Circular elastic inclusions in cylindrical shells

The problem of a circular elastic inclusion in a cylindrical shell subjected to internal pressure or thermal loading is studied. The two shallow-shell equations governing the behaviour of a cylindrical shell are transformed into a single differential equation involving a curvature parameter and a complex potential function in a non-dimensional form. In the shell region, the solution is represented by Hankel functions of first kind, whereas in the inclusion region it is represented by Bessel functions of first kind. Boundary conditions at the shell-inclusion junction are expressed in a simple form involving in-plane strains and change in curvature. The effect of such inclusion parameters as extensional rigidity, bending rigidity, and thermal expansion coefficients on the stress concentrations has been determined. The results are presented in non-dimensional form for ready use.

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed It uses information regarding Limb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage. which is most desired in a Structural Health Monitoring system. (C) 2010 Elsevier Ltd. All rights reserved.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Analysis of a thick plate with a circular hole resting on a smooth rigid bed and subjected to axisymmetric normal load

A solution for the stresses and displacements in an radially infinite thick plate having a circular hole, one face of which resting on a smooth rigid bed and the other face subjected to axisymmetric normal loading is given. The solution is obtained in terms of Fourier-Bessel series and integral for the Love's stress function. Numerical results are presented for one particular ratio of thickness of plate to the hole radius and loading. It is also shown that the Poisson's ratio has a predominant effect on certain stresses and displacements. The solution would be useful in the stress analysis of bolted joints.Eine Lösung für die Spannungen und Verschiebungen in einer radial, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, wobei eine Seite auf einer ebenen, starren Unterlage aufliegt, die andere Seite durch eine achsensymmetrische Vertikallast belastet ist, wird angegeben. Die Lösung wird in Form von Fourier-Bessel-Reihen und Integralen der Loveschen Spannungsfunktion angegeben. Numerische Ergebnisse werden für ein bestimmtes Verhältnis der Plattendicke zum Lochradius sowie zur Belastung angegeben. Es wird auch gezeigt, daß das Poisssonsche Verhältnis einen besonderen Einfluß auf bestimmte Spannungen und Verschiebungen hat. Die Lösung ist anwendbar für die Spannungsermittlung von Bolzenverbindungen.

Constructing Reeb Graphs using Cylinder Maps

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. In this video, we describe a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Arcs in the Reeb graph are computed in the second step using a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The algorithm is also able to handle non-manifold domains.

Free vibration of circular plates of arbitrary thickness

Free vibration of circular plates of arbitrary thickness is investigated using the method of initial functions. State-space approach is used to derive the governing equations of the above method. The formulation is such that theories of any desired order can be obtained by deleting higher terms in the infinite-order differential equations. Numerical results are obtained for flexural and extensional vibration of circular plates. Results are also computed using Mindlin's theory and they are in agreement with the present analysis.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter ? which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when ? is small, whereas the effect of the dissipation parameter is more pronounced when ? is comparatively large.

Edge reinforced circular elastic inclusions in cylindrical shells

The effect of having an edge reinforcement around a circular elastic inclusion in a cylindrical shell is studied. The influence of various parameters of the reinforcement such as area of cross section and moment of inertia on the stress concentrations around the inclusion is investigated. It is found that for certain inclusion parameters it is possible to get an optimum reinforcement, which gives minimum stress concentration around the inclusion. The effect of moment of inertia of the reinforcement of SCF is found to be negligible. The results are plotted in a non-dimensional form and a comparison with flat plate results is made which show the curvature effect. In the limiting case of a rigid reinforcement the results tend to those of a rigid circular inclusion. Results are also presented for different values of μe the ratio of extensional rigidity of shell to that of the inclusion.

Conformations of synthetic alamethicin fragments. Evidence for 310 helical folding from 270-MHz hydrogen-1 nuclear magnetic resonance and circular dichroism studies

IH NMR studies at 270 MHz on the synthetic alamethicin fragments Z-Aib-Pro-Aib-Ala-Aib-Ala-OMe (1-6), Boc-Gln-Aib-Val-Aib-Gly-Leu-Aib-OMe (7-1 3), Boc-Leu-Aib-Pro-Val-Aib-OMe (1 2-16), and Boc-Gly-Leu- Aib-Pro-Val-Aib-OMe (1 1-16) have been carried out in CDC13 and (CD3)2S0. The intramolecularly hydrogen bonded amide hydrogens in these peptides have been delineated by using solvent titration experiments and temperature coefficientsof NH chemical shifts in (CD3)+30. All the peptides adopt highly folded structures, characterized by intramolecular 4 - 1 hydrogen bonds. The 1-6 fragment adopts a 310 helical conformation with four hydrogen bonds, in agreement with earlier studies (Rao, Ch. P., Nagaraj, R., Rao, C. N. R., & Balaram, P. (1980) Biochemistry 19, 425-4311. The 7-13

Peptide models for b-turns.A circular dichroism study

The circular dichroism spectra of four 0-turn model peptides, Z-Aib-Pro-Aib-Pro- OMe (l), Piv-Pro-Aib-NHMe (2), Piv-Pro-D-Ala-NHMe (3) and Piv-Pro-Val-NHMe (4) have been examined under a wide range of solvent conditions, using methanol, hexafluoroisopropanol and cyclohexane. Type I and Type I1 0-turns have been observed for peptides 1 and 2 respectively, in the solid state, while the Pro-D-Ala sequence adopts a Type I1 Sturn in a related peptide crystal structure. A class C spectrum is observed for 1 in various solvents, suggesting a variant of a Type I(II1) structure. The Type I1 f3-turn is characterized by a CD spectrum having two positive CD bands at - 230 nm and - 202 nm, a feature observed in Piv-Pro- D-Ala-NHMe in cyclohexane and methanol and for Piv-Pro-Aib-NHMe in methanol. Peptide 2 exhibits solvent dependent CD spectra, which may be rationalized by considering Type 11, I11 and V reverse turn structures. Piv-Pro- Val-NHMe adopts nonaturn structures in polar solvents, but exhibits a class B spectrum in cyclohexane suggesting a population of Type I &turns.

Cystine peptides. Disulfide conformations in fourteen membered loops investigated by Raman spectroscopy and circular dichroism

NHCH3 (X = Gly 1, Ala 2, Aib 3, Leu 4 and D-Ala 5), have been investigated by Raman and circular dichroism (CD) spectroscopy. Solid state Raman spectra are consistent with β-turn conformations in all five peptides. These peptides exhibit similar conformations of the disulfide segment in the solid state with a characteristic disulfide stretching frequency at 519 ± 3 cm-1, indicative of a trans-gauche-gauche arrangement about the Cα—Cβ—S—S—Cβ—Cα bonds. The results correlate well with the solid state conformations determined by X-ray diffraction for peptides 3 and 4. CD studies in chloroform and dimethylsulfoxide establish solvent dependent conformational changes for peptides 1, 3 and 5. Disulfide chirality has been derived using the quadrant rule. CD results together with previously reported nuclear magnetic resonance (n.m.r.) data suggest a conformational coupling between the peptide backbone and the disulfide segment

Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Wire-cylinder corona discharge with the wire at positive potential studies of iron oxides

A wire-cylinder corona discharge was studied in nitrogen and dry air in crossed electric and magnetic fields for values of magnetic field ranging from 0 to 3000 G with the wire at positive potential. In the absence of a magnetic field pre-onset streamers and pulses were observed in nitrogen. In both nitrogen and dry air breakdown streamers were observed just before spark breakdown of the gap. Furthermore, experiments in dry air at atmospheric pressure in an electric field indicate regular pre-onset streamers appearing at time intervals of 19.5 µs. The appearance of regular pre-onset streamers suggests that it is not possible for negative ions to form a sheath close to the anode as postulated by Hermstein (1960) for the formation of steady or glow corona in a point-plane gap.