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: The Eulerian numerical method is proposed to analyze
the explosion in tunnel. Based on this method, an original software
M-MMIC2D is developed by Cµ program language. With this
software, the explosion problem in the tunnel with three
expansion-chambers is numerically simulated, and the results are
found to be in full agreement with the observed experimental data.
Abstract: This paper studies dynamic stability of homogeneous
beams with piezoelectric layers subjected to periodic axial
compressive load that is simply supported at both ends lies on a
continuous elastic foundation. The displacement field of beam is
assumed based on Bernoulli-Euler beam theory. Applying the
Hamilton's principle, the governing dynamic equation is established.
The influences of applied voltage, foundation coefficient and
piezoelectric thickness on the unstable regions are presented. To
investigate the accuracy of the present analysis, a compression study
is carried out with a known data.
Abstract: Stirred tanks have applications in many chemical
processes where mixing is important for the overall performance of
the system. In present work 5%v of the tank is filled by solid particles
with diameter of 700 m that Rushton Turbine and Propeller impeller
is used for stirring. An Eulerian-Eulerian Multi Fluid Model coupled
and for modeling rotating of impeller, moving reference frame
(MRF) technique was used and standard-k- model was selected for
turbulency. Flow field, radial velocity and axial distribution of solid
for both of impellers was investigation and comparison. Comparisons
of simulation results between Rushton Turbine and propeller impeller
shows that final quality of solid-liquid slurry in different rotating
speed for propeller impeller is better than the Rushton Turbine.
Abstract: In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.
Abstract: We present our ongoing work on the development
of a new quadrotor aerial vehicle which has a tilt-wing
mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using
Newton-Euler formulation. Linear and nonlinear controllers for
the stabilization of attitude of the vehicle and control of its
altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite
effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also
been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide
satisfactory performance in achieving desired maneuvers.
Abstract: This work presents the highly accurate numerical calculation
of the natural frequencies for functionally graded beams with
simply supported boundary conditions. The Timoshenko first order
shear deformation beam theory and the higher order shear deformation
beam theory of Reddy have been applied to the functionally
graded beams analysis. The material property gradient is assumed
to be in the thickness direction. The Hamilton-s principle is utilized
to obtain the dynamic equations of functionally graded beams. The
influences of the volume fraction index and thickness-to-length ratio
on the fundamental frequencies are discussed. Comparison of the
numerical results for the homogeneous beam with Euler-Bernoulli
beam theory results show that the derived model is satisfactory.
Abstract: State Dependent Riccati Equation (SDRE) approach is
a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique
has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP
modeling is based on Euler-Lagrange equations. A procedure is developed
for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.
Abstract: The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.
Abstract: Active Vibration Control (AVC) is an important
problem in structures. One of the ways to tackle this problem is to
make the structure smart, adaptive and self-controlling. The objective
of active vibration control is to reduce the vibration of a system by
automatic modification of the system-s structural response. This
paper features the modeling and design of a Periodic Output
Feedback (POF) control technique for the active vibration control of
a flexible Timoshenko cantilever beam for a multivariable case with
2 inputs and 2 outputs by retaining the first 2 dominant vibratory
modes using the smart structure concept. The entire structure is
modeled in state space form using the concept of piezoelectric
theory, Timoshenko beam theory, Finite Element Method (FEM) and
the state space techniques. Simulations are performed in MATLAB.
The effect of placing the sensor / actuator at 2 finite element
locations along the length of the beam is observed. The open loop
responses, closed loop responses and the tip displacements with and
without the controller are obtained and the performance of the smart
system is evaluated for active vibration control.
Abstract: This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which
is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced
manipulator has a wide workspace and a high capability to reduce
the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by
a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step
arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.
Abstract: This paper presents the use of anti-sway angle control
approaches for a two-dimensional gantry crane with disturbances
effect in the dynamic system. Delayed feedback signal (DFS) and
proportional-derivative (PD)-type fuzzy logic controller are the
techniques used in this investigation to actively control the sway
angle of the rope of gantry crane system. A nonlinear overhead
gantry crane system is considered and the dynamic model of the
system is derived using the Euler-Lagrange formulation. A complete
analysis of simulation results for each technique is presented in time
domain and frequency domain respectively. Performances of both
controllers are examined in terms of sway angle suppression and
disturbances cancellation. Finally, a comparative assessment of the
impact of each controller on the system performance is presented and
discussed.
Abstract: This paper features the modeling and design of a Fast
Output Sampling (FOS) Feedback control technique for the Active
Vibration Control (AVC) of a smart flexible aluminium cantilever
beam for a Single Input Single Output (SISO) case. Controllers are
designed for the beam by bonding patches of piezoelectric layer as
sensor / actuator to the master structure at different locations along
the length of the beam by retaining the first 2 dominant vibratory
modes. The entire structure is modeled in state space form using the
concept of piezoelectric theory, Euler-Bernoulli beam theory, Finite
Element Method (FEM) and the state space techniques by dividing
the structure into 3, 4, 5 finite elements, thus giving rise to three
types of systems, viz., system 1 (beam divided into 3 finite
elements), system 2 (4 finite elements), system 3 (5 finite elements).
The effect of placing the sensor / actuator at various locations along
the length of the beam for all the 3 types of systems considered is
observed and the conclusions are drawn for the best performance and
for the smallest magnitude of the control input required to control the
vibrations of the beam. Simulations are performed in MATLAB. The
open loop responses, closed loop responses and the tip displacements
with and without the controller are obtained and the performance of
the proposed smart system is evaluated for vibration control.
Abstract: The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.
Abstract: This paper presents the buckling analysis of short and
long functionally graded cylindrical shells under thermal and
mechanical loads. The shell properties are assumed to vary
continuously from the inner surface to the outer surface of the shell.
The equilibrium and stability equations are derived using the total
potential energy equations, Euler equations and first order shear
deformation theory assumptions. The resulting equations are solved
for simply supported boundary conditions. The critical temperature
and pressure loads are calculated for both short and long cylindrical
shells. Comparison studies show the effects of functionally graded
index, loading type and shell geometry on critical buckling loads of
short and long functionally graded cylindrical shells.
Abstract: Thermoelastic temperature, displacement, and
stress in heat transfer during laser surface hardening are solved
in Eulerian formulation. In Eulerian formulations the heat flux
is fixed in space and the workpiece is moved through a control
volume. In the case of uniform velocity and uniform heat flux
distribution, the Eulerian formulations leads to a steady-state
problem, while the Lagrangian formulations remains transient.
In Eulerian formulations the reduction to a steady-state
problem increases the computational efficiency. In this study
also an analytical solution is developed for an uncoupled
transient heat conduction equation in which a plane slab is
heated by a laser beam. The thermal result of the numerical
model is compared with the result of this analytical model.
Comparing the results shows numerical solution for uncoupled
equations are in good agreement with the analytical solution.
Abstract: In the classical buckling analysis of rectangular plates
subjected to the concurrent action of shear and uniaxial forces, the
Euler shear buckling stress is generally evaluated separately, so that
no influence on the shear buckling coefficient, due to the in-plane
tensile or compressive forces, is taken into account.
In this paper the buckling problem of simply supported rectangular
plates, under the combined action of shear and uniaxial forces, is
discussed from the beginning, in order to obtain new project formulas
for the shear buckling coefficient that take into account the presence
of uniaxial forces.
Furthermore, as the classical expression of the shear buckling
coefficient for simply supported rectangular plates is considered only
a “rough" approximation, as the exact one is defined by a system of
intersecting curves, the convergence and the goodness of the classical
solution are analyzed, too.
Finally, as the problem of the Euler shear buckling stress
evaluation is a very important topic for a variety of structures, (e.g.
ship ones), two numerical applications are carried out, in order to
highlight the role of the uniaxial stresses on the plating scantling
procedures and the goodness of the proposed formulas.