D. W. Barclay

Impulse propagation in liquid filled distensible tubes: Theory and experiment for intermediate to long wavelengths

SummaryA theory of wave propagation in liquid filled distensible tubes, which extends the region of validity of the linear long wavelength theory commonly employed in haemodynamics, is presented and tested against experiments on water filled latex tubes. The theory which is linear and involves but a single free parameter provides excellent agreement with the impulse experiments.

Cylindrical impact waves in inhomogeneous viscoelastic media

SummaryA detailed study is presented of cylindrical shear waves in inhomogeneous Maxwellian viscoelastic materials whose parameters depend continuously on a single radial coordinate. A formal asymptotic technique is employed to investigate various impact problems. Rigorous arguments are then used to show that the formal technique gives results that are asymptotic to the exact solution even when boundaries or interfaces are present. Simple termination in the Karal-Keller series is shown to be associated with the Baecklund transformation method.ZusammenfassungEine detailierte Studie über zylindrische Scherwellen in inhomogenen Maxwellschen, viskoelastischen Materialien, deren Parameter nur von einer Radialkoordinate abhängen, wird präsentiert. Eine formale asymptotische Methode zur Untersuchung der verschiedenen Stoßprobleme wird angewendet. Strenge Beweise werden angegeben, um zu zeigen, daß die formale Methode Ergebnisse liefert, die asymptotisch zur exakten Lösung sind, wenn Ränder oder Grenzflächen vorhanden sind. Es wird gezeigt, daß einfaches Abbrechen der Karal-Keller Folgen, mit der Bäcklund Transformationsmethode assoziiert ist.

Waves in fluid filled tubes: Theory and experiment

SummaryA viscoelastic shell theory model for transient pressure perturbations in fluid filled tubes is presented and tested against experiments involving water filled latex tubes. The agreement between theory and experiment is good.

Wave propagation and reflection in liquid filled distensible tube systems exhibiting dissipation and dispersion

SummaryIn a previous paper the present authors developed a model describing wave propagation in liquid filled distensible tubes and tested it against impulse experiments involving water filled latex rubber tubes. This model incorporates both dissipative and dispersive mechanism which are absent from the commonly employed linear long wave-length (LLW) theory of haemodynamics. This higher order theory is here employed to study propagation of an impulse in a semi infinite tube, reflection of an impulse from the distal end of a finite length tube, and reflection and transmission of impulses impinging on a function connecting dissimilar liquid filled tubes. Both open and closed type reflections are treated and numerical results presented graphically. To the best of our knowledge this is the first time that such a higher order theory has been employed to treat reflection and transmission of waves in tube systems.

Wave propagation from a cylindrical cavity

SummaryHere we study impact-initiated disturbances propagating from a cylindrical cavity in orthotropic cylindrically anisotropic inhomogeneous elastic materials. Employing a transform technique we ascertain conditions on the various parameters of the medium which, when satisfied, enable us to express the solutions for impact problems in terms of modified Bessel functions. From these we generate asymptotic wavefront expansions and exact closed-form solutions. A formal technique for directly generating such expansions is also employed to solve a variety of problems. Comparisons of results obtained by the two methods are included and an appendix contains a rigorous verification of the leading term in the formal expansion.ZusammenfassungDie durch Stoß hervorgerufenen Störungen ausgehend von einem zylindrischen Hohlraum in orthotropen, zylindrisch anisotropen, inhomogenen elastischen Materialien werden untersucht. Mittels einer Transformationsmethode werden Bedingungen für die verschiedenen Parameter des Mediums bestimmt, die, wenn sie erfüllt sind, die Lösungen für das Stoßproblem in Termen modifizierter Bessel-Funktionen auszudrücken ermöglichen. Damit erhält man asymptotische Wellenfrontentwicklungen und exakte, geschlossene Lösungen. Eine formale Methode zur direkten Bestimmung solcher Entwicklungen wird zur Lösung einer Vielzahl von Problemen verwendet. Ein Vergleich der Ergebnisse der zwei Methoden ist angegeben und im Anhang ist ein genauer Beweis des Hauptterms in der formalen Entwicklung enthalten.

Reflection in liquid filled tube systems: Modelling the effects of mismatched tube segments

SummaryHere we employ an experimentally tested theory of wave propagation in liquid filled distensible tubes to study the interaction of periodic pressure waves with a finite segment of tubing whose characteristic impedance differs from those of the adjoining tubes. Such a tube system occurs when surgical bypass techniques are employed in the arterial system. In this case the source of the pressure pulse (the heart) is periodic and reflections from the insert could reinforce subsequent pulses arriving from the heart causing abnormally high pressures in the adjoining artery. This paper sheds some light on this phenomenon.

A note on the isochromatic lines for a nonuniformly loaded circular cavity

SummaryIsochromatic curves are calculated for the stress field round a nonuniformly loaded circular cavity in an elastic plate.

Propagation and reflection of waves in finite length liquid-filled distensible shells

SummaryEmploying a previously established theory for wave propagation in liquid-filled distensible tubes [1] we analyse the propagation and subsequent reflection of a transient pulse from the distal end of a finite length tube. Conditions pertaining to pulse generation at the proximal end of the tube are specified so as to approximate the conditions of experiments carried out on water-filled latex tubes [1]. Laplace transforms are employed and numerical results presented graphically.

Isochromatic curves for a dynamically loaded elastic plate

SummaryIsochromatic curve patterns are calculated for the dynamic stress field in a semi-infinite thin elastic plate whose edge is subject to a point load.

Isochromatic lines for spatially nonuniform dynamic loading of a circular cavity

SummaryDiagrams of the developing isochromatic curve patterns associated with the dynamic stress field arising when a circular cavity is subjected to a spatially nonuniform dynamic load are computed. These diagrams show for the first time the detailed wave fronts and zones of stress for this technically interesting problem. Since isochromatic lines correspond to the fringe patterns of photoelasticity, the results presented here suggest the possibility of direct experimental confirmation of the theory upon which the computations are based.