Inflation Waves Induced by Axial Acceleration of the Aorta

1986 ◽  
Vol 108 (3) ◽  
pp. 281-288 ◽  
Author(s):  
D. Elad ◽  
A. Foux ◽  
Y. Lanir ◽  
Y. Kivity
Keyword(s):  
Fluid Velocity ◽  
Equations Of Motion ◽  
High Amplitude ◽  
Road Accidents ◽  
Time Intervals ◽  
One Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Nonlinear Viscoelastic ◽  
Axial Acceleration ◽  
Cylindrical Orthotropy

The phenomenon of high-amplitude inflation waves resulting from a sharp axial acceleration of the aorta, as may ocur in road accidents, is investigated theoretically. The aorta is modeled as an axisymmetric tapered membranic shell (tube) made of an incompressible, nonlinear viscoelastic material with cylindrical orthotropy. It is filled with an inviscid, incompressible fluid whose flow is considered as quasi-one dimensional along the tube axis. The equations of motion of the tube and of the fluid are solved numerically, by using a two-step explicit scheme, for several axial acceleration profiles. The solutions shows that an inflation wave is generated and it propagates in opposite direction to that of the acceloeration. The wall stresses, deformations and their time derivatives as well as fluid velocity and pressure are determined along the tube at different time intervals. Peak axial and circumferential stresses are high, with the latter far exceeding the former. These stresses may cause rupture of the aorta.

One- and two-dimensional travelling wave solutions in gas-fluidized beds

1996 ◽  
Vol 306 ◽  
pp. 183-221 ◽  
Author(s):  
B. J. Glasser ◽  
I. G. Kevrekidis ◽  
S. Sundaresan
Keyword(s):  
Fluidized Beds ◽  
Equations Of Motion ◽  
High Amplitude ◽  
Travelling Wave ◽  
Numerical Continuation ◽  
Model Parameters ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Wave Solutions

Making use of numerical continuation techniques as well as bifurcation theory, both one- and two-dimensional travelling wave solutions of the ensemble-averaged equations of motion for gas and particles in fluidized beds have been computed. One-dimensional travelling wave solutions having only vertical structure emerge through a Hopf bifurcation of the uniform state and two-dimensional travelling wave solutions are born out of these one-dimensional waves. Fully developed two-dimensional solutions of high amplitude are reminiscent of bubbles. It is found that the qualitative features of the bifurcation diagram are not affected by changes in model parameters or the closures. An examination of the stability of one-dimensional travelling wave solutions to two-dimensional perturbations suggests that two-dimensional solutions emerge through a mechanism which is similar to the overturning instability analysed by Batchelor & Nitsche (1991).

scholarly journals Validation of a one-dimensional model of the systemic arterial tree

2009 ◽  
Vol 297 (1) ◽  
pp. H208-H222 ◽  
Author(s):  
Philippe Reymond ◽  
Fabrice Merenda ◽  
Fabienne Perren ◽  
Daniel Rüfenacht ◽  
Nikos Stergiopulos
Keyword(s):  
Constitutive Law ◽  
Distributed Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Continuity Equations ◽  
Nonlinear Viscoelastic ◽  
Model Predictions ◽  
The One ◽  
D Model ◽  
Systemic Arterial Tree

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the “generic 1-D model” and the “average subject” of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Dynamics of Spinning Disc Parametrically Excited by Noise

1999 ◽  
Author(s):  
Narayanan Ramakrishnan ◽  
N. Sri Namachchivaya
Keyword(s):  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Averaging ◽  
Transverse Motion ◽  
Probability Density Distribution ◽  
Integral Of Motion ◽  
Parametrically Excited ◽  
One Dimensional ◽  
Small Intensity ◽  
Spinning Disc

Abstract The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

Multi-Parameter Optimization of Damped Linear Continuous Systems

1972 ◽  
Vol 94 (1) ◽  
pp. 1-7 ◽  
Author(s):  
O. B. Dale ◽  
R. Cohen
Keyword(s):  
Optimal Parameter ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
System Response ◽  
Continuous Systems ◽  
Frequency Interval ◽  
State Variables ◽  
Initial Value ◽  
Unknown Parameters ◽  
One Dimensional

A method is presented for obtaining and optimizing the frequency response of one-dimensional damped linear continuous systems. The systems considered are assumed to contain unknown constant parameters in the boundary conditions and equations of motion which the designer can vary to obtain a minimum resonant response in some selected frequency interval. The unknown parameters need not be strictly dissipative nor unconstrained. No analytic solutions, either exact or approximate, are required for the system response and only initial value numerical integrations of the state and adjoint differential equations are required to obtain the optimal parameter set. The combinations of state variables comprising the response and the response locations are arbitrary.

Signal Propagation Along Unidimensional Neuronal Networks

2005 ◽  
Vol 94 (5) ◽  
pp. 3406-3416 ◽  
Author(s):  
Ofer Feinerman ◽  
Menahem Segal ◽  
Elisha Moses
Keyword(s):  
Large Scale ◽  
Signal Transmission ◽  
Signal Propagation ◽  
High Amplitude ◽  
Adhesive Material ◽  
One Dimensional ◽  
Calcium Indicator ◽  
Scale Population ◽  
Population Burst ◽  
Linear Signal

Dissociated neurons were cultured on lines of various lengths covered with adhesive material to obtain an experimental model system of linear signal transmission. The neuronal connectivity in the linear culture is characterized, and it is demonstrated that local spiking activity is relayed by synaptic transmission along the line of neurons to develop into a large-scale population burst. Formally, this can be treated as a one-dimensional information channel. Directional propagation of both spontaneous and stimulated bursts along the line, imaged with the calcium indicator Fluo-4, revealed the existence of two different propagation velocities. Initially, a small number of neighboring neurons fire, leading to a slow, small and presumably asynchronous wave of activity. The signal then spontaneously develops to encompass much larger and further populations, and is characterized by fast propagation of high-amplitude activity, which is presumed to be synchronous. These results are well described by an existing theoretical framework for propagation based on an integrate-and-fire model.

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