Abstract: The main objective of the present paper is to derive an easy numerical technique for the analysis of the free vibration through the stepped regions of plates. Based on the utilities of the step by step integration initial values IV and Finite differences FD methods, the present improved Initial Value Finite Differences (IVFD) technique is achieved. The first initial conditions are formulated in convenient forms for the step by step integrations while the upper and lower edge conditions are expressed in finite difference modes. Also compatibility conditions are created due to the sudden variation of plate thickness. The present method (IVFD) is applied to solve the fourth order partial differential equation of motion for stepped plate across two different panels under the sudden step compatibility in addition to different types of end conditions. The obtained results are examined and the validity of the present method is proved showing excellent efficiency and rapid convergence.
Abstract: In this paper after reviewing some previous studies, in
order to optimize the above knee prosthesis, beside the inertial
properties a new controlling parameter is informed. This controlling
parameter makes the prosthesis able to act as a multi behavior system
when the amputee is opposing to different environments. This active
prosthesis with the new controlling parameter can simplify the
control of prosthesis and reduce the rate of energy consumption in
comparison to recently presented similar prosthesis “Agonistantagonist
active knee prosthesis".
In this paper three models are generated, a passive, an active, and
an optimized active prosthesis. Second order Taylor series is the
numerical method in solution of the models equations and the
optimization procedure is genetic algorithm.
Modeling the prosthesis which comprises this new controlling
parameter (SEP) during the swing phase represents acceptable results
in comparison to natural behavior of shank. Reported results in this
paper represent 3.3 degrees as the maximum deviation of models
shank angle from the natural pattern. The natural gait pattern belongs
to walking at the speed of 81 m/min.
Abstract: A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.
Abstract: We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Abstract: A reduced order modeling approach for natural
gas transient flow in pipelines is presented. The Euler
equations are considered as the governing equations and
solved numerically using the implicit Steger-Warming flux
vector splitting method. Next, the linearized form of the
equations is derived and the corresponding eigensystem is
obtained. Then, a few dominant flow eigenmodes are used to
construct an efficient reduced-order model. A well-known test
case is presented to demonstrate the accuracy and the
computational efficiency of the proposed method. The results
obtained are in good agreement with those of the direct
numerical method and field data. Moreover, it is shown that
the present reduced-order model is more efficient than the
conventional numerical techniques for transient flow analysis
of natural gas in pipelines.
Abstract: This paper deals with the problem of non-uniform
torsion in thin-walled elastic beams with asymmetric cross-section,
removing the basic concept of a fixed center of twist, necessary in the
Vlasov-s and Benscoter-s theories to obtain a warping stress field
equivalent to zero. In this new torsion/flexure theory, despite of the
classical ones, the warping function will punctually satisfy the first
indefinite equilibrium equation along the beam axis and it wont- be
necessary to introduce the classical congruence condition, to take into
account the effect of the beam restraints. The solution, based on the
Fourier development of the displacement field, is obtained assuming
that the applied external torque is constant along the beam axis and
on both beam ends the unit twist angle and the warping axial
displacement functions are totally restrained.
Finally, in order to verify the feasibility of the proposed method
and to compare it with the classical theories, two applications are
carried out. The first one, relative to an open profile, is necessary to
test the numerical method adopted to find the solution; the second
one, instead, is relative to a simplified containership section,
considered as full restrained in correspondence of two adjacent
transverse bulkheads.
Abstract: The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is based
on a combination of a fifth-order Runge-Kutta method and 3-point
Gauss-Legendre quadrature. In this paper we describe the propagation
of local errors in this method, and show that the global order of
RK5GL3 is expected to be six, one better than the underlying Runge-
Kutta method.
Abstract: The dynamics of a predator-prey model with continuous
threshold policy harvesting functions on the prey is studied. Theoretical
and numerical methods are used to investigate boundedness
of solutions, existence of bionomic equilibria, and the stability properties
of coexistence equilibrium points and periodic orbits. Several
bifurcations as well as some heteroclinic orbits are computed.
Abstract: In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.
Abstract: This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.
Abstract: In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.
Abstract: In this paper, a numerical solution based on sinc
functions is used for finding the solution of boundary value problems
which arise from the problems of calculus of variations. This
approximation reduce the problems to an explicit system of algebraic
equations. Some numerical examples are also given to illustrate the
accuracy and applicability of the presented method.
Abstract: By the application of an improved back-propagation
neural network (BPNN), a model of current densities for a solid oxide
fuel cell (SOFC) with 10 layers is established in this study. To build
the learning data of BPNN, Taguchi orthogonal array is applied to
arrange the conditions of operating parameters, which totally 7 factors
act as the inputs of BPNN. Also, the average current densities
achieved by numerical method acts as the outputs of BPNN.
Comparing with the direct solution, the learning errors for all learning
data are smaller than 0.117%, and the predicting errors for 27
forecasting cases are less than 0.231%. The results show that the
presented model effectively builds a mathematical algorithm to predict
performance of a SOFC stack immediately in real time.
Also, the calculating algorithms are applied to proceed with the
optimization of the average current density for a SOFC stack. The
operating performance window of a SOFC stack is found to be
between 41137.11 and 53907.89. Furthermore, an inverse predicting
model of operating parameters of a SOFC stack is developed here by
the calculating algorithms of the improved BPNN, which is proved to
effectively predict operating parameters to achieve a desired
performance output of a SOFC stack.
Abstract: Avalanche release of snow has been modeled in the present studies. Snow is assumed to be represented by semi-solid and the governing equations have been studied from the concept of continuum approach. The dynamical equations have been solved for two different zones [starting zone and track zone] by using appropriate initial and boundary conditions. Effect of density (ρ), Eddy viscosity (η), Slope angle (θ), Slab depth (R) on the flow parameters have been observed in the present studies. Numerical methods have been employed for computing the non linear differential equations. One of the most interesting and fundamental innovation in the present studies is getting initial condition for the computation of velocity by numerical approach. This information of the velocity has obtained through the concept of fracture mechanics applicable to snow. The results on the flow parameters have found to be in qualitative agreement with the published results.
Abstract: The Goursat partial differential equation arises in
linear and non linear partial differential equations with mixed
derivatives. This equation is a second order hyperbolic partial
differential equation which occurs in various fields of study such as
in engineering, physics, and applied mathematics. There are many
approaches that have been suggested to approximate the solution of
the Goursat partial differential equation. However, all of the
suggested methods traditionally focused on numerical differentiation
approaches including forward and central differences in deriving the
scheme. An innovation has been done in deriving the Goursat partial
differential equation scheme which involves numerical integration
techniques. In this paper we have developed a new scheme to solve
the Goursat partial differential equation based on the Adomian
decomposition (ADM) and associated with Boole-s integration rule to
approximate the integration terms. The new scheme can easily be
applied to many linear and non linear Goursat partial differential
equations and is capable to reduce the size of computational work.
The accuracy of the results reveals the advantage of this new scheme
over existing numerical method.
Abstract: Three dimensional simulations in tube in tube heat
exchangers are investigated numerically in this study. In these
simulations forced convective heat transfer and laminar flow of
single-phase water are considered. In order to measure heat transfer
parameters in these heat exchangers, FLUENT CFD Solver is used in
this numerical method. For the purpose of creating geometry and
exert boundary and initial conditions in the present model, finite
volume method in Computational Fluid Dynamics is used in this
study. In the present study, at each Z-location, variation of local
temperatures, heat flux and Nusselt number at the whole tube is
investigated in detail. Thereafter, averaged computational Nusselt
number in this model is calculated. In addition, conceivable pressure
drops have been obtained at each Z-location in this model. Then,
pressure drop values in the present model are explored. Finally, all
the numerical results for this kind of heat exchanger will be discussed
precisely.
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and cvazistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine 1st stage nozzle blade
Abstract: Implicit equations play a crucial role in Engineering.
Based on this importance, several techniques have been applied to
solve this particular class of equations. When it comes to practical
applications, in general, iterative procedures are taken into account.
On the other hand, with the improvement of computers, other
numerical methods have been developed to provide a more
straightforward methodology of solution. Analytical exact approaches
seem to have been continuously neglected due to the difficulty
inherent in their application; notwithstanding, they are indispensable
to validate numerical routines. Lagrange-s Inversion Theorem is a
simple mathematical tool which has proved to be widely applicable to
engineering problems. In short, it provides the solution to implicit
equations by means of an infinite series. To show the validity of this
method, the tree-parameter infiltration equation is, for the first time,
analytically and exactly solved. After manipulating these series,
closed-form solutions are presented as H-functions.
Abstract: This paper focuses on cost and profit analysis of
single-server Markovian queuing system with two priority classes. In
this paper, functions of total expected cost, revenue and profit of the
system are constructed and subjected to optimization with respect to
its service rates of lower and higher priority classes. A computing
algorithm has been developed on the basis of fast converging
numerical method to solve the system of non linear equations formed
out of the mathematical analysis. A novel performance measure of
cost and profit analysis in view of its economic interpretation for the
system with priority classes is attempted to discuss in this paper. On
the basis of computed tables observations are also drawn to enlighten
the variational-effect of the model on the parameters involved
therein.
Abstract: The electrokinetic flow resistance (electroviscous
effect) is predicted for steady state, pressure-driven liquid flow at
low Reynolds number in a microfluidic contraction of rectangular
cross-section. Calculations of the three dimensional flow are
performed in parallel using a finite volume numerical method. The
channel walls are assumed to carry a uniform charge density and the
liquid is taken to be a symmetric 1:1 electrolyte. Predictions are
presented for a single set of flow and electrokinetic parameters. It is
shown that the magnitude of the streaming potential gradient and the
charge density of counter-ions in the liquid is greater than that in
corresponding two-dimensional slit-like contraction geometry. The
apparent viscosity is found to be very close to the value for a
rectangular channel of uniform cross-section at the chosen Reynolds
number (Re = 0.1). It is speculated that the apparent viscosity for the
contraction geometry will increase as the Reynolds number is
reduced.