Two-dimensional motion of a rolling non-circular cylinder on a flat horizontal surface

2018 ◽  
Vol 96 (6) ◽  
pp. 627-632
Author(s):  
Amir Aghamohammadi ◽  
Mohammad Khorrami
Keyword(s):  
Circular Cylinder ◽  
Energy Conservation ◽  
Cross Section ◽  
Equilibrium Configuration ◽  
Focal Point ◽  
Center Of Mass ◽  
Horizontal Surface ◽  
Two Dimensional ◽  
Small Oscillations ◽  
Equilibrium Configurations

The two dimensional motion of a generally non-circular non-uniform cylinder on a flat horizontal surface is investigated. Assuming that the cylinder does not slip, energy conservation is used to study the motion in general. Points of returns, and small oscillations around equilibrium configuration are studied. As examples, cylinders are studied for which the cross section is an ellipse, with the center of mass at the center of the ellipse or at a focal point, and the frequencies of small oscillations around their equilibrium configurations are found. The conditions for losing contact or sliding are also investigated. Finally, the motion is studied in more detail for the case of a nearly circular cylinder.

Optimum profiles in two-dimensional Stokes flow

1995 ◽  
Vol 450 (1940) ◽  
pp. 603-622 ◽  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Stokes Flow ◽  
Unit Length ◽  
Three Dimensional ◽  
Variational Formula ◽  
Effective Radius ◽  
Two Dimensional ◽  
Equivalent Radius ◽  
Optimum Profile

We consider the problem of designing the section of a cylinder to minimize the drag per unit length it experiences when placed perpendicular to a uniform stream at low Reynolds number; we suppose the area of the cross-section to be given, and the flow to be two-dimensional. The relevant properties of a cylinder of general cross-section in a particular orientation can conveniently be expressed in terms of its equivalent radius; when the drag and flow at infinity are parallel, this equivalent radius is the radius of the circular cylinder giving rise to the same drag per unit length. We obtain a variational formula for this equivalent radius when the surface of the cylinder is perturbed; this shows that the optimum profile we seek must be such that the flow past it has a vorticity of constant magnitude at its surface, and this fact enables the optimum to be determined analytically. The efficacy of a particular section may be measured by its effective radius, this being the equivalent radius when the length scale is chosen to give the section an area π ; thus a circular cylinder has an effective radius of 1. The minimum possible effective radius, achieved by the optimum profile, is 0.88876. To illustrate some of the arguments we exploit in a more familiar setting, we also obtain a variational formula for the drag on a three-dimensional body in Stokes flow when its surface is perturbed.

Flow regimes for a square cross-section cylinder in oscillatory flow

2017 ◽  
Vol 813 ◽  
pp. 85-109 ◽  
Author(s):  
Feifei Tong ◽  
Liang Cheng ◽  
Chengwang Xiong ◽  
Scott Draper ◽  
Hongwei An ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Oscillatory Flow ◽  
Vortex Formation ◽  
Flow Regimes ◽  
Oscillation Period ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Square Cylinder ◽  
Vortex Formation Time

Two-dimensional direct numerical simulation and Floquet stability analysis have been performed at moderate Keulegan–Carpenter number ($KC$) and low Reynolds number ($Re$) for a square cross-section cylinder with its face normal to the oscillatory flow. Based on the numerical simulations a map of flow regimes is formed and compared to the map of flow around an oscillating circular cylinder by Tatsuno & Bearman (J. Fluid Mech., vol. 211, 1990, pp. 157–182). Two new flow regimes have been observed, namely A$^{\prime }$ and F$^{\prime }$. The regime A$^{\prime }$ found at low $KC$ is characterised by the transverse convection of fluid particles perpendicular to the motion; and the regime F$^{\prime }$ found at high $KC$ shows a quasi-periodic feature with a well-defined secondary period, which is larger than the oscillation period. The Floquet analysis demonstrates that when the two-dimensional flow breaks the reflection symmetry about the axis of oscillation, the quasi-periodic instability and the synchronous instability with the imposed oscillation occur alternately for the square cylinder along the curve of marginal stability. This alternate pattern in instabilities leads to four distinct flow regimes. When compared to the vortex shedding in otherwise unidirectional flow, the two quasi-periodic flow regimes are observed when the oscillation frequency is close to the Strouhal frequency (or to half of it). Both the flow regimes and marginal stability curve shift in the $(Re,KC)$-space compared to the oscillatory flow around a circular cylinder and this shift appears to be consistent with the change in vortex formation time associated with the lower Strouhal frequency of the square cylinder.

Organization of the Dynamics in a Parameter Plane of a Tumor Growth Mathematical Model

2014 ◽  
Vol 24 (02) ◽  
pp. 1450023 ◽  
Author(s):  
Cristiane Stegemann ◽  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Tumor Growth ◽  
Cross Section ◽  
Periodic Structures ◽  
Focal Point ◽  
Parameter Plane ◽  
Two Dimensional ◽  
First Order ◽  
Self Organized ◽  
Chaotic Region

We report results of a numerical investigation on a two-dimensional cross-section of the parameter-space of a set of three autonomous, eight-parameter, first-order ordinary differential equations, which models tumor growth. The model considers interaction between tumor cells, healthy tissue cells, and activated immune system cells. By using Lyapunov exponents to characterize the dynamics of the model in a particular parameter plane, we show that it presents typical self-organized periodic structures embedded in a chaotic region, that were before detected in other models. We show that these structures organize themselves in two independent ways: (i) as spirals that coil up toward a focal point while undergoing period-adding bifurcations and, (ii) as a sequence with a well-defined law of formation, constituted by two mixed period-adding bifurcation cascades.

The Numerical Analysis of Contaminant Migration from Sanitary Landfill Sites

1977 ◽  
Vol 12 (1) ◽  
pp. 233-255
Author(s):  
J.F. Sykes ◽  
A.J. Crutcher
Keyword(s):  
Contaminant Transport ◽  
Cross Section ◽  
Element Model ◽  
Sanitary Landfill ◽  
Saturated Porous Media ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Southern Ontario ◽  
Galerkin Finite Element ◽  
Chloride Concentrations

Abstract A two-dimensional Galerkin finite element model for flow and contaminant transport in variably saturated porous media is used to analyze the transport of chlorides from a sanitary landfill located in Southern Ontario. A representative cross-section is selected for the analysis. Predicted chloride concentrations are presented for the cross section at various horizon years.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Sign in / Sign up

Export Citation Format

Share Document