Acoustic propagation in 3-D, rectangular ducts with flexible walls

This article is posted here with the permission of the publishers, INCE/USA. Personal use of the material is permitted,; however, permission to reprint or republish any part of this article must be obtained from the publisher.24th National Conference on Noise Control Engineering 2010 (Noise-Con 10) Held Jointly with the 159th Meeting of the Acoustical Society of America. Baltimore, MD, USA, 19-21 April, 2010. INCE Conference Proceedings, 3: 1960-1968, Apr 2010. New York, NY, USA.In this article some analytic expressions for acoustic propagation in 3-D ducts of rectangular cross-section and with flexible walls are explored. Consideration is first given to the propagation of sound in an unlined 3-D duct formed by three rigid walls and closed by a thin elastic plate. An exact closed form expression for the fluid-structure coupled waves is presented. The effect of incorporating internal structures, such as a porous lining, into the duct is also discussed. Such configurations are directly relevant to the heating, ventilation and airconditioning industry

Blockade of current through single calcium channels by trivalent lanthanide cations. Effect of ionic radius on the rates of ion entry and exit.

Currents flowing through single dihydropyridine-sensitive Ca2+ channels were recorded from cell-attached patches on C2 myotubes. In the presence of dihydropyridine agonist to prolong the duration of single-channel openings, adding micromolar concentrations of lanthanum (La), cerium (Ce), neodymium (Nd), gadolinium (Gd), dysprosium (Dy), or ytterbium (Yb) to patch electrodes containing 110 mM BaCl2 caused the unitary Ba2+ currents to fluctuate between fully open and shut states. The kinetics of channel blockade followed the predictions of a simple open channel block model in which the fluctuations of the single-channel current arose from the entry and exit of blocking ions from the pore. Entry rates for all the lanthanides tested were relatively insensitive to membrane potential, however, exit rates depended strongly on membrane potential increasing approximately e-fold per 23 mV with hyperpolarization. Individual lanthanide ions differed in both the absolute rates of ion entry and exit: entry rates decreased as cationic radius decreased; exit rates also decreased with cationic radius during the first part of the lanthanide series but then showed little change during the latter part of the series. Overall, the results support the idea that smaller ions enter the channel more slowly, presumably because they dehydrate more slowly; smaller ions also bind more tightly to a site within the channel pore, but lanthanide residence time within the channel approaches a maximum for the smaller cations with radii less than or equal to that of Ca2+

A brief historical perspective of the Wiener-Hopf technique

It is a little over 75 years since two of the most important mathematicians of the 20th century collaborated on finding the exact solution of a particular equation with semi-infinite convolution type integral operator. The elegance and analytical sophistication of the method, now called the Wiener–Hopf technique, impress all who use it. Its applicability to almost all branches of engineering, mathematical physics and applied mathematics is borne out by the many thousands of papers published on the subject since its conception. The Wiener–Hopf technique remains an extremely important tool for modern scientists, and the areas of application continue to broaden. This special issue of the Journal of Engineering Mathematics is dedicated to the work of Wiener and Hopf, and includes a number of articles which demonstrate the relevance of the technique to a representative range of model problems

Scattering of flexural waves by a semi-infinite crack in an elastic plate carrying an electric current

Copyright @ 2011 Sage Publications LtdSmart structures are components used in engineering applications that are capable of sensing or reacting to their environment in a predictable and desired manner. In addition to carrying mechanical loads, smart structures may alleviate vibration, reduce acoustic noise, change their mechanical properties as required or monitor their own condition. With the last point in mind, this article examines the scattering of flexural waves by a semi-infinite crack in a non-ferrous thin plate that is subjected to a constant current aligned in the direction of the crack edge. The aim is to investigate whether the current can be used to detect or inhibit the onset of crack growth. The model problem is amenable to an exact solution via the Wiener–Hopf technique, which enables an explicit analysis of the bending (and twisting) moment intensity factors at the crack tip, and also the diffracted field. The latter contains an edge wave component, and its amplitude is determined explicitly in terms of the current and angle of incidence of the forcing flexural wave. It is further observed that the edge wave phase speed exhibits a dual dependence on frequency and current, resulting in two distinct asymptotic behaviours

The utility of the nitric oxide electrochemical sensor in biomedical research

In recent years World Precision Instruments Inc. (WPI) produced for commercial use a selective and sensitive electrochemical sensor for the detection of the important biological free radical nitric oxide (NO). Though many kinds of NO sensors are now commercially available WPI offers a range of sensors of variable size and applicability for the detection of NO in vivo and in in vitro biomedical samples. This article overviews the working characteristics of the sensors and their utility for biomedical research

Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides

Copyright 2013 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in the Journal of the Acoustical Society of America, 134(3), 1939 - 1949 and may be found at http://scitation.aip.org/content/asa/journal/jasa/134/3/10.1121/1.4817891.The scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides is investigated. The flange is assumed to be rigid on one side and soft on the other; this enables a solution to be formulated using mode-matching. It is shown that both the choice of the edge conditions imposed on the plates at the junction and the choice of incident forcing significantly affect the transmission of energy along the duct. In particular, the edge conditions crucially affect the transmission of structure-borne vibration but have little effect on fluid-borne noise. Given the singular nature of the velocity field at the flange tip, particular attention is paid to the validity of the mode-matching method. It is demonstrated that the velocity field can be accurately reconstructed by incorporating the Lanczos filter into the truncated modal expansions. The mode-matching method is thus confirmed as an viable tool for this class of problem.The Higher Education Commission, Pakista

Edge waves and resonance on elastic structures: An overview

Copyright @ 2011 SAGE PublicationsOver 50 years have elapsed since the first experimental observations of dynamic edge phenomena on elastic structures, yet the topic remains a diverse and vibrant source of research activity. This article provides a focused history and overview of such phenomena with a particular emphasis on structures such as strips, rods, plates and shells. Within this context, some of the recent research highlights are discussed and the contents of this special issue of Mathematics and Mechanics of Solids on dynamical edge phenomena are introduced

An orthogonality condition for a class of problems with high order boundary conditions: Applications in sound/structure interaction

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version: Lawrie, J.B. & Abrahams, I.D. (1999) “An orthogonality condition for a class of problems with high order boundary conditions; applications in sound/structure interaction.” Q. Jl. Mech. Appl. Math., 52(2), 161-181. is available online at: http://qjmam.oxfordjournals.org/cgi/content/abstract/52/2/161There are numerous interesting physical problems, in the fields of elasticity, acoustics and electromagnetism etc., involving the propagation of waves in ducts or pipes. Often the problems consist of pipes or ducts with abrupt changes of material properties or geometry. For example, in car silencer design, where there is a sudden change in cross-sectional area, or when the bounding wall is lagged. As the wavenumber spectrum in such problems is usually discrete, the wave-field is representable by a superposition of travelling or evanescent wave modes in each region of constant duct properties. The solution to the reflection or transmission of waves in ducts is therefore most frequently obtained by mode-matching across the interface at the discontinuities in duct properties. This is easy to do if the eigenfunctions in each region form a complete orthogonal set of basis functions; therefore, orthogonality relations allow the eigenfunction coefficients to be determined by solving a simple system of linear algebraic equations. The objective of this paper is to examine a class of problems in which the boundary conditions at the duct walls are not of Dirichlet, Neumann or of impedance type, but involve second or higher derivatives of the dependent variable. Such wall conditions are found in models of fluid/structural interaction, for example membrane or plate boundaries, and in electromagnetic wave propagation. In these models the eigenfunctions are not orthogonal, and also extra edge conditions, imposed at the points of discontinuity, must be included when mode matching. This article presents a new orthogonality relation, involving eigenfunctions and their derivatives, for the general class of problems involving a scalar wave equation and high-order boundary conditions. It also discusses the procedure for incorporating the necessary edge conditions. Via two specific examples from structural acoustics, both of which have exact solutions obtainable by other techniques, it is shown that the orthogonality relation allows mode matching to follow through in the same manner as for simpler boundary conditions. That is, it yields coupled algebraic systems for the eigenfunction expansions which are easily solvable, and by which means more complicated cases, such as that illustrated in figure 1, are tractable

Comments on a class of orthogonality relations relevant to fluid-structure interaction

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Comment on "Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous"

In a recent Physical Review Letter [1] Valanju Walser and Valanju (VWV) called into question the basis of work on the so called negative index media (NIM). See for example [2,3]. The key point at issue is, `what is the group velocity of a wave in NIM?'Comment: Comment on Phys. Rev. Lett., v. 88, 187401 (2002