Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions

1995 ◽  
Vol 117 (4) ◽  
pp. 445-451 ◽  
Author(s):  
J. A. C. Martins ◽  
J. Guimara˜es ◽  
L. O. Faria
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Deformable Body ◽  
The Body ◽  
Dynamic Surface ◽  
Linear Elastic ◽  
Finite Dimensional ◽  
Rigid Plane ◽  
Short Time ◽  
Plane Oscillations

This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson’s ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

Surface Instabilities in Linear Orthotropic Half-Spaces With a Frictional Interface

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
M. A. Agwa ◽  
A. Pinto da Costa
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Coefficient Of Friction ◽  
Isotropic Case ◽  
Flutter Instability ◽  
The Coefficient Of Friction ◽  
Frictional Interface ◽  
Rigid Plane ◽  
Plane Oscillations ◽  
Plane Strain Case

This paper studies the friction induced vibrations that may develop in the neighborhood of steady sliding states of elastic orthotropic half-spaces compressed against a rigid plane moving tangentially with a prescribed speed. These vibrations may lead to flutter instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given. The way how the coefficient of friction varies with changes in some of the system’s parameters is investigated. It is shown that for certain combinations of material data, low coefficients of friction are found for surface flutter instability (lower than in the isotropic case).

Boundary Conditions and Craig-Bampton Substructuring Technique With Free-Free Modes

2017 ◽  
Author(s):  
Grzegorz Orzechowski ◽  
Aki M. Mikkola
Keyword(s):  
Boundary Conditions ◽  
Reference Frame ◽  
Deformable Body ◽  
Order Reduction ◽  
The Body ◽  
Model Order ◽  
Practical Applications ◽  
Static Correction ◽  
Local Reference ◽  
Deformation Modes

The floating frame of reference formulation allows for description of the kinematics of a deformable body using generalized coordinates that define the body local reference frame and deformations with respect to that frame. In practical applications, the formulation need to be used in conjunction with of a model order reduction approach. The paper investigates the usage of the model reduction through the Craig-Bampton method with the mean-axis reference frame conditions. Analysis involves static numerical examples of the beam structures, modeled using commercial packages with different boundary conditions and loads. It is shown that commonly employed orthonormalization technique dissolves the influence of the static correction modes in many assumed deformation modes of a deformable body. Consequently, a care should be taken in model validation when this popular approach for modeling flexible bodies is used.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

2015 ◽  
Vol 26 (01) ◽  
pp. 59-110 ◽  
Author(s):  
Claude Bardos ◽  
Denis Grebenkov ◽  
Anna Rozanova-Pierrat
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Order Term ◽  
Heat Content ◽  
Resistance Coefficient ◽  
Small Time ◽  
Heat Diffusion ◽  
Heat Problem ◽  
Short Time ◽  
Mathematical Justification

We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and infinite resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

Developmental stages in the Digenea

Parasitology ◽  
1964 ◽  
Vol 54 (2) ◽  
pp. 295-312 ◽  
Author(s):  
Elon E. Byrd ◽  
William P. Maples
Keyword(s):  
Body Wall ◽  
Developmental Stages ◽  
Snail Host ◽  
The Body ◽  
Body Movements ◽  
Hatching Enzyme ◽  
Apical Papilla ◽  
Short Time ◽  
Membranous Body ◽  
Egg Capsule

The naturally oviposited egg of Dasymetra conferta is fully embryonated and it hatches only after it is ingested by the snail host, Physa spp.Hatching appears to be in response to some stimulus supplied by the living snail. The stimulus causes the larva to exercise a characteristic series of body movements and to liberate a granular sustance (hatching enzyme) from the larger pair of its cephalic glands. This enzyme reacts with the vitelline fluid to create pressure within the egg capsule, and with the cementum of the operculum, so that it may be lifted away. The larva's escape from the shell, therefore, is due to a combination of pressure and body movements.The hatched larva has a membranous body wall, supporting six epidermal plates, an apical papilla, two penetration glands and a central matrix (the presumptive brood mass).It lives for about an hour within the snail and during this time there is a reorganization of the central matrix which terminates in the formation of an 8-nucleated syncytial brood mass.The miracidial ‘case’, consisting of the body wall and the epidermal plates, ultimately ruptures to liberate the brood mass. Once the brood mass is free it penetrates through the gut wall in an incredibly short time.

Isolation of myosalvarsan'a

1930 ◽  
Vol 26 (9) ◽  
pp. 942-942
Author(s):  
H. Bauer
Keyword(s):  
Maximum Amount ◽  
The Body ◽  
Drug Excretion ◽  
Clinical Observations ◽  
Short Time ◽  
Detailed Technique ◽  
Cessation Of Treatment

Abstracts. Venereology and Dermatology. Hugo Bauer (D. Z. Bd. 57, H. 4, 29), aiming to study the secretion of myosalvarsan'a, took under observation 4 syphilitics treated with injections of the drug. Excretion of myosalvarsan'a, as well as its absorption, is similar to 'neo' and sulfoxylsalvarsan'y. Most of the arsenobenzol'a introduced into the body is released within a "short time" after injection; four weeks after the cessation of treatment, the body is freed from the maximum amount of introduced As. The author believes that the clinical observations, on the basis of which it is argued that if certain intervals are observed between courses, the cumulative action of As does not occur, are completely fair. The author gives a detailed technique for determining As in selections and supplies the article with visual tables and curves of his own observations.

Determination of albumin content in blood serum based on the results of dynamic surface tension

2021 ◽  
Vol 1 (6) ◽  
pp. 68-73
Author(s):  
M. S. Tsarkova ◽  
◽  
I. V. Milaeva ◽  
S. Yu. Zaytsev ◽  
◽  
...  
Keyword(s):  
Surface Tension ◽  
Blood Serum ◽  
Objective Assessment ◽  
Dynamic Surface Tension ◽  
The Body ◽  
Maximum Pressure ◽  
Dynamic Surface ◽  
Good Convergence ◽  
Albumin Content

The blood test allows you to give an objective assessment of the state of health of animals and timely identify changes occurring in the body. To assess the content of albumins in the blood serum, the method of measuring the dynamic surface tension on the VRA-1P device, which works according to the method of maximum pressure in the bubble, was used. Based on the results of the measurements, a mathematical model was proposed, and using the regression analysis method, formulas for determining the concentration of albumins were developed, which showed good convergence with other measurement methods.

Numerical Solution of a Hydrofoil Moving Near an Interface

1996 ◽  
Vol 40 (04) ◽  
pp. 269-277
Author(s):  
G. X. Wu ◽  
T. Miloh ◽  
G. Zilman
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Body Surface ◽  
Iteration Scheme ◽  
The Body ◽  
Two Fluids ◽  
Linearized Theory

The problem of a hydrofoil moving near an interface of two fluids of different densities is analyzed. An iteration scheme is proposed which imposes the boundary conditions on the body surface and on the interface alternately. The numerical solution is obtained by using the linearized theory and a Glauert-type expansion for the vortex distribution. Results are provided for various cases with different densities and different speeds.

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