scholarly journals Spiralling liquid jets: verifiable mathematical framework, trajectories and peristaltic waves

2017 ◽  
Vol 819 ◽  
pp. 352-400 ◽  
Author(s):  
Yulii D. Shikhmurzaev ◽  
Grigori M. Sisoev
Keyword(s):  
Coordinate System ◽  
Equations Of Motion ◽  
Local Coordinate System ◽  
Industrial Applications ◽  
Liquid Jets ◽  
Mathematical Framework ◽  
Frenet Equations ◽  
Curvilinear Coordinate ◽  
Curvature And Torsion ◽  
Spinning Disc

The dynamics of a jet of an inviscid incompressible liquid spiralling out under the action of centrifugal forces is considered with both gravity and the surface tension taken into account. This problem is of direct relevance to a number of industrial applications, ranging from the spinning disc atomization process to nanofibre formation. The mathematical description of the flow by necessity requires the use of a local curvilinear non-orthogonal coordinate system centred around the jet’s baseline, and we present the general formulation of the problem without assuming that the jet is slender. To circumvent the inconvenience inherent in the non-orthogonality of the local coordinate system, the orthonormal Frenet basis is used in parallel with the local non-orthogonal basis, and the equation of motion, with the velocity considered with respect to the local coordinate system, is projected onto the Frenet basis. The variation of the latter along the baseline is then described by the Frenet equations which naturally brings the baseline’s curvature and torsion into the equations of motion. This technique allows one to handle different line-based non-orthogonal curvilinear coordinate systems in a straightforward and mathematically transparent way. An analysis of the slender-jet approximation that follows the general formulation shows how a set of ordinary differential equations describing the jet’s trajectory can be derived in two cases: $\mathit{We}=O(1)$ and $\unicode[STIX]{x1D716}\mathit{We}=O(1)$ as $\unicode[STIX]{x1D716}\rightarrow 0$, where $\unicode[STIX]{x1D716}$ is the ratio of characteristic length scales across and along the jet and $\mathit{We}$ is the Weber number. A one-dimensional model for the propagation of nonlinear peristaltic disturbances along the jet is derived in each of these cases. A critical review of the work published on this topic is presented showing where errors typically occur and how to identify and avoid them.

scholarly journals EQUATION OF MOTION MAGNETIC LEVITATION ROLLING STOCK

2015 ◽  
Vol 1 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Nikolai N PASHKOV
Keyword(s):  
Coordinate System ◽  
Magnetic Levitation ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Local Coordinate System ◽  
Center Of Mass ◽  
Rigid Bodies ◽  
Rolling Stock ◽  
Track Structure ◽  
Centers Of Mass

This article deals with the problem of control the trajectory of the crew magnetic levitation relative trajectory of the software regarding the track structure of the perturbation of the gravitational and magnetic fields levitation systems, lateral stabilization and traction. The crew is presented as a system of rigid bodies, whose motion is subject to gravitational and electromagnetic forces. The spatial displacement with limited powers of levitation and lateral stabilization regarding a discrete track structure are selected by drawing up the estimated equations of the dynamics of the crew as inertial coordinates of the centers of mass of solids. The coordinates of any point on the carriage in a local coordinate system are converted in the coordinate system associated with the center of mass of the crew to bring the point of application of external force to the center of mass of the crew. A general model of the dynamics of the crew is based on the equation of Lagrange-Maxwell which binds to the active mass of the external forces of gravity that govern the electromagnetic force, the force of inertia and friction. The kinetic energy of the mechanical system is defined by the velocity projections on the axis of the fixed coordinate system as a quadratic form. The crew simulated magneto elastic coupling with the track structure changing the potential energy of magnetic levitation and lateral stabilization at the deformation of the object or the displacement and rotation of the center of mass of the crew in three-dimensional space. The inverse problem of dynamics is solved to determine the control forces for a given trajectory of the crew magnetic levitation. The equations of motion the crew on a magnetic cushion are linearized regarding increments relative coordinates of the centers of mass of the crew vector and presented in the form of equations of the phase space of states.

A Computational Method for Planar Kinematic Analysis of Beam Pumping Units

2007 ◽  
Vol 129 (4) ◽  
pp. 300-306 ◽  
Author(s):  
Ramkamal Bhagavatula ◽  
Olu A. Fashesan ◽  
Lloyd R. Heinze ◽  
James F. Lea
Keyword(s):  
Coordinate System ◽  
Kinematic Analysis ◽  
Equations Of Motion ◽  
Local Coordinate System ◽  
Computational Method ◽  
Joint Analysis ◽  
Global Coordinate System ◽  
Rotational Angle ◽  
Design And Optimization ◽  
Pumping Units

A generalized computational method for planar kinematic analysis of pumping units is presented in this study. In this method, a local coordinate system is assigned to each body with respect to a fixed global coordinate system. The position of each point in a body is determined by specifying the global translational coordinates of the local coordinate system origin and its rotational angle relative to the global coordinate system. Constraint equations of motion are developed using the vector of coordinates of the connected bodies. These equations are solved to yield the position, velocity, and acceleration of the individual linkages at each instance of time. Both rotational and translational types of joints are considered in the analysis. The translational joint analysis is not discussed in this paper as they are not applicable for beam pumping units. This method can be used as an effective tool for pumping unit design and optimization. An example is provided to show the application of this method.

Structural Synthesis of Serial Robotic Manipulators Subject to Specific Motion Constraints

2010 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Coordinate System ◽  
Local Coordinate System ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Industrial Applications ◽  
Global Coordinate System ◽  
Structural Synthesis ◽  
End Effector ◽  
Serial Manipulators ◽  
Motion Constraints

An intuitive approach for the structural synthesis of serial robotic manipulator subject to specific motion constraints is presented in this paper. According to the required f-DOF αRβT motion of the end-effector, for f = 2, 3, … or 6 and α, β = 0, 1, 2 or 3, all feasible serial-type robot structures can be systematically generated via the proposed method. The approach begins at the enumeration of joint connectivity, proceeds with the assignment of joint types, and continues by the consideration of motion constraints for the robot. A couple of examples, including the synthesis of the 3-, 4- and 5-DOF serial manipulators, are furnished for illustration. It shows that this method is especially exploitable when the end-effector is required to be immovable in certain orientations or directions with respect to either local coordinate system or global coordinate system. The result is particularly beneficial for practical industrial applications.

Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011

2017 ◽  
Vol 929 (11) ◽  
pp. 2-10
Author(s):  
A.V. Vinogradov
Keyword(s):  
Coordinate System ◽  
Small Businesses ◽  
Transition Period ◽  
Local Coordinate System ◽  
Initial Point ◽  
Central Meridian ◽  
Administrative District ◽  
Local Networks ◽  
Small Areas ◽  
Geodetic System

Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

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.

scholarly journals MEASUREMENT OF VERTICALITY CONSTRUCTION OF BUSHINGS FOR LABORATORY CONSTRUCTION MATERIALS

2014 ◽  
Vol 40 (4) ◽  
pp. 171-174 ◽  
Author(s):  
Petr Jadviščok ◽  
Rostislav Dandoš ◽  
Tomaš Jiroušek
Keyword(s):  
Coordinate System ◽  
Building Materials ◽  
Civil Engineering ◽  
Local Coordinate System ◽  
Construction Materials ◽  
Polar Method ◽  
Standard Equipment ◽  
Final Number ◽  
Loading Tests ◽  
Design And Manufacture

This contribution describes process which was used for verticality measurement of the bushings for laboratory construction materials in the pavilion of testing. This pavilion is newly built in VŠB-TU Ostrava, Faculty of Civil Engineering, as part of the Testing house of the building materials. The requirement of the building investor was to determine the verticality of the bushings placed between the first aboveground and the first underground floor. After the building finishing, the bushings with the diameter 70 mm will be used for loading tests of various building materials. The final number of bushings is 169, and they are placed lengthwise and crosswise in the step of 750 mm. The centres of the bushings were measured by polar method in pavilion local coordinate system. The precision of the bushing centres determination was }5 mm according to the investor´s requirement. The precision would not be followed if the standard equipment for reflector fixing was used. In that case, it was necessary to design and manufacture special tool in the shape of truncated cone. On the top part was placed central pivot for reflector with additional plate bubble.

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals Computation of electrostatic fields in anisotropic human tissues using the Finite Integration Technique (FIT)

2005 ◽  
Vol 2 ◽  
pp. 309-313 ◽  
Author(s):  
V. C. Motresc ◽  
U. van Rienen
Keyword(s):  
Coordinate System ◽  
Electromagnetic Fields ◽  
Human Body ◽  
Local Coordinate System ◽  
Anisotropic Materials ◽  
The Body ◽  
Integration Technique ◽  
Data Set ◽  
Computer Data ◽  
Finite Integration Technique

Abstract. The exposure of human body to electromagnetic fields has in the recent years become a matter of great interest for scientists working in the area of biology and biomedicine. Due to the difficulty of performing measurements, accurate models of the human body, in the form of a computer data set, are used for computations of the fields inside the body by employing numerical methods such as the method used for our calculations, namely the Finite Integration Technique (FIT). A fact that has to be taken into account when computing electromagnetic fields in the human body is that some tissue classes, i.e. cardiac and skeletal muscles, have higher electrical conductivity and permittivity along fibers rather than across them. This property leads to diagonal conductivity and permittivity tensors only when expressing them in a local coordinate system while in a global coordinate system they become full tensors. The Finite Integration Technique (FIT) in its classical form can handle diagonally anisotropic materials quite effectively but it needed an extension for handling fully anisotropic materials. New electric voltages were placed on the grid and a new averaging method of conductivity and permittivity on the grid was found. In this paper, we present results from electrostatic computations performed with the extended version of FIT for fully anisotropic materials.

Sign in / Sign up

Export Citation Format

Share Document