Jarosław Latalski

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled beam is discussed. The nonclassical effects like material anisotropy, rotary inertia and transverse shear are considered in the mathematical model of the structure. Moreover, the hub mass moment of inertia is taken into account. The differential equations of motion featuring beam bending–twist elastic coupling are derived using the Hamilton principle, and the Galerkin method is applied in order to reduce the partial differential governing equations to the ordinary differential equations. Parametric studies are conducted to evaluate beam stiffness coefficients depending on the fiber lamination angle. Next, numerical results are obtained to investigate the impact of hub to beam relative inertia on the natural frequencies of the structure. Cases of forced vibrations of the system are examined where the driving torque is considered as the sum of a constant (mean value) and a periodic component. Simulations show the importance of the hub inertia on the complete system dynamics. A shift of the resonance zones and a vibration absorption are observed.

Rational Placement of a Macro Fibre Composite Actuator in Composite Rotating Beams

In the presented research the dynamics of a thin rotating composite beam with surface bonded MFC actuator are considered. A parametric analysis aimed at finding the most efficient location of the actuator on the beam is presented. Gyroscopic effects resulting in the beams initial strain and therefore non-zero voltage in PZT are taken into account. Within the frame of the study maximising the systems response observed in vibration modes for uncoupled and coupled motions is examined. The results are compared to the case of a nonrotating beam and also to the maximum response of the beam with the actuator placed at different positions. To perform the analysis an ABAQUS finite element model of an electromechanical system under consideration is developed. The multi-layer composite beam structure is modelled by shell elements according to a layup-ply technique; the MFC actuator is modelled by 3D coupled field piezoelectric elements. Both modal analysis and frequency response spectra are performed to obtain the structural modal parameters and response amplitude, respectively. The analysis is repeated for three different orientations of the beams cross-section with respect to the plane of rotation (i.e. arbitrary assumed pitch angles); in all cases the condition constant angular speed is preserved. This work is fundamental for continuing the research for control of dynamics of rotating composite beams with active elements.

Modelling of a Rotating Active Thin-Walled Composite Beam System Subjected to High Electric Fields

An electromechanical coupled theory is used to develop the equations of motion of a rotating thin-walled composite beam with surface bonded/embedded piezoelectric transducers. The higher order constitutive relations for the piezoceramic material are used to take into account the impact of a high electric field. In the mathematical model of the hybrid structure, the non-classical effects like material anisotropy, rotary inertia and transverse shear deformation as well as an arbitrary beam pitch angle are incorporated. Moreover, the model considers the hub mass moment of inertia and a non-constant rotating speed case. This approach results in an additional equation of motion for the hub sub-system and enhances the generality of the formulation. It is shown that final equations of motion of the hub–beam system are mutually coupled and form a nonlinear system of partial differential equations. Comparing to the purely mechanical model, the proposed electromechanical one introduces additional stiffness-type couplings between individual degrees of freedom of the system.

Nonlinear Control of Flexural–Torsional Vibrations of a Rotating Thin-Walled Composite Beam

In this paper, the effectiveness of a saturation control strategy in suppressing vibration of a rotating composite thin walled beam is studied. The mathematical model of the flexible beam takes into account a shear deformation effect, a warping function, a centrifugal force and the Coriolis acceleration. To extend the generality of the proposed formulation an inertia of the hub is also considered. Adaptive capability of the beam is achieved through the implementation of the saturation control algorithm. Within the performed tests, the discussed control strategy is applied for different magnitudes of flexural–torsional vibration modes resulting from different orientations of beam laminate-reinforcing fiber’s. The obtained results prove the applied nonlinear control to be the effective method for beam vibration suppression in near-by resonance zones for all studied cases. Parametric studies considered different rotating speeds of the system. It is shown that the vibration of the beam can be suppressed to similar levels independently of the transportation motion rotating speed. However, significant differences in the width of vibration suppression zones are observed.

Dynamics and Saturation Control of Rotating Composite Beam with Embedded Nonlinear Piezoelectric Actuator

In this research we consider a saturation adaptive control strategy to suppress vibrations of a system consisting of a rotating rigid hub and a thin-walled composite blade with an embedded piezoelectric active element. The adopted mathematical model of the beam considers non-classical effects like a circumferentially asymmetric stiffness lamination scheme that result in strong mutual coupling of the bending-twisting deformations as well as a higher order piezoceramic constitutive relation. The discussed structure has been investigated for possible levels of original system simplifications starting from the fully linearised one up-to the control applied to the nonlinear structure performing the full rotation. Obtained results of numerical simulations prove the applied nonlinear saturation control to be the robust and effective method for beam vibration suppression in near-by resonance zones for a non-rotating as well as rotating structures. It is shown that vibration of the beam can be suppressed to similar levels independently of the model simplification degree presuming the condition of proper controller tuning is preserved. However, significant differences in the width of vibration suppression zones are observed for studied subcases. Moreover, the analysis of the system response sensitivity to feedback and control gains is discussed.

Synchronisation Analysis of a De-Tuned Three-Bladed Rotor

The aim of the paper is to study a synchronisation phenomenon as observed in a rotating structure consisting of three composite beams and a hub. The beams are made of eighteen carbon-epoxy prepreg material layers stacked in a specific sequence. In the performed analysis it is assumed one of the beams is de-tuned due to small misalignment of its reinforcing fibers orientation with regard to the two remaining nominal design blades. The non-classical effects like transverse shear, material anisotropy, non-uniform torsion and cross-section warping are taken into account in the mathematical model of the blades. The partial differential equations of motion of the structure are derived by the Hamilton principle; next the reduction to the ordinary differential ones is done by the Galerkin method. Finally, the equations are solved numerically and the resonance curves for the hub and the individual beams are plotted. In the performed studies two possible variants of the rotor excitation are considered: (a) driving torque expressed by a harmonic function or (b) torque given by a chaotic oscillator formula. The analysis of the synchronisation phenomenon of the hub and the blades motion is based on the study of the resonance curves and time histories in the prepared graphs. The analysis of the structure driven by chaotic oscillator revealed the existence of the strange chaotic attractor for every beam of the rotor; in the particular, nominal beams are fully synchronised, but the de-tuned one is synchronised with a small difference in amplitude.