2 edition of Nonlinear wave propagation in viscoelastic tubes found in the catalog.
Nonlinear wave propagation in viscoelastic tubes
|Statement||by Y. Kivity and R. Collins.|
additional physics is required such as wavenumber dispersion, tube-wall viscoelasticity and fluid viscosity (see (13)). As well, phenomena such as elastic jump formation and propagation, the onset of a collapse (14), or wave-wave interactions will require a nonlinear theory; for example, (15, 16, 4, 5, 17). PDF | In the present work, the propagation of weakly non-linear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid | Find, read and cite all the research you.
Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of N AVIER and POISSON, through an astounding application of conjoined. Wave propagation and attenuation Measures of damping Nonlinear materials Summary 4 Conceptual structure of linear viscoelasticity Introduction Spectra in linear viscoelasticity Approximate interrelations Conceptual organization Summary 5 Viscoelastic stress and deformation analysis Introduction.
Nonlinear guided waves are promising candidates for interrogating long waveguide-like structures as they conveniently combine high sensitivity to peculiar structural conditions (defects, quasi-static loads, instability conditions), typical of nonlinear parameters, with large inspection ranges, characteristic of wave propagation in confined media. In this study the growth and decay of one-dimensional acceleration waves in nonlinear viscoelastic solids are considered. The conditions governing the growth and decay, including the concept of a critical acceleration level derived by Coleman and Gurtin, are discussed .
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Nonlinear wave propagation in viscoelastic tubes: Application to aortic rupture Article (PDF Available) in Journal of Biomechanics 7(1) February with 41 Reads How we measure 'reads'. Printed in Great Britain NONLINEAR WAVE PROPAGATION IN VISCOELASTIC TUBES: APPLICATION TO AORTIC RUPTURE* Y.
KIVITYt and R. COLLINSI University of California, Los Angeles, California, U.S.A. Abstract-Recent statistical surveys into the causes of automobile fatalities have shown that traumatic rupture of the aorta followed by immediate exsanguination is responsible Cited by: Nonlinear wave propagation in viscoelastic tubes the thoracic aorta towards the aortic arch, correspond- ing to the type of decelerations measured by Hanson () in which a series of anesthetized beagle dogs was exposed to head-first impact (-G,) over a range of 5- 60G.
Summary The present work considers one dimensional wave propagation in an infinitely long, straight and homogeneous nonlinear viscoelastic tube filled with an incompressible, inviscid fluid.
In order to include the geometric dispersion in the analysis, the tube wall inertia effects are added to the pressure-area by: Abstract Using the reductive perturbation method, wave propagation in fluid-filled nonlinear viscoelastic thin tubes is investigated in the long wave approximation.
For different scales of the relaxation constant τ the Korteweg-de Vries (KdV), Burgers and Korteweg-de Vries-Burgers (KdVB) equations are by: 2. Viscoelasticity affects the propagation of waves in a rather significant manner. Time-harmonic waves in an unbounded medium are subjected to dispersion and attenuation due to the viscoelastic constitutive behavior.
The chapter also discusses the problem of transient nonlinear wave propagation. Nonlinear Wave Propagation in Viscoelastic Tubes: Application to Aortic Rupture Blunt impact to the thorax often results in traumatic rupture of the aorta, leading to immediate exsanguination.
Using the reductive perturbation technique, and assuming the weakness of dissipative effects, the amplitude modulation of weakly nonlinear waves is examined. Small amplitude, axially symmetric waves in a thin-walled viscoelastic tube containing a viscous compressible fluid are considered.
Previous authors have found two modes of propagation for such waves but have studied them only in the low frequency, long wavelength limit. The dispersion and attenuation of nonlinear viscoelastic waves mainly depend on the effective nonlinearity and the high frequency relaxation time θ 2.
An “effective influence distance/time” is defined to characterize the wave propagation range where θ 2 dominates the impact relaxation process. Finite‐amplitude wave propagation in a viscoelastic fluid has been investigated with a perturbation approach using multiple time scales.
A generalized Burgers' equation (GBE) for planar and nonplanar (i.e., cylindrical and spherical) waves has been developed for a continuum, simple fluid representation of Coleman and Noll.
Simultaneous chemical reactions are coupled in the analysis by. removed the corresponding term in the proposed viscoelastic model. Conversely the nonlinear term in _ 2 seems to play an important role in the wall dynam-ics.
Reference  used this nonlinear term to study the wave propagation in nonlinear viscoelastic tubes, and the theoretical basis of the approach is in .
We computed the unsteady blood. ISBN: OCLC Number: Description: pages: illustrations ; 24 cm. Contents: Mathematical models and waves in linear viscoelasticity / D.
Graffi --Viscoelastic plane waves / M. Hayes --Properties of transverse and longitudinal harmonic waves / S. Zahorski --Transient linear and weakly non-linear viscoelastic waves / L. Brun & A. Molinari --Waves in non-linear.
In the present work, by employing the nonlinear equations of a viscoelastic thick tube filled with an incompressible inviscid fluid, the propagation of weakly nonlinear waves is investigated.
Considering the physiological conditions under which the large blood vessels function, in the analysis, the tube is assumed to be subjected to a uniform inner pressure P 0 i and a stretch ratio λ z in the. In the present work, by employing the nonlinear equations of an isotropic viscoelastic material the inner pressure–inner radius relation of a thick tube is obtained.
Then, by using this pressure–displacement relation, the propagation of weakly nonlinear waves in a thick walled tube filled with an inviscid fluid is examined. The study of non-linear wave propagation in liquid-filled visco-elastic tubes is often motivated by its application to the arterial blood flow.
It is known from both static and dynamic measurements (BergelMilnor ) that the walls of the large blood vessels exhibit non-linear. PRESSURE WAVE PROPAGATION IN LIQUID-FILLED TUBES p(t) R 2 R 1 Y t Fig. Diagram of the arterial tree model as a tube with a terminal element Y t curves should be based on more detailed.
In essence, the arteries have variable radius along the axis of the tube. present work, treating the arteries as a prestressed and linearly tapered thin elastic tube, and using the long-wave approximation we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method .
A system of nonlinear equations for describing the perturbations of the pressure and radius in fluid flow through a viscoelastic tube is derived. A differential relation between the pressure and the radius of a viscoelastic tube through which fluid flows is obtained.
The validation of the model shows its ability to retrieve low amplitude seismic ground motion. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content).This book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption.The propagation of ﬁnite amplitude waves in ﬂuid-ﬁlled elastic or visco-elastic tubes has been examined, for instance, by Rudinger , Anliker et al.
 and Tait and Moodie  by using the method of characteristics, in studying the shock formation. On the other hand, the propagation .