**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3254

# Search results for: analytical solution

##### 3254 Hydrodynamic Analysis of Reservoir Due to Vertical Component of Earthquake Using an Analytical Solution

**Authors:**
M. Pasbani Khiavi,
M. A. Ghorbani

**Abstract:**

This paper presents an analytical solution to get a reliable estimation of the hydrodynamic pressure on gravity dams induced by vertical component earthquake when solving the fluid and dam interaction problem. Presented analytical technique is presented for calculation of earthquake-induced hydrodynamic pressure in the reservoir of gravity dams allowing for water compressibility and wave absorption at the reservoir bottom. This new analytical solution can take into account the effect of bottom material on seismic response of gravity dams. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.

**Keywords:**
Dam,
Reservoir,
Analytical solution,
Vertical
component,
Earthquake

##### 3253 Analytical Solutions of Three Dimensional Steady-State Heat Transfer in Rectangular Ribs

**Authors:**
Tao Nie,
Weiqiang Liu

**Abstract:**

**Keywords:**
variable separation method,
analytical solution,
rib,
heat transfer

##### 3252 Analytical solution of Gas Flow Through a Micro-Nano Porous Media by Homotopy Perturbation method

**Authors:**
Jamal Amani Rad,
Kourosh Parand

**Abstract:**

**Keywords:**
Unsteady gas equation,
Homotopy perturbation method(HPM),
Porous medium,
Nonlinear ODE

##### 3251 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.

##### 3250 Contribution to the Analytical Study of Barrier Surface Waves: Decomposition of the Solution

**Authors:**
T. Zitoun,
M. Bouhadef

**Abstract:**

**Keywords:**
Free-surface wave,
inviscid fluid,
analytical solution,
hydraulic channel.

##### 3249 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

**Authors:**
Saeideh Hesam,
Alireza Nazemi,
Ahmad Haghbin

**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.

**Keywords:**
Zakharov-Kuznetsov equation,
differential transform method,
closed form solution.

##### 3248 HPM Solution of Momentum Equation for Darcy-Brinkman Model in a Parallel Plates Channel Subjected to Lorentz Force

**Authors:**
Asghar Shirazpour,
Seyed Moein Rassoulinejad Mousavi,
Hamid Reza Seyf

**Abstract:**

In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

**Keywords:**
Lorentz Force,
Porous Media,
Homotopy Perturbation method

##### 3247 Unsteady Reversed Stagnation-Point Flow over a Flat Plate

**Authors:**
Vai Kuong Sin,
Chon Kit Chio

**Abstract:**

**Keywords:**
reversed stagnation-point flow,
similarity solutions,
analytical solution,
numerical solution

##### 3246 An Analytical Solution for Vibration of Elevator Cables with Small Bending Stiffness

**Authors:**
R. Mirabdollah Yani,
E. Darabi

**Abstract:**

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.

**Keywords:**
variational iteration method (VIM),
cable vibration,
closed-form solution

##### 3245 General Formula for Water Surface Profile over Side Weir in the Combined, Trapezoidal and Exponential, Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

**Keywords:**
Analytical solution,
combined channel,
exponential channel,
side weirs,
trapezoidal channel,
water surface profile.

##### 3244 Laser Surface Hardening Considering Coupled Thermoelasticity using an Eulerian Formulations

**Authors:**
Me. Sistaninia,
G.H.Farrahi,
Ma. Sistaninia

**Abstract:**

**Keywords:**
Coupled thermoelasticity,
Finite element,
Laser
surface hardening,
Eulerian formulation.

##### 3243 Transient Heat Conduction in Nonuniform Hollow Cylinders with Time Dependent Boundary Condition at One Surface

**Authors:**
Sen Yung Lee,
Chih Cheng Huang,
Te Wen Tu

**Abstract:**

**Keywords:**
Analytical solution,
nonuniform hollow cylinder,
time-dependent boundary condition,
transient heat conduction.

##### 3242 Unsteady Temperature Distribution in a Finite Functionally Graded Cylinder

**Authors:**
A. Amiri Delouei

**Abstract:**

In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

**Keywords:**
Functionally graded materials,
unsteady heat conduction,
cylinder,
Temperature distribution.

##### 3241 An Approximate Solution of the Classical Van der Pol Oscillator Coupled Gyroscopically to a Linear Oscillator Using Parameter-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Samad Kheybari

**Abstract:**

In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.

**Keywords:**
Parameter-expansion method,
classical Van der Pol oscillator.

##### 3240 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinsonâ€™s Disease

**Authors:**
H. N. Agiza,
M. A. Sohaly,
M. A. Elfouly

**Abstract:**

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs*.*

**Keywords:**
Parkinson's disease,
Step method,
delay differential equation,
simulation.

##### 3239 Simulation of Robotic Arm using Genetic Algorithm and AHP

**Authors:**
V. K. Banga,
Y. Singh,
R. Kumar

**Abstract:**

**Keywords:**
Inverse Kinematics,
Genetic Algorithm (GA),
Analytical Hierarchy Process (AHP),
Fitness Value,
Fitness Function.

##### 3238 Analytical Formulae for the Approach Velocity Head Coefficient

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

**Keywords:**
Broad crested weir,
combined control meter,
control structures,
critical flow,
discharge measurement,
flow control,
hydraulic engineering,
hydraulic structures,
open channel flow.

##### 3237 Analytical Based Truncation Principle of Higher-Order Solution for a x1/3 Force Nonlinear Oscillator

**Authors:**
Md. Alal Hosen

**Abstract:**

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^{1/3}. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^{1/3} force nonlinear oscillator but it is also useful for many other nonlinear problems.

**Keywords:**
Approximate solutions,
Harmonic balance method,
Nonlinear oscillator,
Perturbation.

##### 3236 Quasilinearizationâ€“Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem

**Authors:**
Alireza Rezaei,
Fatemeh Baharifard,
Kourosh Parand

**Abstract:**

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

**Keywords:**
Quasilinearization method,
Barycentric lagrange interpolation,
nonlinear ODE,
fin problem,
heat transfer.

##### 3235 Analytical Solution of Stress Distribution ona Hollow Cylindrical Fiber of a Composite with Cylindrical Volume Element under Axial Loading

**Authors:**
M. H. Kargarnovin,
K. Momeni

**Abstract:**

**Keywords:**
Axial Loading,
Composite,
Hollow CylindricalFiber,
Stress Distribution.

##### 3234 Power Series Solution to Sliding Velocity in Three-Dimensional Multibody Systems with Impact and Friction

**Authors:**
Hesham A. Elkaranshawy,
Amr M. Abdelrazek,
Hosam M. Ezzat

**Abstract:**

**Keywords:**
Impact with friction,
nonlinear ordinary differential
equations,
power series solutions,
rough collision.

##### 3233 Numerical Solution of Manning's Equation in Rectangular Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

**Keywords:**
Channel design,
civil engineering,
hydraulic engineering,
open channel flow,
Manning's equation,
normal depth,
uniform flow.

##### 3232 Analytical Solutions of Kortweg-de Vries(KdV) Equation

**Authors:**
Foad Saadi,
M. Jalali Azizpour,
S.A. Zahedi

**Abstract:**

**Keywords:**
Variational Iteration Method (VIM),
HomotopyPerturbation Method (HPM),
Homotopy Analysis Method (HAM),
KdV Equation.

##### 3231 Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model

**Authors:**
NicolĂ˛ Vaiana,
Filip C. Filippou,
Giorgio Serino

**Abstract:**

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

**Keywords:**
Base-isolated structures,
earthquake engineering,
mixed time integration,
nonlinear exponential model.

##### 3230 Toward a New Simple Analytical Formulation of Navier-Stokes Equations

**Authors:**
Gunawan Nugroho,
Ahmed M. S. Ali,
Zainal A. Abdul Karim

**Abstract:**

**Keywords:**
Navier-Stokes Equations,
potential function,
turbulent flows.

##### 3229 Analytical Solution for Free Vibration of Rectangular Kirchhoff Plate from Wave Approach

**Authors:**
Mansour Nikkhah-Bahrami,
Masih Loghmani,
Mostafa Pooyanfar

**Abstract:**

**Keywords:**
Kirchhoff plate,
propagation matrix,
reflection
matrix,
vibration analysis.

##### 3228 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

**Authors:**
M. Saravi,
F. Ashrafi,
S.R. Mirrajei

**Abstract:**

**Keywords:**
Chebyshev polynomials,
Clenshaw method,
ODEs,
Spectral methods

##### 3227 Two-dimensional Analytical Drain Current Model for Multilayered-Gate Material Engineered Trapezoidal Recessed Channel(MLGME-TRC) MOSFET: a Novel Design

**Authors:**
Priyanka Malik A,
Rishu Chaujar B,
Mridula Gupta C,
R.S. Gupta D

**Abstract:**

**Keywords:**
ATLAS,
DEVEDIT,
NJD,
MLGME- TRCMOSFET.

##### 3226 Response of Pavement under Temperature and Vehicle Coupled Loading

**Authors:**
Yang Zhong,
Mei-jie Xu

**Abstract:**

**Keywords:**
Asphalt pavement,
dynamic modulus,
integral
transformation,
transfer matrix,
thermal stress.

##### 3225 Calculation of the Thermal Stresses in an Elastoplastic Plate Heated by Local Heat Source

**Authors:**
M. Khaing,
A. V. Tkacheva

**Abstract:**

**Keywords:**
Temperature stresses,
elasticity,
plasticity,
Ishlinsky-Ivlev condition,
plate,
annular heating,
elastic moduli.