Large-amplitude unsteady flow in liquid-filled elastic tubes

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

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Amplitude Incremental Method: A Novel Approach to Capture Stable and Unstable Solutions of Harmonically Excited Vibration Response of Functionally Graded Beams under Large Amplitude Motion

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0235 ◽

2019 ◽

Vol 20 (5) ◽

pp. 581-594 ◽

Cited By ~ 1

Author(s):

B. Panigrahi ◽

G. Pohit

Keyword(s):

Large Amplitude ◽

Harmonic Balance Method ◽

Functionally Graded ◽

Vibration Response ◽

Algebraic Equations ◽

Unstable Solution ◽

Linear Algebraic Equations ◽

Excited Vibration ◽

Non Linear ◽

Large Amplitude Motion

AbstractAn interesting phenomenon is observed while conducting numerical simulation of non-linear dynamic response of FGM (functionally graded material) beam having large amplitude motion under harmonic excitation. Instead of providing a frequency sweep (forward or backward), if amplitude is incremented and response frequency is searched for a particular amplitude of vibration, solution domain can be enhanced and stable as well as unstable solution can be obtained. In the present work, first non-linear differential equations of motion for large amplitude vibration of a beam, which are obtained using Timoshenko beam theory, are converted into a set of non-linear algebraic equations using harmonic balance method. Subsequently an amplitude incremental iterative technique is imposed in order to obtain steady-state solution in frequency amplitude plane. It is observed that the method not only shows very good agreement with the available research but the domain of applicability of the method is enhanced up to a considerable extent as the stable and unstable solution can be captured. Subsequently forced vibration response of FGM beams are analysed.

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The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

Zeitschrift für Naturforschung A ◽

10.1515/zna-2006-1205 ◽

2006 ◽

Vol 61 (12) ◽

pp. 641-651

Author(s):

Hilmi Demiray

Keyword(s):

Evolution Equation ◽

Wave Speed ◽

Kdv Equation ◽

Order Term ◽

Perturbation Expansion ◽

Reductive Perturbation Method ◽

Elastic Tube ◽

Inviscid Fluid ◽

Weakly Nonlinear ◽

Elastic Tubes

Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid, we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term, which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation, and it is observed that the wave speed is variable, which results from the stenosis. We study the variation of the wave speed with the distance parameter τ for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However, sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small.

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MICROWAVE SPECTRUM OF A SUPERACID AND ITS MONOHYDRATE: TUNNELING AND LARGE AMPLITUDE MOTION IN CF3SO2OH AND CF3SO2OH-H2O

Proceedings of the 74th International Symposium on Molecular Spectroscopy ◽

10.15278/isms.2019.wb07 ◽

2019 ◽

Author(s):

Anna Huff ◽

Kenneth Leopold ◽

CJ Smith ◽

Nathan Love

Keyword(s):

Large Amplitude ◽

Microwave Spectrum ◽

Large Amplitude Motion

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An Optimal Ninth Order Iterative Method for Solving Non-Linear Equations

International Journal of Psychosocial Rehabilitation ◽

10.37200/ijpr/v24i5/pr201697 ◽

2020 ◽

Vol 24 (5) ◽

pp. 325-331

Author(s):

Rajesh Kumar Palli

Keyword(s):

Iterative Method ◽

Linear Equations ◽

Non Linear ◽

Non Linear Equations

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Study on the Flow Characteristics of Shengli Oilfield Super Heavy Oil

The Open Fuels & Energy Science Journal ◽

10.2174/1876973x01710010069 ◽

2017 ◽

Vol 10 (1) ◽

pp. 69-78 ◽

Cited By ~ 1

Author(s):

Wang Shou-long ◽

Li Ai-fen ◽

Peng Rui-gang ◽

Yu Miao ◽

Fu Shuai-shi

Keyword(s):

Pressure Drop ◽

Pressure Gradient ◽

Heavy Oil ◽

Flow Characteristics ◽

Fluid Viscosity ◽

Linear Flow ◽

Start Up ◽

Non Linear ◽

Core Permeability ◽

Velocity Pressure

Objective:The rheological properties of oil severely affect the determination of percolation theory, development program, production technology and oil-gathering and transferring process, especially for super heavy oil reservoirs. This paper illustrated the basic seepage morphology of super heavy oil in micro pores based on its rheological characteristics.Methods:The non-linear flow law and start-up pressure gradient of super heavy oil under irreducible water saturation at different temperatures were performed with different permeable sand packs. Meanwhile, the empirical formulas between start-up pressure gradient, the parameters describing the velocity-pressure drop curve and the ratio of gas permeability of a core to fluid viscosity were established.Results:The results demonstrate that temperature and core permeability have significant effect on the non-linear flow characteristics of super heavy oil. The relationship between start-up pressure gradient of oil, the parameters representing the velocity-pressure drop curve and the ratio of core permeability to fluid viscosity could be described as a power function.Conclusion:Above all, the quantitative description of the seepage law of super heavy oil reservoir was proposed in this paper, and finally the empirical diagram for determining the minimum and maximum start-up pressure of heavy oil with different viscosity in different permeable formations was obtained.

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A master exceptional field theory

Journal of High Energy Physics ◽

10.1007/jhep06(2021)185 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Guillaume Bossard ◽

Axel Kleinschmidt ◽

Ergin Sezgin

Keyword(s):

Field Theory ◽

Gauge Invariance ◽

Sigma Model ◽

Linear Equations ◽

Field Theories ◽

Gauge Invariant ◽

Non Linear ◽

Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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Steady Motion of Ice Sheets

Journal of Glaciology ◽

10.3189/s0022143000010467 ◽

1980 ◽

Vol 25 (92) ◽

pp. 229-246 ◽

Cited By ~ 10

Author(s):

L. W. Morland ◽

I. R. Johnson

Keyword(s):

Differential Equation ◽

Linear Differential Equation ◽

Power Law ◽

Perturbation Expansion ◽

Ice Sheet ◽

Leading Order ◽

Plane Flow ◽

General Law ◽

Non Linear ◽

Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

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Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1964.0007 ◽

1964 ◽

Vol 277 (1368) ◽

pp. 92-106 ◽

Cited By ~ 8

Keyword(s):

Large Amplitude ◽

Critical Speed ◽

Torsional Oscillation ◽

Degree Of Freedom ◽

Non Linear ◽

Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

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