Abstract: A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.
Abstract: In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.
Abstract: DSTATCOM is one of the equipments for voltage sag mitigation in power systems. In this paper a new control method for balanced and unbalanced voltage sag mitigation using DSTATCOM is proposed. The control system has two loops in order to regulate compensator current and load voltage. Delayed signal cancellation has been used for sequence separation. The compensator should protect sensitive loads against different types of voltage sag. Performance of the proposed method is investigated under different types of voltage sags for linear and nonlinear loads. Simulation results show appropriate operation of the proposed control system.
Abstract: In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.
Abstract: This research proposes the change of damping coefficient regarding minimum displacement. From the mass with external forced and damper problem, when is the constant external forced transmitted to the understructure in the difference angle between 30 and 60 degrees. This force generates the vibration as general known; however, the objective of this problem is to have minimum displacement. As the angle is changed and the goal is the same; therefore, the damper of the system must be varied while keeping constant spring stiffness. The problem is solved by using nonlinear programming and the suitable changing of the damping coefficient is provided.
Abstract: This paper describes topic of computer simulation with regard to the ground movement above an underground mine. Simulation made with software package ADINA for nonlinear elastic-plastic analysis with finite elements method. The one of representative profiles from Mine 'Stara Jama' in Zenica has been investigated. A collection and selection of both geo-mechanical data and geometric parameters of the mine was necessary for performing these simulations. Results of estimation have been compared with measured values (vertical displacement of surface), and then simulation performed with assumed dynamic and dimensions of excavation, over a period of time. Results are presented with bitmaps and charts.
Abstract: Lateral expansion is a factor defining the level of
confinement in reinforced concrete columns. Therefore, predicting
the lateral strain relationship with axial strain becomes an important
issue. Measuring lateral strains in experiments is difficult and only
few report experimental lateral strains. Among the existing analytical
formulations, two recent models are compared with available test
results in this paper with shortcomings highlighted. A new analytical
model is proposed here for lateral strain axial strain relationship and
is based on the supposition that the concrete behaves linear elastic in
the early stages of loading and then nonlinear hardening up to the
peak stress and then volumetric expansion. The proposal for the
lateral strain axial strain relationship after the peak stress is mainly
based on the hypothesis that the plastic lateral strain varies linearly
with the plastic axial strain and it is shown that this is related to the
lateral confinement level.
Abstract: The paper is concerned with the existence of solution
of nonlinear second order neutral stochastic differential inclusions
with infinite delay in a Hilbert Space. Sufficient conditions for the
existence are obtained by using a fixed point theorem for condensing
maps.
Abstract: We discuss the signal detection through nonlinear
threshold systems. The detection performance is assessed by the
probability of error Per . We establish that: (1) when the signal is
complete suprathreshold, noise always degrades the signal detection
both in the single threshold system and in the parallel array of
threshold devices. (2) When the signal is a little subthreshold, noise
degrades signal detection in the single threshold system. But in the
parallel array, noise can improve signal detection, i.e., stochastic
resonance (SR) exists in the array. (3) When the signal is predominant
subthreshold, noise always can improve signal detection and SR
always exists not only in the single threshold system but also in the
parallel array. (4) Array can improve signal detection by raising the
number of threshold devices. These results extend further the
applicability of SR in signal detection.
Abstract: In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.
Abstract: Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.
Abstract: Polarization-interferometric nonlinear confocal
microscopy is proposed for measuring a nano-sized particle with
optical anisotropy. The anisotropy in the particle was
spectroscopically imaged through a three-dimensional distribution of
third-order nonlinear dielectric polarization photoinduced.
Abstract: In order to consider the effects of the higher modes in
the pushover analysis, during the recent years several multi-modal
pushover procedures have been presented. In these methods the
response of the considered modes are combined by the square-rootof-
sum-of-squares (SRSS) rule while application of the elastic modal
combination rules in the inelastic phases is no longer valid. In this
research the feasibility of defining an efficient alternative
combination method is investigated. Two steel moment-frame
buildings denoted SAC-9 and SAC-20 under ten earthquake records
are considered. The nonlinear responses of the structures are
estimated by the directed algebraic combination of the weighted
responses of the separate modes. The weight of the each mode is
defined so that the resulted response of the combination has a
minimum error to the nonlinear time history analysis. The genetic
algorithm (GA) is used to minimize the error and optimize the weight
factors. The obtained optimal factors for each mode in different cases
are compared together to find unique appropriate weight factors for
each mode in all cases.
Abstract: In many applications, magnetic suspension systems
are required to operate over large variations in air gap. As a result,
the nonlinearities inherent in most types of suspensions have a
significant impact on performance. Specifically, it may be difficult to
design a linear controller which gives satisfactory performance,
stability, and disturbance rejection over a wide range of operating
points. in this paper an optimal controller based on discontinuous
mathematical model of the system for an electromagnetic suspension
system which is applied in magnetic trains has been designed .
Simulations show that the new controller can adapt well to the
variance of suspension mass and gap, and keep its dynamic
performance, thus it is superior to the classic controller.
Abstract: This article is dedicated to development of
mathematical models for determining the dynamics of
concentration of hazardous substances in urban turbulent
atmosphere. Development of the mathematical models implied
taking into account the time-space variability of the fields of
meteorological items and such turbulent atmosphere data as vortex
nature, nonlinear nature, dissipativity and diffusivity. Knowing the
turbulent airflow velocity is not assumed when developing the
model. However, a simplified model implies that the turbulent and
molecular diffusion ratio is a piecewise constant function that
changes depending on vertical distance from the earth surface.
Thereby an important assumption of vertical stratification of urban
air due to atmospheric accumulation of hazardous substances
emitted by motor vehicles is introduced into the mathematical
model. The suggested simplified non-linear mathematical model of
determining the sought exhaust concentration at a priori unknown
turbulent flow velocity through non-degenerate transformation is
reduced to the model which is subsequently solved analytically.
Abstract: Robot manipulators are highly coupled nonlinear
systems, therefore real system and mathematical model of dynamics
used for control system design are not same. Hence, fine-tuning of
controller is always needed. For better tuning fast simulation speed
is desired. Since, Matlab incorporates LAPACK to increase the speed
and complexity of matrix computation, dynamics, forward and
inverse kinematics of PUMA 560 is modeled on Matlab/Simulink in
such a way that all operations are matrix based which give very less
simulation time. This paper compares PID parameter tuning using
Genetic Algorithm, Simulated Annealing, Generalized Pattern Search
(GPS) and Hybrid Search techniques. Controller performances for all
these methods are compared in terms of joint space ITSE and
cartesian space ISE for tracking circular and butterfly trajectories.
Disturbance signal is added to check robustness of controller. GAGPS
hybrid search technique is showing best results for tuning PID
controller parameters in terms of ITSE and robustness.
Abstract: In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.
Abstract: In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.
Abstract: In this paper, a system level behavioural model for RF
power amplifier, which exhibits memory effects, and based on multibranch
system is proposed. When higher order terms are included,
the memory polynomial model (MPM) exhibits numerical
instabilities. A set of memory orthogonal polynomial model
(OMPM) is introduced to alleviate the numerical instability problem
associated to MPM model. A data scaling and centring algorithm was
applied to improve the power amplifier modeling accuracy.
Simulation results prove that the numerical instability can be greatly
reduced, as well as the model precision improved with nonlinear
model.
Abstract: In the present article, nonlinear vibration analysis of
single layer graphene sheets is presented and the effect of small
length scale is investigated. Using the Hamilton's principle, the three
coupled nonlinear equations of motion are obtained based on the von
Karman geometrical model and Eringen theory of nonlocal
continuum. The solutions of Free nonlinear vibration, based on a one
term mode shape, are found for both simply supported and clamped
graphene sheets. A complete analysis of graphene sheets with
movable as well as immovable in-plane conditions is also carried out.
The results obtained herein are compared with those available in the
literature for classical isotropic rectangular plates and excellent
agreement is seen. Also, the nonlinear effects are presented as
functions of geometric properties and small scale parameter.