Friction Damping of Circular Motion and Its Implications to Vibration Control

1991 ◽  
Vol 113 (2) ◽  
pp. 225-229 ◽  
Author(s):  
J. H. Griffin ◽  
C.-H. Menq
Keyword(s):  
Friction Force ◽  
Extreme Case ◽  
Circular Motion ◽  
Circular Path ◽  
Two Dimensional ◽  
Friction Contact ◽  
Constrained System ◽  
Peak Response ◽  
One Dimensional ◽  
Straight Line

When vibrating bodies are mutually constrained through friction contact they may move with respect to each other and dissipate energy at the interface. If the relative motion of the contacting surfaces follows a straight line the motion is said to be one-dimensional. This case has been examined extensively in the literature. More generally the point of contact can follow a path which is not a straight line. For the case of a periodic response the path will form a closed loop. In this paper we investigate the simplest, yet most extreme case of two dimensional motion—when the contacting point moves in a circular path. It is found that an exact solution can be derived for the problem of a frictionally constrained system when it is subjected to a circular excitation. The solution is used to determine the characteristics of the system’s response and they are compared with those for one-dimensional motion. In the case of one-dimensional motion if the contacting surfaces are compliant they will stick for at least a portion of each cycle. This is not the case for circular motion as it is found that the interface is either always stuck for small motions or always slipping if the excitation is above a certain level. This result suggests that the slip/stick transition which occurs during every cycle for the one-dimensional case may not be as important for the more general two-dimensional friction contact problem. Friction is often a major source of energy dissipation in vibrating machinery. As a result, the friction contact is sometimes used to reduce the peak response of the system by designing the contacting parts so as to have an optimum friction constraint. In order to investigate this effect expressions are derived for the peak amplitude as a function of the friction force, for the friction force that will minimize peak response, and for the amplitude of the peak response under optimum friction conditions. The results for circular motion are compared with those for straight line motion in order to assess the importance of two-dimensional effects.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

scholarly journals The Linear Equation for 2D Graphs

2020 ◽  
Vol 5 (6) ◽  
pp. 1448-1450
Author(s):  
Rumani Dey
Keyword(s):  
Linear Equation ◽  
Two Dimensional ◽  
One Dimensional ◽  
Circular Pattern ◽  
Symmetrical Pattern ◽  
Straight Line

What is y=mx+c? What is one dimensional? If a thing like fish/bird while in motion in water/air cannot turn left, right and backward. It can only move forward in a medium or fly in air. When I try to determine its motion, I see it as one dimensional. It is not necessary that the bird/fish is moving in a straight line. It is the sheer concentration of the medium the fish /bird is traversing in. So, the behavior of a one dimensional motion maybe a function of the medium with a concentration/penetration quotient of the medium based on the weight of the fish/bird which penetrates the medium and the effect of gravity on it. We can depict a one dimensional motion as, One Dimensional motion=f(weight)* f(penetration quotient)*f(Force exerted by the fish/bird while it is penetrating the medium) What is one dimensional coordinate? We can say that it is a vector (V) which moves in any direction but not necessarily a straight line . If “x” is a one dimensional coordinate value, it is very difficult to find the value of “x” . If suppose the path traversed by “x ” is not a definite symmetrical pattern but an ambiguous pattern like below: Fig 1 Then we do not have a numerical value for “x”. It is not measurable through a scale. We cannot find the value of “x”. In this case the only way “x” can be measured is through a straight line if “x” is moving in one direction only. A question arises whether time is moving in a circular pattern or in a straight line .We measure it as a distance/displacement and we have deemed such a scale of measurement as one dimensional. But I want to measure the quantity the fish/bird had travelled in one minute. We might get some value by defining the area it had traversed in one minute which is a two dimensional quantity.

Reflection from Curved Mirrors in a Plane

2019 ◽  
Vol 7 (1) ◽  
pp. 46-54 ◽  
Author(s):  
Л. Жихарев ◽  
L. Zhikharev
Keyword(s):  
Dimensional Space ◽  
Spherical Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
Straight Line ◽  
The Family ◽  
Dimensional Object ◽  
Three Dimensional Space

Reflection from a certain mirror is one of the main types of transformations in geometry. On a plane a mirror represents a straight line. When reflecting, we obtain an object, each point of which is symmetric with respect to this straight line. In this paper have been considered examples of reflection from a circle – a general case of a straight line, if the latter is defined through a circle of infinite radius. While analyzing a simple reflection and generalization of this process to the cases of such curvature of the mirror, an interesting phenomenon was found – an increase in the reflection dimension by one, that is, under reflection of a one-dimensional object from the circle, a two-dimensional curve is obtained. Thus, under reflection of a point from the circle was obtained the family of Pascal's snails. The main cases, related to reflection from a circular mirror the simplest two-dimensional objects – a segment and a circle at their various arrangement, were also considered. In these examples, the reflections are two-dimensional objects – areas of bizarre shape, bounded by sections of curves – Pascal snails. The most interesting is the reflection of two-dimensional objects on a plane, because the reflection is too informative to fit in the appropriate space. To represent the models of obtained reflections, it was proposed to move into three-dimensional space, and also developed a general algorithm allowing obtain the object reflection from the curved mirror in the space of any dimension. Threedimensional models of the reflections obtained by this algorithm have been presented. This paper reveals the prospects for further research related to transition to three-dimensional space and reflection of objects from a spherical surface (possibility to obtain four-dimensional and five-dimensional reflections), as well as studies of reflections from geometric curves in the plane, and more complex surfaces in space.

Continuation of potential fields between arbitrary surfaces

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 787-795 ◽  
Author(s):  
R. O. Hansen ◽  
Y. Miyazaki
Keyword(s):  
Volcanic Rocks ◽  
Potential Fields ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Aeromagnetic Data ◽  
Line Segments ◽  
One Dimensional ◽  
Straight Line ◽  
The One ◽  
Topographic Relief

An equivalent source algorithm is described for continuing either one‐ or two‐dimensional potential fields between arbitrary surfaces. In the two‐dimensional case, the dipole surface is approximated as a set of plane faces with constant moments over each face. In the one‐dimensional case, the plane faces of the dipole surface reduce to straight line segments. Application of the algorithm to model and field examples of aeromagnetic data shows the method to be effective and accurate even when the terrain has strong topographic relief and is composed of highly magnetic volcanic rocks.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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