• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• 대한전기학회논문지
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• 제41권3호
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• pp.300-310
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• 1992

This paper deals with the problem of robust pole-assignment control for linear systems with structured uncertainty. It considers two cases whose colsed-loop characteristic equations are presented as a family of interval polynomial and polytopic polynomial family respectively. We propose a method of finding the pole-placement region in which the fixed gain controller guarantees the required damping ratio and stability margin despite parameter perturbation. Some results of Kharitonov like stability and two kinds of transformations are included. As an illustrative example, we show that the proposed method can apply effectivly to the single magnet levitation system including some uncertainties (mass, inductance etc.).

• Korea-Australia Rheology Journal
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• 제20권4호
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• pp.189-196
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• 2008

The pulsatile flow of blood through a stenosed artery under the influence of external periodic body acceleration is studied. The effect of non-Newtonian nature of blood in small blood vessels has been taken into account by modeling blood as a Casson fluid. The non-linear coupled equations governing the flow are solved using perturbation analysis assuming that the Womersley frequency parameter is small which is valid for physiological situations in small blood vessels. The effect of pulsatility, stenosis, body acceleration, yield stress of the fluid and pressure gradient on the yield plane locations, velocity distribution, flow rate, shear stress and frictional resistance are investigated. It is noticed that the effect of yield stress and stenosis is to reduce flow rate and increase flow resistance. The impact of body acceleration is to enhance the flow rate and reduces resistance to flow.

• 한국소음진동공학회논문집
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• 제20권9호
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• pp.849-855
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• 2010

Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.

• 소음진동
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• 제9권6호
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• pp.1218-1226
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• 1999

In this paper, the extended Biot's semilinear model was developed. Combining the extended Biot model with the dynamic equation yields the nonlinear wave equation in poproelastic sound absorbing materials. Both perturbation and matching techniques are used to find solutions for nonlinear wave equations. By comparing results between linear and nonlinear wave solutions, characteristics of nonlinear waves in poroelastic sound abosrbing materials have been studied. Nonlinear waves were found to be attenuated faster than the linear ones. A maximum amplitude of the nonlinear wave occurred near its surface boundaries and decay quickly with distance from the surface. It has also been found that, if the amplitudes of linear waves are known at the surface boundaries, those of nonlinear ones can be determined. This will be the basis of finding effects of nonlinearity on the absorption coefficient and the transmission loss.

• Structural Engineering and Mechanics
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• 제31권5호
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• pp.481-506
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• 2009

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

• 대한조선학회논문집
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• 제28권1호
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• pp.69-82
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• 1991

축방향의 주기적인 하중으로 가진되는 긴 수직보의 동적안정성에 관하여 연구하였다. 해석방법으로서 Galerkin방법을 이용하여 무한원 연립 Mathieu형 미분 방정식을 얻었으며, 안정성영역을 나타내는 도표를 얻기 위하여, 섭동법과 수치적인 방법을 사용하였다. 또한 이두가지 방법으로 구한 결과를 서로 비교 검토하였다. 여러가지 경계조건에 대한 안정영역을 구했으며, 김쇠의 영향, 평균인장력 및 다중 주파수 파라메터 기진의 영향에 관해서 집중적으로 연구하였다.

• 대한화학회지
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• 제14권1호
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• pp.127-131
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• 1970

The variational approach for the direct evaluation of the energy difference ${\Delta}$E is studied. The method is based on the differential equation corresponding to the integral Hellmann-Feynman formula. The ${\Delta}$E is given by the expectation value of the Hermitian operator which does not involve the 1/$r_{ij}$ term. Because of its variational nature of the method, the coupling problem of the differential equations which are encountered in perturbation treatment does not occur. The method is applied to the evaluation of the electric polarizabilities of the Helium isoelectronic series atoms. The result is in good agreement with the experiment. The method is compared with the recent works of Karplus et al.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• Structural Engineering and Mechanics
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• 제62권2호
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• pp.171-178
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• 2017

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.