• International Journal of Aerospace System Engineering
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• 제6권2호
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• pp.1-10
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• 2019

In this paper, the probabilistic free vibration analysis of a geometrically coupled cantilever wing with uncertain material properties is carried out using stochastic finite element (SFEM) based on first order perturbation technique. Here, both stiffness and damping of the system are considered as random parameters. The bending and torsional rigidities are assumed as spatially varying second order Gaussian random fields and represented by Karhunen Loeve (K-L) expansion. Here, the expected value, standard deviation, and probability distribution of random natural frequencies and damping ratios are computed. The results obtained from the present approach are also compared with Monte Carlo simulations (MCS). The results show that the uncertain bending rigidity has more influence on the damping ratio and frequency of modes 1 and 3 while uncertain torsional rigidity has more influence on the damping ratio and frequency of modes 2 and 3.

• Structural Engineering and Mechanics
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• 제56권5호
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• pp.767-785
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• 2015

The stochastic finite element method is employed to obtain a stochastic dynamic model of angled beams subjected to impact loads when uncertain material properties are described by random fields. Using the perturbation technique in conjunction with a precise time integration method, a random analysis approach is developed for efficient analysis of random elastic waves. Formulas for the mean, variance and covariance of displacement, strain and stress are introduced. Statistics of displacement and stress waves is analyzed and effects of bend angle and material stochasticity on wave propagation are studied. It is found that the elastic wave correlation in the angled section is the most significant. The mean, variance and covariance of the stress wave amplitude decrease with an increase in bend angle. The standard deviation of the beam material density plays an important role in longitudinal displacement wave covariance.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.19-27
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• 1999

An orientation-shift model for unit random vectors in $R^3$ is defined. The Euler angles are introduced to parametrize orientation-shifts and their moment estimators are found. Through the analytic perturbation method, the asymptotic distributions of the estimators are obtained.

• Geotechnical Engineering
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• 제5권2호
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• pp.33-44
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• 1989

In this paper, uncertainties in dynamic soil structure interaction (SSI) of nuclear poi.or plants subjected to seismic loading are studied considering the random characteristics of soils surround- ing the structure. Firstly sensitivity analysis is performed to study the effect of uncertain dynamic soil properties on the response of the structure. Secondly, to take into account the non-neterministic characteristics in analysis caused by random characteristics of the soil properties, Perturbation method and Rosenblueth's Two point estimates were used for this studu. The procedure is based on the comptex response method which is constituted by a combined usage of conventional finite elements for the near field and infinite elements for the far field. Results of the sensitivity analysis show that dynamic soil properties greatly affect the response of the sol.uc- lure. Results of the probabilistic analysis show that the Two-point estimate method produces good agreements with the Perturbation method.

• Structural Engineering and Mechanics
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• 제13권1호
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• pp.53-74
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• 2002

Composites exhibit larger dispersion in their material properties compared to conventional materials due to larger number of parameters associated with their manufacturing processes. A $C^0$ finite element method has been used for arriving at an eigenvalue problem using higher order shear deformation theory for initial buckling of laminated composite plates. The material properties have been modeled as basic random variables. A mean-centered first order perturbation technique has been used to find the probabilistic characteristics of the buckling loads with different edge conditions. Results have been compared with Monte Carlo simulation, and those available in literature.

• Computational Structural Engineering
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• 제7권3호
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• pp.115-122
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• 1994

Design sensitivity analysis of the second order perturbed eigenproblems for random structural system is presented. Dynamic response of random system including uncertainties for the design variable is calculated with the first order and second order perturbation method to original governing equation. In optimal design methods, there is fundamental requirement for design gradients. A method for calculating the sensitivity coefficients is developed using the direct differentiation method for the governing equation and first order and second order perturbed equation.

• Advances in Computational Design
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• 제2권3호
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• Structural Engineering and Mechanics
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• 제11권4호
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• pp.373-392
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• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• The Transactions of the Korean Institute of Electrical Engineers C
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• 제49권4호
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• pp.249-257
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• 2000

In this paper, we propose the use of stochastic finite element method, that is popularly employed in mechanical structure analysis, for more practical designing purpose of RF device. The proposed method is formulated based on the vector finite element method cooperated by pertubation analysis. The method utilizes sensitivity analysis algorithm with covariance matrix of the random variables that represent for uncertain physical quantities such as length or various electrical constants to compute the probabilities of the measure of performance of the structure. For this computation one need to know the variance and covariance of the random variables that might be determined by practical experiences. The presenting algorithm has been verified by analyzing several device with different be determined by practical experiences. The presenting algorithm has been verified by analysis several device with different measure of performanes. For the convenience of formulation, two dimensional analysis has been performed to apply it into waveguide with dielectric slab. In the problem the dielectric constant of the dielectric slab is considered as random variable. Another example is matched waveguide and cavity problem. In the problem, the dimension of them are assumed to be as random variables and the expectations and variances of quality factor have been computed.

• Proceedings of the KIEE Conference
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• 대한전기학회 2006년도 학술대회 논문집 전문대학교육위원
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• pp.154-158
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• 2006

The switching-mode power converter has been widely used because of its features of high efficiency and small weight and size. These features are brought by the ON-OFF operation of semiconductor switching devices. However, this switching operation causes the surge and EMI(Electromagnetic Interference) which deteriorate the reliability of the converter themselves and entire electronic systems. This problem on the surge and noise is one of the most serious difficulties in AC-to-DC converter. Random Pulse Width Modulation (RPWM) is peformed by adding a random perturbation to switching instant while output-voltage regulation of converter is performed. RPWM method for reducing conducted EMI in single switch three phase discontinuous conduction mode boost converter is presented. The more white noise is injected, the more conducted EMI is reduced. But output-voltage is not sufficiently regulated. This is the reason why carrier frequency selection topology is proposed. In the case of carrier frequency selection, output-voltage of steady state and transient state is fully regulated. A RPWM control method was proposed in order to smooth the switching noise spectrum and reduce it's level. Experimental results are verified by converter operating at 300v/1kW with $5%{\sim}30%$ white noise input. Spectrum analysis is performed on the Phase current and the CM noise voltage. The former is measured with Current Probe and the latter is achieved with LISN, which are connected to the spectrum analyzer respectively.