Abstract: A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
Abstract: The Stokes equation connected with the fluid flow
over the axisymmetric bodies in a cylindrical area is considered. The
equation is studied in a moving coordinate system with the
appropriate boundary conditions. Effective formulas for the velocity
components are obtained. The graphs of the velocity components and
velocity profile are plotted.
Abstract: This paper presents a procedure of forming the
mathematical model of radial electric power systems for simulation
of both transient and steady-state conditions. The research idea has
been based on nodal voltages technique and on differentiation of
Kirchhoff's current law (KCL) applied to each non-reference node of
the radial system, the result of which the nodal voltages has been
calculated by solving a system of algebraic equations. Currents of the
electric power system components have been determined by solving
their respective differential equations. Transforming the three-phase
coordinate system into Cartesian coordinate system in the model
decreased the overall number of equations by one third. The use of
Cartesian coordinate system does not ignore the DC component
during transient conditions, but restricts the model's implementation
for symmetrical modes of operation only. An example of the input
data for a four-bus radial electric power system has been calculated.
Abstract: The primary objective of this paper was to construct a
“kinematic parameter-independent modeling of three-axis machine
tools for geometric error measurement" technique. Improving the
accuracy of the geometric error for three-axis machine tools is one of
the machine tools- core techniques. This paper first applied the
traditional method of HTM to deduce the geometric error model for
three-axis machine tools. This geometric error model was related to the
three-axis kinematic parameters where the overall errors was relative
to the machine reference coordinate system. Given that the
measurement of the linear axis in this model should be on the ideal
motion axis, there were practical difficulties. Through a measurement
method consolidating translational errors and rotational errors in the
geometric error model, we simplified the three-axis geometric error
model to a kinematic parameter-independent model. Finally, based on
the new measurement method corresponding to this error model, we
established a truly practical and more accurate error measuring
technique for three-axis machine tools.
Abstract: The Navier–Stokes equations for unsteady, incompressible, viscous fluids in the axisymmetric coordinate system are solved using a control volume method. The volume-of-fluid (VOF) technique is used to track the free-surface of the liquid. Model predictions are in good agreement with experimental measurements. It is found that the dynamic processes after impact are sensitive to the initial droplet velocity and the liquid pool depth. The time evolution of the crown height and diameter are obtained by numerical simulation. The critical We number for splashing (Wecr) is studied for Oh (Ohnesorge) numbers in the range of 0.01~0.1; the results compares well with those of the experiments.
Abstract: The objective of this research is to examine the shear thinning behaviour of mixing flow of non-Newtonian fluid like toothpaste in the dissolution container with rotating stirrer. The problem under investigation is related to the chemical industry. Mixing of fluid is performed in a cylindrical container with rotating stirrer, where stirrer is eccentrically placed on the lid of the container. For the simulation purpose the associated motion of the fluid is considered as revolving of the container, with stick stirrer. For numerical prediction, a time-stepping finite element algorithm in a cylindrical polar coordinate system is adopted based on semi-implicit Taylor-Galerkin/pressure-correction scheme. Numerical solutions are obtained for non-Newtonian fluids employing power law model. Variations with power law index have been analysed, with respect to the flow structure and pressure drop.
Abstract: In this paper we study the transformation of Euler equations 1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.
Abstract: In this article an isotropic linear elastic half-space with
a cylindrical cavity of finite length is considered to be under the
effect of a ring shape time-harmonic torsion force applied at an
arbitrary depth on the surface of the cavity. The equation of
equilibrium has been written in a cylindrical coordinate system. By
means of Fourier cosine integral transform, the non-zero
displacement component is obtained in the transformed domain. With
the aid of the inversion theorem of the Fourier cosine integral
transform, the displacement is obtained in the real domain. With the
aid of boundary conditions, the involved boundary value problem for
the fundamental solution is reduced to a generalized Cauchy singular
integral equation. Integral representation of the stress and
displacement are obtained, and it is shown that their degenerated
form to the static problem coincides with existing solutions in the
literature.
Abstract: The data measurement of mean velocity has been
taken for the wake of single circular cylinder with three different diameters for two different velocities. The effects of change in
diameter and in velocity are studied in self-similar coordinate system.
The spatial variations of velocity defect and that of the half-width
have been investigated. The results are compared with those
published by H.Schlichting. In the normalized coordinates, it is also observed that all cases except for the first station are self-similar. By attention to self-similarity profiles of mean velocity, it is observed for all the cases at the each station curves tend to zero at a same point.
Abstract: The numerical simulation of the slip effect via
vicoelastic fluid for 4:1 contraction problem is investigated with
regard to kinematic behaviors of streamlines and stress tensor by
models of the Navier-Stokes and Oldroyd-B equations. Twodimensional
spatial reference system of incompressible creeping flow
with and without slip velocity is determined and the finite element
method of a semi-implicit Taylor-Galerkin pressure-correction is
applied to compute the problem of this Cartesian coordinate system
including the schemes of velocity gradient recovery method and the
streamline-Upwind / Petrov-Galerkin procedure. The slip effect at
channel wall is added to calculate after each time step in order to
intend the alteration of flow path. The result of stress values and the
vortices are reduced by the optimum slip coefficient of 0.1 with near
the outcome of analytical solution.
Abstract: Localization is one of the critical issues in the field of
robot navigation. With an accurate estimate of the robot pose, robots will be capable of navigating in the environment autonomously and efficiently. In this paper, a hybrid Distributed Vision System (DVS)
for robot localization is presented. The presented approach integrates
odometry data from robot and images captured from overhead cameras
installed in the environment to help reduce possibilities of fail
localization due to effects of illumination, encoder accumulated errors,
and low quality range data. An odometry-based motion model is applied to predict robot poses, and robot images captured by overhead
cameras are then used to update pose estimates with HSV histogram-based measurement model. Experiment results show the
presented approach could localize robots in a global world coordinate system with localization errors within 100mm.
Abstract: Any rotation of a 3-dimensional object can be performed by three consecutive rotations over Euler angles. Intrinsic rotations produce the same result as extrinsic rotations in transformation. Euler rotations are the movement obtained by changing one of the Euler angles while leaving the other two constant. These Euler rotations are applied in a simple two-axis gimbals set mounted on an automotives. The values of Euler angles are [π/4, π/4, π/4] radians inside the angles ranges for a given coordinate system and these actual orientations can be directly measured from these gimbals set of moving automotives but it can occur the gimbals lock in application at [π/2.24, 0, 0] radians. In order to avoid gimbals lock, the values of quaternion must be [π/4.8, π/8.2, 0, π/4.8] radians. The four-gimbals set can eliminate gimbals lock.
Abstract: To satisfy the need of outfield tests of star sensors, a
method is put forward to construct the reference attitude benchmark.
Firstly, its basic principle is introduced; Then, all the separate
conversion matrixes are deduced, which include: the conversion
matrix responsible for the transformation from the Earth Centered
Inertial frame i to the Earth-centered Earth-fixed frame w according to
the time of an atomic clock, the conversion matrix from frame w to the
geographic frame t, and the matrix from frame t to the platform frame
p, so the attitude matrix of the benchmark platform relative to the
frame i can be obtained using all the three matrixes as the
multiplicative factors; Next, the attitude matrix of the star sensor
relative to frame i is got when the mounting matrix from frame p to the
star sensor frame s is calibrated, and the reference attitude angles for
star sensor outfield tests can be calculated from the transformation
from frame i to frame s; Finally, the computer program is finished to
solve the reference attitudes, and the error curves are drawn about the
three axis attitude angles whose absolute maximum error is just 0.25ÔÇ│.
The analysis on each loop and the final simulating results manifest that
the method by precise timing to acquire the absolute reference attitude
is feasible for star sensor outfield tests.
Abstract: The radiative exchange method is introduced as a
numerical method for the simulation of radiative heat transfer in an
absorbing, emitting and isotropically scattering media. In this
method, the integro-differential radiative balance equation is solved
by using a new introduced concept for the exchange factor. Even
though the radiative source term is calculated in a mesh structure that
is coarser than the structure used in computational fluid dynamics,
calculating the exchange factor between different coarse elements by
using differential integration elements makes the result of the method
close to that of integro-differential radiative equation. A set of
equations for calculating exchange factors in two and threedimensional
Cartesian coordinate system is presented, and the
method is used in the simulation of radiative heat transfer in twodimensional
rectangular case and a three-dimensional simple cube.
The result of using this method in simulating different cases is
verified by comparing them with those of using other numerical
radiative models.
Abstract: In the crack growth analysis, the Stress Intensity
Factor (SIF) is a fundamental prerequisite. In the present study, the
mode I stress intensity factor (SIF) of three-dimensional penny-
Shaped crack is obtained in an isotropic elastic cylindrical medium
with arbitrary dimensions under arbitrary loading at the top of the
cylinder, by the semi-analytical method based on the Rayleigh-Ritz
method. This method that is based on minimizing the potential
energy amount of the whole of the system, gives a very close results
to the previous studies. Defining the displacements (elastic fields) by
hypothetical functions in a defined coordinate system is the base of
this research. So for creating the singularity conditions at the tip of
the crack the appropriate terms should be found.