability expressed in terms of the critical load is investigated. The temperature change is also shown to affect the characteristics of the column nonlinear response, because it can lead to conversion of subcritical bifurcation into a supercritical one.

Stochastic stability and nonstability of a linear cylindrical shell

SummaryThe regions of almost sure stochastic stability and nonstability of a uniform elastic cylindrical shell subjected to radial and axial stochastic compressions are investigated. Both radial and axial loadings are assumed to be correlated ergodic Gaussian random processes. The stability and nonstability regions are determined as functions of intensities of the acting loadings and the external damping coefficient. The problem is solved by means of Liapunov functionals method.ÜbersichtMit der direkten Methode von Ljapunov werden Bereiche der fast gewissen Stabilität und Instabilität einer homogenen, elastischen, zylindrischen Schale untersucht. Als Belastung der Schale wird außer einer achsialen Kraft ein äußerer Druck berücksichtigt. Es wird angenommen, daß die Belastungen als korrelierte, Gaußsche Prozesse betrachtet werden können. Die untersuchten Stabilitäts- und Instabilitätsbereiche werden als Funktionen der Intensitäten der Belastungen und des Dämpfungsfaktors bestimmt.

Application of Piezoelements in a Structured Thin-Walled Shaft Material to Active Control of Stability and Vibration

The paper is concerned with damping of beam and shaft vibrations using piezoelements with external shunting circuits. Usually, distributed piezoactuators are applied to beams or plates to contract curvature occurring during transverse vibrations. Here, an alternative concept of vibration control is explored consisting in utilising additional dissipation in shunting circuits of piezoelements bonded to a beam or shaft surface. Attention is focused on a cantilever beam subject to tip-concentrated follower load (Beck’s column) and/or to kinematic excitation by clamped edge motion. Efficiency of piezodamping is studied in both stabilising the equilibrium and reduction of resonance. On the other hand, the effect of shunting is examined in case of ring-like piezotransducers controlling torsional vibrations of a shaft under harmonic excitation. A shift of resonance zone and reduction of top vibration amplitudes are shown as functions of shunting parameters. Application of piezoelements in vibration control of shafts is developed into a concept of a structural piezoactive material controlled by external voltage coupled with the current state of the shaft. Making use of smart technology combining passive composites with active fibers permanently embedded into their structure is discussed. Fundamentals of active reduction of torsional vibration of a shaft entirely made of the smart piezoceramic composite are proposed and analysed. It is proved that this method may occur advantageous both because of increased strength-to-weight properties as well as enhanced ability to damp torsional vibrations of the system.