Abstract: Estimation of natural frequency of structures is very
important and isn-t usually calculated simply and sometimes
complicated. Lack of knowledge about that caused hard damage and
hazardous effects.
In this paper, with using from two different models in FEM
method and based on hydrodynamic mass of fluids, natural frequency
of an especial bearing (Fig. 1) in an electric field (or, a periodic
force) is calculated in different stiffness and different geometric. In
final, the results of two models and analytical solution are compared.
Abstract: The paper deals with the estimation of amplitude and phase of an analogue multi-harmonic band-limited signal from irregularly spaced sampling values. To this end, assuming the signal fundamental frequency is known in advance (i.e., estimated at an independent stage), a complexity-reduced algorithm for signal reconstruction in time domain is proposed. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. The proposed algorithm for the calculation of the unknown parameters requires O((2M+1)2) flops, while the straightforward solution of the obtained equations takes O((2M+1)3) flops (M is the number of the harmonic components). It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise RMS measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.
Abstract: In this paper, we investigate the study of techniques
for scheduling users for resource allocation in the case of multiple
input and multiple output (MIMO) packet transmission systems. In
these systems, transmit antennas are assigned to one user or
dynamically to different users using spatial multiplexing. The
allocation of all transmit antennas to one user cannot take full
advantages of multi-user diversity. Therefore, we developed the case
when resources are allocated dynamically. At each time slot users
have to feed back their channel information on an uplink feedback
channel. Channel information considered available in the schedulers
is the zero forcing (ZF) post detection signal to interference plus
noise ratio. Our analysis study concerns the round robin and the
opportunistic schemes.
In this paper, we present an overview and a complete capacity
analysis of these schemes. The main results in our study are to give
an analytical form of system capacity using the ZF receiver at the
user terminal. Simulations have been carried out to validate all
proposed analytical solutions and to compare the performance of
these schemes.
Abstract: In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Abstract: This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Abstract: Based on the homotopy perturbation method (HPM)
and Padé approximants (PA), approximate and exact solutions are
obtained for cubic Boussinesq and modified Boussinesq equations.
The obtained solutions contain solitary waves, rational solutions.
HPM is used for analytic treatment to those equations and PA for
increasing the convergence region of the HPM analytical solution.
The results reveal that the HPM with the enhancement of PA is a
very effective, convenient and quite accurate to such types of partial
differential equations.
Abstract: In this work the numerical simulation of transient heat
transfer in a cylindrical probe is done. An experiment was conducted
introducing a steel cylinder in a heating chamber and registering its
surface temperature along the time during one hour. In parallel, a
mathematical model was solved for one dimension transient heat
transfer in cylindrical coordinates, considering the boundary
conditions of the test. The model was solved using finite difference
method, because the thermal conductivity in the cylindrical steel bar
and the convection heat transfer coefficient used in the model are
considered temperature dependant functions, and both conditions
prevent the use of the analytical solution. The comparison between
theoretical and experimental results showed the average deviation is
below 2%. It was concluded that numerical methods are useful in
order to solve engineering complex problems. For constant k and h,
the experimental methodology used here can be used as a tool for
teaching heat transfer in mechanical engineering, using mathematical
simplified models with analytical solutions.
Abstract: An analytical solution for dispersion of a solute in the
peristaltic motion of a couple stress fluid in the presence of magnetic
field with both homogeneous and heterogeneous chemical reactions is
presented. The average effective dispersion coefficient has been found
using Taylor-s limiting condition and long wavelength approximation.
The effects of various relevant parameters on the average effective
coefficient of dispersion have been studied. The average effective
dispersion coefficient tends to decrease with magnetic field parameter,
homogeneous chemical reaction rate parameter and amplitude ratio
but tends to increase with heterogeneous chemical reaction rate
parameter.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.
Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: To achieve reliable solutions, today-s numerical and
experimental activities need developing more accurate methods and
utilizing expensive facilities, respectfully in microchannels. The analytical
study can be considered as an alternative approach to alleviate
the preceding difficulties. Among the analytical solutions, those with
high robustness and low complexities are certainly more attractive.
The perturbation theory has been used by many researchers to analyze
microflows. In present work, a compressible microflow with constant
heat flux boundary condition is analyzed. The flow is assumed to be
fully developed and steady. The Mach and Reynolds numbers are also
assumed to be very small. For this case, the creeping phenomenon
may have some effect on the velocity profile. To achieve robustness
solution it is assumed that the flow is quasi-isothermal. In this study,
the creeping term which appears in the slip boundary condition
is formulated by different mathematical formulas. The difference
between this work and the previous ones is that the creeping term
is taken into account and presented in non-dimensionalized form.
The results obtained from perturbation theory are presented based
on four non-dimensionalized parameters including the Reynolds,
Mach, Prandtl and Brinkman numbers. The axial velocity, normal
velocity and pressure profiles are obtained. Solutions for velocities
and pressure for two cases with different Br numbers are compared
with each other and the results show that the effect of creeping
phenomenon on the velocity profile becomes more important when
Br number is less than O(ε).
Abstract: The effect of streamwise conduction on the thermal
characteristics of forced convection for nanofluidic flow in
rectangular microchannel heat sinks under isothermal wall has been
investigated. By applying the fin approach, models with and without
streamwise conduction term in the energy equation were developed
for hydrodynamically and thermally fully-developed flow. These two
models were solved to obtain closed form analytical solutions for the
nanofluid and solid wall temperature distributions and the analysis
emphasized details of the variations induced by the streamwise
conduction on the nanofluid heat transport characteristics. The effects
of the Peclet number, nanoparticle volume fraction, thermal
conductivity ratio on the thermal characteristics of forced convection
in microchannel heat sinks are analyzed. Due to the anomalous
increase in the effective thermal conductivity of nanofluid compared
to its base fluid, the effect of streamwise conduction is expected to be
more significant. This study reveals the significance of the effect of
streamwise conduction under certain conditions of which the
streamwise conduction should not be neglected in the forced
convective heat transfer analysis of microchannel heat sinks.
Abstract: The paper presents coupled electromagnetic and
thermal field analysis of busbar system (of rectangular cross-section
geometry) submitted to short circuit conditions. The laboratory model
was validated against both analytical solution and experimental
observations. The considered problem required the computation of
the detailed distribution of the power losses and the heat transfer
modes. In this electromagnetic and thermal analysis, different
definitions of electric busbar heating were considered and compared.
The busbar system is a three phase one and consists of aluminum,
painted aluminum and copper busbar. The solution to the coupled
field problem is obtained using the finite element method and the
QuickField™ program. Experiments have been carried out using two
different approaches and compared with computed results.
Abstract: This paper presents a generalized formulation for the
problem of buckling optimization of anisotropic, radially graded,
thin-walled, long cylinders subject to external hydrostatic pressure.
The main structure to be analyzed is built of multi-angle fibrous
laminated composite lay-ups having different volume fractions of the
constituent materials within the individual plies. This yield to a
piecewise grading of the material in the radial direction; that is the
physical and mechanical properties of the composite material are
allowed to vary radially. The objective function is measured by
maximizing the critical buckling pressure while preserving the total
structural mass at a constant value equals to that of a baseline
reference design. In the selection of the significant optimization
variables, the fiber volume fractions adjoin the standard design
variables including fiber orientation angles and ply thicknesses. The
mathematical formulation employs the classical lamination theory,
where an analytical solution that accounts for the effective axial and
flexural stiffness separately as well as the inclusion of the coupling
stiffness terms is presented. The proposed model deals with
dimensionless quantities in order to be valid for thin shells having
arbitrary thickness-to-radius ratios. The critical buckling pressure
level curves augmented with the mass equality constraint are given
for several types of cylinders showing the functional dependence of
the constrained objective function on the selected design variables. It
was shown that material grading can have significant contribution to
the whole optimization process in achieving the required structural
designs with enhanced stability limits.
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.