Wave propagation in a thin-walled liquid-filled initially stressed tube

1984 ◽  
Vol 141 ◽  
pp. 289-308 ◽  
Author(s):  
G. D. C. Kuiken
Keyword(s):  
Blood Pressure ◽  
Wave Propagation ◽  
Dispersion Equation ◽  
Newtonian Fluid ◽  
Initial Value Problem ◽  
Wave Mode ◽  
Initial Value ◽  
Thin Walled ◽  
Speed Of Propagation ◽  
Infinite Tube

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.

An initial value problem in the theory of nonlinear wave propagation

1980 ◽  
Vol 4 (4) ◽  
pp. 781-789
Author(s):  
M.N. Oğuztörel[doti] ◽  
E.S. Şuhubi ◽  
M. Teymur
Keyword(s):  
Wave Propagation ◽  
Nonlinear Wave ◽  
Initial Value Problem ◽  
Nonlinear Wave Propagation ◽  
Initial Value

Dynamic Instability in Ice-Lifting From a Flat Road Surface Through Penetration With a Sharp Blade

1982 ◽  
Vol 49 (1) ◽  
pp. 187-190 ◽  
Author(s):  
N. C. Huang
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Initial Value Problem ◽  
Initial Velocity ◽  
Flat Surface ◽  
Dynamic Instability ◽  
Inertia Force ◽  
Initial Value ◽  
Impulsive Load ◽  
Horizontal Thrust

This paper is concerned with the problem of dynamic instability during ice-lifting from a flat surface through penetration of the interface by means of a sharp blade. The blade is subjected to a horizontal impulsive load and a constant horizontal thrust, both applied suddenly and simultaneously. The principle of the balance of energy is used to analyze the deformation of the ice associated with the crack propagation along the interface. In our formulation, the effect of wave propagation in the ice is neglected. However, the inertia force due to the acceleration of the blade is included. The motion of the blade is investigated by the numerical solution of a complex, nonlinear, initial value problem. It is found that under a given horizontal thrust, if the initial velocity of the blade is sufficiently small, the motion of the blade may stop. However, if the initial velocity of the blade is sufficiently large, the motion of the blade is always forward and the crack can propagate indefinitely along the interface.

Invariant Imbedding Applied to Eigenvalue Problems in Mechanics

1965 ◽  
Vol 32 (1) ◽  
pp. 47-50 ◽  
Author(s):  
E. M. Shoemaker
Keyword(s):  
Wave Propagation ◽  
Eigenvalue Problem ◽  
Initial Value Problem ◽  
Present Method ◽  
Eigenvalue Problems ◽  
Transport Theory ◽  
Formal Method ◽  
Point Boundary ◽  
Invariant Imbedding ◽  
Initial Value

A formal method is presented for obtaining eigenvalues of ordinary differential equations associated with problems of buckling and vibration. The method utilizes the idea of invariant imbedding which has previously been applied to two point boundary value problems in transport theory and wave propagation. The present method reduces the eigenvalue problem to an initial value problem for a matrix of Riccati equations. The numerical solution of such formulations has proved to be generally more efficient than known methods.

Wave propagation in a stratified shear flow

1975 ◽  
Vol 71 (1) ◽  
pp. 89-104 ◽  
Author(s):  
R. J. Hartman
Keyword(s):  
Wave Propagation ◽  
Shear Flow ◽  
Wave Packet ◽  
Initial Value Problem ◽  
Two Dimensional ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Initial Value ◽  
Stratified Shear Flow ◽  
The Mean

The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J > ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J > ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J [gsim ] ¼ conclusions of an earlier treatment by Booker & Bretherton.

Asymptotic Speed of Propagation for Fisher-Type Degenerate Reaction-Diffusion-Convection Equations

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Luisa Malaguti ◽  
Stefano Ruggerini
Keyword(s):  
Initial Value Problem ◽  
Reaction Diffusion ◽  
Initial Condition ◽  
Initial Value ◽  
Convection Equation ◽  
All Solutions ◽  
Asymptotic Speed ◽  
Speed Of Propagation ◽  
Diffusion Convection

AbstractThe paper deals with the initial value problem for the degenerate reaction-diffusion-convection equationuwhere h is continuous, m > 1, and f is of Fisher-type. By means of comparison type techniques, we prove that the equilibrium u ≡ 1 is an attractor for all solutions with a continuous, bounded, non-negative initial condition u

Sideband growth in nonlinear Landau wave-particle interaction

1972 ◽  
Vol 7 (3) ◽  
pp. 385-402 ◽  
Author(s):  
A. L. Brinca
Keyword(s):  
Wave Propagation ◽  
Initial Value Problem ◽  
Large Amplitude ◽  
Particle Interaction ◽  
Electron Velocity ◽  
Large Magnitude ◽  
Initial Value ◽  
Electron Velocity Distribution ◽  
Wave Particle Interaction ◽  
Vlf Emissions

The distortion of the electron velocity distribution caused by a large amplitude Landau wave is determined analytically for the initial-value problem. The resulting stability of electrostatic perturbations impressed on the evolving plasma is studied. Narrow sidebands of the applied frequency experience consecutive growths of large magnitude during the early stages of the nonlinear wave-particle interaction. The significance of the derived results to both wave propagation experiments and triggered VLF emissions in the magnetosphere is discussed.

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