Lamb wave based identification and parameter estimation of corrosion in metallic plate structure using a circular PWAS array

A circular array of Piezoelectric Wafer Active Sensor (PWAS) has been employed to detect surface damages like corrosion using lamb waves. The array consists of a number of small PWASs of 10 mm diameter and 1 mm thickness. The advantage of a circular array is its compact arrangement and large area of coverage for monitoring with small area of physical access. Growth of corrosion is monitored in a laboratory-scale set-up using the PWAS array and the nature of reflected and transmitted Lamb wave patterns due to corrosion is investigated. The wavelet time-frequency maps of the sensor signals are employed and a damage index is plotted against the damage parameters and varying frequency of the actuation signal (a windowed sine signal). The variation of wavelet coefficient for different growth of corrosion is studied. Wavelet coefficient as function of time gives an insight into the effect of corrosion in time-frequency scale. We present here a method to eliminate the time scale effect which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the corrosion with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed for varying damage sizes and the results appear promising.

Ultrasonic Lamb wave based monitoring of corrosion type of damage in plate using a circular array of piezoelectric transducers

In this paper we propose a concept and report experimental results based on a circular array of Piezoelectric Wafer Active Sensors (PWASs) for rapid localization and parametric identification of corrosion type damage in metallic plates. Implementation of this circular array of PWASs combines the use of ultrasonic Lamb wave propagation technique and an algorithm based on symmetry breaking in the signal pattern to locate and monitor the growth of a corrosion pit on a metallic plate. Wavelet time-frequency maps of the sensor signals are employed to obtain an insight regarding the effect of corrosion growth on the Lamb wave transmission in time-frequency scale. We present here a method to eliminate the time scale, which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the damage with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed from the wavelet coefficients for varying damage sizes and the results appear promising. Damage index is plotted against the damage parameters for frequency sweep of the excitation signal (a windowed sine signal). Results of corrosion damage are compared with circular holes of various sizes to demonstrate the applicability of present method to different types of damage. (C) 2011 Elsevier Ltd. All rights reserved.

Executable Analysis using Abstract Interpretation with Circular Linear Progressions

We propose a new abstract domain for static analysis of executable code. Concrete states are abstracted using circular linear progressions (CLPs). CLPs model computations using a finite word length as is seen in any real life processor. The finite abstraction allows handling overflow scenarios in a natural and straight-forward manner. Abstract transfer functions have been defined for a wide range of operations which makes this domain easily applicable for analyzing code for a wide range of ISAs. CLPs combine the scalability of interval domains with the discreteness of linear congruence domains. We also present a novel, lightweight method to track linear equality relations between static objects that is used by the analysis to improve precision. The analysis is efficient, the total space and time overhead being quadratic in the number of static objects being tracked.

Boxicity of Circular Arc Graphs

A k-dimensional box is a Cartesian product R(1)x...xR(k) where each R(i) is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least pi(alpha-1/alpha) for some alpha is an element of N(>= 2), then box(G) <= alpha (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree Delta < [n(alpha-1)/2 alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. We also demonstrate a graph having box(G) > alpha but with Delta = n (alpha-1)/2 alpha + n/2 alpha(alpha+1) + (alpha+2). For a proper circular arc graph G, we show that if Delta < [n(alpha-1)/alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) <= r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k <= 3 arcs covers the circle, then box(G) <= 3 and if G admits a circular arc representation in which no family of k <= 4 arcs covers the circle, then box(G) <= 2. We also show that both these bounds are tight.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

Stability numbers for an unsupported vertical circular excavation in c-phi soil

By using an axisymmetric lower bound finite element limit analysis formulation, the stability numbers (gamma H/C) for an unsupported vertical circular excavation in a cohesive-frictional soil have been generated. The numerical results are obtained for values of normalized excavation height (H/b) and friction angle (phi) greater than those considered previously in the literature. The results compare well with those available in literature. The stability numbers presented in this note would be beneficial from a design point of view. (C) 2011 Elsevier Ltd. All rights reserved.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Enhancement of circular differential deflection of light in an optically active medium

In this letter, we investigate the circular differential deflection of a light beam refracted at the interface of an optically active medium. We show that the difference between the angles of deviation of the two circularly polarized components of the transmitted beam is enhanced manyfold near total internal reflection, which suggests a simple way of increasing the limit of detection of chiro-optical measurements. (C) 2012 Optical Society of America

Two-dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first-order and second-order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth-order RungeKutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two-dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side-by-side. Results of these simulations were extensively compared with the previous numerical data. Copyright (C) 2011 John Wiley & Sons, Ltd.

Seismic stability of a long unsupported circular tunnel

The stability of a long unsupported circular tunnel (opening) in a cohesive frictional soil has been assessed with the inclusion of pseudo-static horizontal earthquake body forces. The analysis has been performed under plane strain conditions by using upper bound finite element limit analysis in combination with a linear optimization procedure. The results have been presented in the form of a non-dimensional stability number (gamma H-max/c); where H = tunnel cover, c refers to soil cohesion and gamma(max) is the maximum unit weight of soil mass which the tunnel can support without collapse. The results have been obtained for various values of H/D (D = diameter of the tunnel), internal friction angle (phi) of soil, and the horizontal earthquake acceleration coefficient (alpha(h)). The computations reveal that the values of the stability numbers (i) decrease quite significantly with an increase in alpha(h), and (ii) become continuously higher for greater values of H/D and phi. As expected, the failure zones around the periphery of the tunnel becomes always asymmetrical with an inclusion of horizontal seismic body forces. (c) 2012 Elsevier Ltd. All rights reserved.