Piotr M. Przybyłowicz

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.

Active Stabilization of a Rotating Shaft Transmitting Static Torque

The paper is concerned with the problem of stability of a power transmitting thin-walled shaft made of the active laminate PFC (piezoelectric fiber composite). The shaft rotates with a given operational angular velocity, and is loaded by a static torque. Such a system is known to exhibit divergence or oscillating type of instability. On the one hand presence of internal friction in the material of the shaft leads to loss of stability at a certain critical rotation speed. The static torque can be responsible for spatial deformation of the shaft axis on the other. A method preventing the system from such behavior is discussed in the paper. The method is based on application of a composite material, which contains active piezoelectric fibers. The fibers produce bending moments, and this way affect the dynamics of the entire system. Two control strategies are investigated. Results of numerical simulations are presented graphically.

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.

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.

Active Damping of Torsional Vibration in a Piezoelectric Fiber Composite Shaft

Problem of active damping of torsional vibration with the help of piezoelectric materials has been taken up since late 80s. The most popular piezoelectrics applied to control systems were piezoceramics based on lead zirconate titanate (PZT) and piezopolymers made of polyvinylidene fluoride (PVDF). Admittedly, they enjoy a special favour up to present.