Analytical approximations for the modal acoustic impedances of simply supported, rectangular plates.

Coupling of the in vacuo modes of a fluid-loaded, vibrating structure by the resulting acoustic field, while known to be negligible for sufficiently light fluids, is still only partially understood. A particularly useful structural geometry for the study of this problem is the simply supported, rectangular flat plate, since it exhibits all the relevant physical features while still admitting an analytical description of the modes. Here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number: the modal acoustic impedances. Closed-form solutions for these impedances do not exist and, while their numerical evaluation is possible, it greatly increases the computational cost of solving the coupled system of modal equations. There is thus a need for accurate analytical approximations. In this work, such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions. It is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations. Previous approximations [Davies, J. Sound Vib. 15(1), 107-126 (1971)] are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components, but (in general) erroneous expressions for imaginary parts.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Feasibility of damage detection using vibration data in a population of cylinders

The feasibility of vibration data to identify damage in a population of cylindrical shells is assessed. Vibration data from a population of cylinders were measured and modal analysis was employed to obtain natural frequencies and mode shapes. The mode shapes were transformed into the Coordinate Modal Assurance Criterion (COMAC). The natural frequencies and the COMAC before and after damage for a population of structures show that modal analysis is a viable route to damage identification in a population of nominally identical cylinders. Modal energies, which are defined as the integrals of the real and imaginary components of the frequency response functions over various frequency ranges, were extracted and transformed into the Coordinate Modal Energy Assurance Criterion (COMEAC). The COMEAC before and after damage show that using modal energies is a viable approach to damage identification in a population of cylinders.

Complex wavelets and shift invariance

Recently we have developed a new form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2 m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. In this paper we analyse why the new transform can be designed to be shift invariant, and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this.

Density of photon states in dye-doped chiral nematic liquid crystal cells in the presence of losses and gain

We calculate the density of photon states (DOS) of the normal modes in dye-doped chiral nematic liquid crystal (LC) cells in the presence of various loss mechanisms. Losses and gain are incorporated into the transmission characteristics through the introduction of a small imaginary part in the dielectric constant perpendicular and along the director, for which we assume no frequency dispersion. Theoretical results are presented on the DOS in the region of the photonic band gap for a range of values of the loss coefficient and different values of the optical anisotropy. The obtained values of the DOS at the photonic band gap edges predict a reversal of the dominant modes in the structure. Our results are found to be in good agreement with the experimentally obtained excitation thresholds in chiral nematic LC lasers. The behavior of the DOS is also discussed for amplifying LC cells providing additional insight to the lasing mechanism of these structures. © 2012 American Physical Society.

Density of photon states in dye-doped chiral nematic liquid crystal cells in the presence of losses and gain.

We calculate the density of photon states (DOS) of the normal modes in dye-doped chiral nematic liquid crystal (LC) cells in the presence of various loss mechanisms. Losses and gain are incorporated into the transmission characteristics through the introduction of a small imaginary part in the dielectric constant perpendicular and along the director, for which we assume no frequency dispersion. Theoretical results are presented on the DOS in the region of the photonic band gap for a range of values of the loss coefficient and different values of the optical anisotropy. The obtained values of the DOS at the photonic band gap edges predict a reversal of the dominant modes in the structure. Our results are found to be in good agreement with the experimentally obtained excitation thresholds in chiral nematic LC lasers. The behavior of the DOS is also discussed for amplifying LC cells providing additional insight to the lasing mechanism of these structures.

Spin glass behaviour and spin-dependent scattering in la 0.7Ca 0.3Mn 0.9Cr 0.1O 3 perovskites

The magnetic, electrical and thermal transport properties of the perovskite La 0.7Ca 0.3Mn 0.9Cr 0.1O 3 have been investigated by measuring dc magnetization, ac susceptibility, the magnetoresistance and thermal conductivity in the temperature range of 5-300K. The spin glass behaviour with a spin freezing temperature of 70 K has been well confirmed for this compound, which demonstrates the coexistence and competition between ferromagnetic and antiferromagnetic clusters by the introduction of Cr. Colossal magnetoresistance has been observed over the temperature range investigated. The introduction of Cr causes the "double-bump" feature in electrical resistivity ρ(T). Anomalies on the susceptibility and the thermal conductivity associated with the double-bumps in ρ(T) are observed simultaneously. The imaginary part of ac susceptibility shows a sharp peak at the temperature of insulating-metallic transition where the first resistivity bump was observed, but it is a deep-set valley near the temperature where the second bump in ρ(T) emerges. The thermal conductivity shows an increase below the temperature of the insulating-metallic transition, but the phonon scattering is enhanced accompanying the appearance of the second peak of double-bumps in ρ(T). We relate those observed in magnetic and transport properties of La 0.7Ca 0.3Mn 0.9Cr 0.1O 3 to the spin-dependent scattering. The results reveal that the spin-phonon interaction may be of more significance than the electron (charge)-phonon interaction in the mixed perovskite system. © 2005 Chinese Physical Society and IOP Publishing Ltd.

Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.