• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.425-436
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• 1996

An application of the perturbation method to optimum structural design with random parameters is presented. It is formulated on the basis of the first-order stochastic finite element perturbation method. It also takes into full account the stress, displacement and eigenvalue constraints, together with the rates of change of the random variables. A method for calculating the sensitivity coefficients in regard to the governing equation and the first-order perturbed equation has been derived, by using a direct differentiation approach. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.167-175
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• 2001

In this study, a general perturbation method is presented to reanalysis dynamic response of base-isolated systems. The perturbation is expanded to general order and which provide the formulation of perturbed solutions. in which eigensolutions of non-modified system are treated as unperturbed solutions. The accuracy of present method is tested using a 2-DOF system with isolator, where the stiffness and damping coefficients of isolator are changed, respectively, The reanalyzed eigensolutions and response using perturbed solutions are successfully approached to exact ones after just first perturbation. Supposing the practical criterion as ${\pm}5%$ error, the modification range of -50%~30% from original system can be allowed for the first order perturbation. Using higher order solutions, the applicable range will be wide.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.427-440
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• 2000

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.9
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• pp.907-913
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• 2012

High-order perturbation solutions have been obtained for the simple physical model describing the liquid pool spreading with a continuous spill, and these are shown to improve over first-order perturbation solutions. The non-dimensional governing equations for the model are derived to obtain more general solutions. Non-dimensional parameters are sought as the governing parameters for the non-dimensional equations, and the non-dimensional evaporation rate is used as the perturbation parameter. The results show that the high-order solutions exhibit an improvement over the first-order solutions with respect to the pool volume as well as the spreading radius. In addition, as the order of the perturbation solutions increases, the difference between the numerical solutions and the perturbation solutions is significantly reduced. Finally, it is revealed that the third-order solutions are reasonable because they almost agree with the numerical solutions.

• Journal of the Korean Physical Society
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• v.73 no.12
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• pp.1800-1807
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• 2018

In this paper, we study the gravitational perturbation of traversable wormhole spacetime, especially the Morris-Thorne wormhole spacetime, by using the linearized theory of gravity. We restrict our interest to the first order term and ignore the higher order terms. We assume that the perturbation is axisymmetric. We also assume that the time dependence follows the Fourier decomposition and the angular dependence is expressed in terms of the Legendre functions. As a result, we derive the gravitational perturbation equation of traversable wormhole in terms of a single linear second-order differential equation. As a consequence, we could analyze the unstability of the spacetime with the effective potentials. Furthermore, we consider the interaction between the external gravitational perturbation and the exotic matter, constituting traversable wormholes and its effect on the stability of traversable wormholes.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.2
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• pp.1-6
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• 1982

This paper reviews and describes some applications of perturbation theory in the practical analysis of linear systems which involve random parameters. Statistical measures of the system outputs are derived in terms of statistical measures of the system parameters and inputs (i.e., in the way of perturbed linear operator equations). Perturbed state transition matrix is also derived. With simple first-order and second-order linear system models, we compare the accuracy of perturbation results with the exact ones. And the convergence of perturbation series is also investigated.

• Journal of the Optical Society of Korea
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• v.9 no.1
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• pp.6-12
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• 2005

The perturbation approach is applied to solve the nonlinear Schrodinger equation, and its valid range has been determined by comparing with the results of the split-step Fourier method over a wide range of parameter values. With γ= 2㎞/sup -1/mW/sup -1/, the critical distance for the first order perturbation approach is estimated to be(equation omitted). The critical distance, Z/sub c/, is defined as the distance at which the normalized square deviation compared to the split-step Fourier method reaches 10/sup -3/. Including the second order perturbation will increase Z/sub c/ more than a factor of two, but the increased computation load makes the perturbation approach less attractive. In addition, it is shown mathematically that the perturbation approach is equivalent to the Volterra series approach, which can be used to design a nonlinear equalizer (or compensator). Finally, the perturbation approach is applied to obtain the sinusoidal response of the fiber, and its range of validity has been studied.

• Steel and Composite Structures
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• v.26 no.1
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• pp.1-15
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• 2018

This study reported, the effect of random variation in system properties on bending response of single wall carbon nanotube reinforced composite (SWCNTRC) plates subjected to transverse uniform loading is examined. System parameters such as the SWCNT armchair, material properties, plate thickness and volume fraction of SWCNT are modelled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behaviour of the SWCNTRC composite plate. A C0 finite element method in conjunction with the first order perturbation technique procedure developed earlier by the authors for the plate subjected to lateral loading is employed to obtain the mean and variance of the transverse deflection of the plate. The performance of the stochastic SWCNTRC composite model is demonstrated through a comparison of mean transverse central deflection with those results available in the literature and standard deviation of the deflection with an independent First Order perturbation Technique (FOPT), Second Order perturbation Technique (SOPT) and Monte Carlo simulation.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.75-82
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• 2020

In this study, the problem of torsion of bars with open cross section surrounded by corrugated boundaries is analyzed. An approximate analytical solution is given using perturbation technique. First, the stress analysis for circular open cross-section for arbitrary opening angle is formulated and the problem is analytically solved. Second, the open cross-section with corrugated cross section is analyzed using perturbation method. First order contributions to the stresses and the torques have been added. The results have been exemplified and compared by considering special examples.