Fotios Georgiades

Vibro-impact attachments as shock absorbers

The use of vibro-impact (VI) attachments as shock absorbers is studied. By considering different configurations of primary linear oscillators with VI attachments, the capacity of these attachments to passively absorb and dissipate significant portions of shock energy applied to the primary systems is investigated. Parametric studies are performed to determine the dependence of energy dissipation by the VI attachment in terms of its parameters. Moreover, non-linear shock spectra are used to demonstrate that appropriately designed VI attachments can significantly reduce the maximum levels of vibration of primary systems over wide frequency ranges. This is in contrast to the classical linear vibration absorber, whose action is narrowband. In addition, it is shown that VI attachments can significantly reduce or even completely eliminate resonances appearing in the linear shock spectra, thus providing strong, robust, and broadband shock protection to the primary structures to which they are attached.

Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry

This paper carries out modal analysis of a nonlinear periodic structure with cyclic symme- try. The nonlinear normal mode (NNM) theory is brie°y described, and a computational algorithm for the NNM computation is presented. The results obtained on a simpli¯ed model of a bladed assembly show that this system possesses a very complicated struc- ture of NNMs, including similar and nonsimilar NNMs, nonlocalized and localized NNMs, bifurcating and internally resonant NNMs. Modal interactions that occur without neces- sarily having commensurate natural frequencies in the underlying linear system are also discussed.

Characterisation of pit geometry in cold-rolled stainless steel strip

Abstract Three-dimensional profilometry measurements of the surface roughness on industrially cold-rolled stainless steel samples are used to identify individual pits on the samples. The changes in key pit geometry parameters are extracted from these measurements. As the pits are gradually eliminated through the pass schedule, the ‘characteristic’ pit diameter, spacing and depth fall sharply, while the pit slope rises, from a value of about 15° up to 50°. The contribution of various pit sizes to the pit area is explored. A regime map is constructed for the measured pit sample statistics to indicate the effects of lubricant entrainment at the inlet to the bite or micro-plastic hydrodynamic lubrication of the pits inside the bite.

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.

Nonlinear modal analysis and energy localization in a bladed disk assembly

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.Copyright

Localization of energy in a perfectly symmetric bladed disk assembly due to nonlinearities

Although a bladed disk is typically designed to have identical blades, manufacturing tolerances, wear, and other causes may cause random deviations among the blades. The blade-to-blade discrepancies, denoted as mistuning, lead to vibratory responses mostly concentrated in small regions of the bladed-disk assembly, according to a phenomenon called localization. The resulting spatial confinement of the vibration energy causes the responses of some blades to become dangerously high and increases the amplitude of the bladed-disk assembly’s overall response. The attendant increase in stresses can lead to premature high cycle fatigue (HCF) of the blades. In this study we investigate whether vibration localization in a perfectly symmetric bladed disk assembly may occur in the presence of nonlinearity. To this end, the nonlinear normal modes (NNMs) of a simplified model of a bladed disk assembly are computed. The NNMs are then carefully examined to highlight possible vibration localization phenomena.Copyright

Passive targeted energy transfers and strong modal interactions in a thin plate with strongly nonlinear end attachments of different configurations

In this paper we examine Targeted Energy Transfers (TETs) and nonlinear modal interactions occurring in a thin cantilever plate lying on an elastic foundation with strongly nonlinear lightweight attachments of different configurations. Under shock excitation of the plate we systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena between the plate and attachments of the following configurations: a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) NES; multiple SDOF attachments attached at different points of the plate; and a single multi-degree-of-freedom (MDOF) attachment with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and location of the attachments, in order to optimize TETs from the plate to the NES. We examine in detail the underlying mechanisms influencing TETs by means of Hilbert-Huang Transforms in combination with Wavelet Transforms. These transforms enable one to systematically study the strong modal interactions between the essentially nonlinear attachments and different plate modes. The efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed.Copyright

Towards Determination of Critical Speeds of a Rotating Shaft with Eccentric Sleeves: Equations of Motion

A primary problem in the turbine industry is associated with the mitigation of bending vibration modes of high-speed rotating shafts. This is especially pertinent at speeds approaching the critical frequencies. Here, a shaft, complete with eccentric sleeves at the free ends, is designed and developed, with a view to passively control critical speeds and vibration induced bending. In this article, using the Extended Hamilton’s principle, the equations of motion (axial, torsional, in-plane and out-of-plane bending) for a rotating flexible shaft are derived; considering non-constant rotating speed, Coriolis and centrifugal forces, with the associated boundary conditions due to the eccentric sleeves and torsional springs in angular deformations of lateral vibrations in bending. The numerical dynamic analysis showed that considering the sleeves as flexible only had a small effect upon the first critical speed of the shaft. Therefore, rigid body modelling of the sleeves is sufficient to capture the essential dynamics of the system. The derived equations of motion with the associated boundary conditions show that in the case of constant rotating speed, the eccentric sleeves are coupling xy-bending with xz-bending and also torsion. Also the derived equations of motion and the associated boundary conditions in the case of non-constant rotating speed are essentially nonlinear due to inertia terms. This work is essential to the advance of linear and nonlinear dynamic analysis of the system by means of determination of normal modes and critical speeds of the shaft.

Linear Modal Analysis of L-shaped Beam Structures – Parametric Studies

Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration.

Sensitivity of Experimental Dynamic Stiffness of the Vibrator-Earth System

The dynamics of the vibrator-earth system is driven by the properties of both the vibrator and the earth. Using a model for the dynamics of this system, we determine theoretically the dynamic stiffness curves that describe the system. In order to define them we need to specify the ground force and the acceleration at the surface of the earth. In our case we use a simplified model of the vibrator to determine the ground force and then assuming that the vibrator baseplate is properly coupled to the surface of the earth (that is very close to the reality due to the hold down force) we use the acceleration of the baseplate to extract these characteristic dynamic stiffness curves of the system. Then we examine, using experimental data, the effect of location, and vibration polarity in dynamic stiffness curves of the system. The sensitivity analysis showed that at low frequencies there is no effect but at medium and high frequencies these curves are very sensitive to the variations. This work is a starting point for the determination of effective earth properties through dynamic stiffness.