On reducing uncertainty on the Elliptical Plane modal identification method

The Elliptical Plane has been recently introduced as a modal identification method that uses an alternative plot of the receptance. The method uses the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produces quite accurate results, especially when compared to the well-known method of the inverse. When represented in the Elliptical Plane, the shape of the receptance is elliptical near resonant frequencies. The modal damping factor can be determined from the angle of the ellipse’s major axis with the horizontal axis, whereas the real and imaginary parts of the modal constants can be determined from numerical curve-fitting (as in the method of the circle - Nyquist plot). However, the lack of points that can be used near the resonance (due to limitations in the frequency resolution, and effects from other modes near each resonance) and the fact that measurements are polluted by noise, bring uncertainty to the numerical curve-fitting. This paper aims at providing the first steps on the improvement of the quality of the modal identification of the receptance in the Elliptical Plane. The method and results are discussed with a multiple degree-of-freedom numerical example

On reducing uncertainty on the Elliptical Plane modal identification method

The Elliptical Plane has been recently introduced as a modal identification method that uses an alternative plot of the receptance. The method uses the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produces quite accurate results, especially when compared to the well-known method of the inverse. When represented in the Elliptical Plane, the shape of the receptance is elliptical near resonant frequencies. The modal damping factor can be determined from the angle of the ellipse’s major axis with the horizontal axis, whereas the real and imaginary parts of the modal constants can be determined from numerical curve-fitting (as in the method of the circle - Nyquist plot). However, the lack of points that can be used near the resonance (due to limitations in the frequency resolution, and effects from other modes near each resonance) and the fact that measurements are polluted by noise, bring uncertainty to the numerical curve-fitting. This paper aims at providing the first steps on the improvement of the quality of the modal identification of the receptance in the Elliptical Plane. The method and results are discussed with a multiple degree-of-freedom numerical example

Analysis of the Response of Modal Parameters to Damage in CFRP Laminates Using a Novel Modal Identification Method

Nowadays, composite materials are widely used in several industries, e.g. the aeronautical, automotive, and marine, due to their excellent properties, such as stiffness and strength to weight ratios and high resistance to corrosion. However, they are prone to develop Barely Visible Impact Damage (BVID) from low to medium energy impacts (i.e. 1 – 10 m/s and 11 – 30 m/s respectively) that are reported to occur during both service and maintenance, such as bird strike; hailstones and tool drops. Therefore, Structural Health Monitoring (SHM) techniques have been developed to allow identifying damage at an early stage, in an attempt to avoid catastrophic consequences. Vibration measurement was conducted on healthy and damaged Carbon Fibre Reinforced Polymers (CFRPs) specimens. Damage is introduced to the specimen through a static indentation and the work done by the hemispherical indenter measured. This test was mainly for the purpose of damage introduction in the test samples. In this work, the effects of damage on the individual mode were studied to understand the response pattern of the modal parameters. It is intended that the current study will inform the development of a new damage identification method based on the variations between healthy and damaged specimen’s dynamic results. A new modal identification method (“Elliptical Plane”) that uses an alternative plot of the receptance has been developed in this work. The Elliptical Plane method used the energy dissipated per cycle of vibration as a starting point, to identify modal constants from Frequency Response Functions (FRFs). In comparison with the method of inverse, this new method produces accurate results, for systems that are lightly damped with its modes well-spaced. The sine of the phase of the receptance is plotted against the amplitude of the receptance, through which damping was calculated from the slope of a linear fit to the resulting plot. The results show that, there are other relevant properties of the plot that were not yet delve into by researchers. The shape of the plot is elliptical, near the resonant frequencies, whereby both parts of the modal constants (real and imaginary) can be determined from numerical curve-fitting. The method offers a new perspective on the way the receptance may be represented, in the Elliptical Plane, which may bring valuable insights for other researchers in the field. The novel method is discussed through both numerical and experimental examples. It is a simple method and easy to use. Interestingly, as the energy level increases, the percentage changes in both the modal frequency and damping increases. The linear equations reveal that there is a correlation between the increase in energy and the percentage variation in modal frequency and damping, especially from a threshold energy level determined to be between 15J and 20J for the analysed cases. Finally, modal identification is conducted on the healthy and damaged specimens, and the results were analysed with BETAlab software and the Elliptical Modal identification method. It was observed that the Elliptical Modal identification method provides some interesting results. For instance, a comparison between the modal damping from the ellipse and BETAlab methods revealed that, the level of reduction in the modal damping from the ellipse method is higher than that of the BETAlab. This behaviour offers a promising future in the area of damage identification in structures

A Bayesian approach to strong lensing modelling of galaxy clusters

In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC) sampler ('Bayesys'), allowing us to avoid local minima in the likelihood functions. To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos. We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations. We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ~1-5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre. The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius. Finally, we describe how to rank models quantitatively using the Bayesian evidence. We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way. Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology. The implementation of the MCMC sampler used in this paper has been done within the framework of the Lenstool software package, which is publicly available.Comment: Accepted to "Gravitational Lensing" Focus Issue of the New Journal of Physics (invited), 35 pages, 11 figures at reduced resolutio

Experimental and analytical investigation of dynamic characteristics of extension-twist-coupled composite tubular spars

The results from a study aimed at improving the dynamic and aerodynamic characteristics of composite rotor blades through the use of extension-twist coupling are presented. A set of extension-twist-coupled composite spars was manufactured with four plies of graphite-epoxy cloth prepreg. These spars were noncircular in cross-section design and were therefore subject to warping deformations. Three different cross-sectional geometries were developed: D-shape, square, and flattened ellipse. Three spars of each type were fabricated to assess the degree of repeatability in the manufacturing process of extension-twist-coupled structures. Results from free-free vibration tests of the spars were compared with results from normal modes and frequency analyses of companion shell-finite-element models. Five global modes were identified within the frequency range from 0 to 2000 Hz for each spar. The experimental results for only one D-shape spar could be determined, however, and agreed within 13.8 percent of the analytical results. Frequencies corresponding to the five global modes for the three square spars agreed within 9.5, 11.6, and 8.5 percent of the respective analytical results and for the three elliptical spars agreed within 4.9, 7.7, and 9.6 percent of the respective analytical results

Elliptic supersonic jet morphology manipulation using sharp-tipped lobes

Elliptic nozzle geometry is attractive for mixing enhancement of supersonic jets. However, jet dynamics, such as flapping, gives rise to high-intensity tonal sound. We experimentally manipulate the supersonic elliptic jet morphology by using two sharp-tipped lobes. The lobes are placed on either end of the minor axis in an elliptic nozzle. The design Mach number and the aspect ratio of the elliptic nozzle and the lobed nozzle are 2.0 and 1.65. The supersonic jet is exhausted into ambient at almost perfectly expanded conditions. Time-resolved schlieren imaging, longitudinal and cross-sectional planar laser Mie-scattering imaging, planar Particle Image Velocimetry, and near-field microphone measurements are performed to assess the fluidic behavior of the two nozzles. Dynamic Mode and Proper Orthogonal Decomposition (DMD and POD) analysis are carried out on the schlieren and the Mie-scattering images. Mixing characteristics are extracted from the Mie-scattering images through the image processing routines. The flapping elliptic jet consists of two dominant DMD modes, while the lobed nozzle has only one dominant mode, and the flapping is suppressed. Microphone measurements show the associated noise reduction. The jet column bifurcates in the lobed nozzle enabling a larger surface contact area with the ambient fluid and higher mixing rates in the near-field of the nozzle exit. The jet width growth rate of the two-lobed nozzle is about twice as that of the elliptic jet in the near-field, and there is a 40\% reduction in the potential core length. Particle Image Velocimetry (PIV) contours substantiate the results.Comment: 19 pages, 16 figures. Revised version submitted to Physics of Fluids for peer review. URL of the Video files (Fig. 6 & Fig. 14) are given in the text files (see in '/anc/*.txt'

On the Fundamental Plane of the Galactic Globular Cluster System

The globular clusters (GC) of our Galaxy have been found to lie close to a plane in the log(R_e), log(sigma), SB_e space, on the continuation of the Fundamental Plane (FP) known to characterize the properties of early-type galaxies. We reexamine the issue on a sample of 48 GCs selected in terms of homogeneity criteria for the photometric data available from the literature and perform a model-independent analysis of surface brightness profiles (SBP) and distance moduli, estimating error bars and studying selection effects with non-parametric statistical tests. We determine the coefficients of the FP and their error bars. The scatter from the FP relation is likely to be intrinsic, i.e. not due to measurement errors only. We find that in the standard FP coordinates our sample occupies a slim, axisymmetric region of parameter space, suggesting that the scaling relation might be around a Fundamental Line, rather than a plane, confirming a result noted earlier. This is likely to be the origin of the difficulties in the fit by a plane mentioned in previous investigations. Such FL relation would imply a pure photometric scaling law, which might be tested on wider samples and on extra-galactic GC systems. We find a correlation of the residuals from the FP relation with the central slope of the SBP. No other correlations are found. Finally, we reconstruct the distribution of the values of the quantity log(K_V/(M/L)) (virial coefficient divided by the mass-to-light ratio) through kernel density estimation and find evidence for bimodality, which suggests that the galactic GC system may be composed of at least two dynamically different populations. Yet, these populations do not reflect the standard dichotomy between disk and halo clusters. (abridged).Comment: 11 pages, 4 figures, accepted for publication in A&A, no boldface tex

A Rigorous Free-form Lens Model of Abell 2744 to Meet the Hubble Frontier Fields Challenge

Hubble Frontier Fields (HFF) imaging of the most powerful lensing clusters provides access to the most magnified distant galaxies. The challenge is to construct lens models capable of describing these complex massive, merging clusters so that individual lensed systems can be reliably identified and their intrinsic properties accurately derived. We apply the free-form lensing method (WSLAP+) to A2744, providing a model independent map of the cluster mass, magnification, and geometric distance estimates to multiply-lensed sources. We solve simultaneously for a smooth cluster component on a pixel grid, together with local deflections by the cluster member galaxies. Combining model prediction with photometric redshift measurements, we correct and complete several systems recently claimed, and identify 4 new systems - totalling 65 images of 21 systems spanning a redshift range of 1.4<z<9.8. The reconstructed mass shows small enhancements in the directions where significant amounts of hot plasma can be seen in X-ray. We compare photometric redshifts with "geometric redshifts", finding a high level of self-consistency. We find excellent agreement between predicted and observed fluxes - with a best-fit slope of 0.999+-0.013 and an RMS of ~0.25 mag, demonstrating that our magnification correction of the lensed background galaxies is very reliable. Intriguingly, few multiply-lensed galaxies are detected beyond z~7.0, despite the high magnification and the limiting redshift of z~11.5 permitted by the HFF filters. With the additional HFF clusters we can better examine the plausibility of any pronounced high-z deficit, with potentially important implications for the reionization epoch and the nature of dark matter.Comment: Accepted for publication in ApJ with newly identified lensed images in complete HFF dat

Multicolour-metallicity Relations from Globular Clusters in NGC 4486 (M87)

We present Gemini griz photometry for 521 globular cluster (GC) candidates in a 5.5 x 5.5 arcmin field centered 3.8 arcmin to the south and 0.9 arcmin to the west of the center of the giant elliptical galaxy NGC 4486. All these objects have previously published (C-T1) photometry. We also present new (C-T1) photometry for 338 globulars, within 1.7 arcmin in galactocentric radius, which have (g-z) colors in the photometric system adopted by the Virgo Cluster Survey of the Advanced Camera for Surveys of the Hubble Space Telescope. These photometric data are used to define a self-consistent multicolor grid (avoiding polynomial fits) and preliminary calibrated in terms of two chemical abundance scales. The resulting multicolor color-chemical abundance relations are used to test GC chemical abundance distributions. This is accomplished by modelling the ten GC color histograms that can be defined in terms of the Cgriz bands. Our results suggest that the best fit to the GC observed color histograms is consistent with a genuinely bimodal chemical abundance distribution NGC(Z). On the other side, each (blue and red) GC subpopulation follows a distinct color-color relation.Comment: 12 pages, 21 figures, 8 tables. Accepted to be published in MNRA