• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.20 no.2
• /
• pp.72-79
• /
• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.7
• /
• pp.1127-1140
• /
• 1997

With the study for identifying the transmission characteristics of vibration and noise generated by operating engine system of a vehicle, recently many engineers have studied actively the reduction of vibration and noise inducing uncomfortableness to the passenger. In this study, output noise was analyzed by multi-dimensional spectral analysis and vector synthesis method. The multi-dimensional analysis method is very effective in case of identification of primary source, but this method has little effect on suggestion for interior noised reduction. For compensation of this, vector synthesis method was used to obtain effective method for interior noise reduction, after identifying primary source for output noise. In this paper, partial coherence function of each input was calculated to know which input was most coherent to output noise, then with simulation of changes for input magnitude and phase by vector synthesis diagram, the trends of synthesized output vector was obtained. As a result, the change of synthesized output vector could be estimated.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.201-211
• /
• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Wind and Structures
• /
• v.27 no.3
• /
• pp.149-161
• /
• 2018

A reliability analysis method is proposed in this paper based on the maximum entropy (MaxEnt) principle in which constraints are specified in terms of the fractional moments instead of integer moments. Then a multiplicative dimensional reduction method (M-DRM) is introduced to compute the fractional moments. The method is applicable for both explicit and implicit limit state functions of complex structures. After two examples illustrate the accuracy and efficiency of this method in comparison to the Monte Carlo simulation (MCS), the method is used to analyze the flutter reliability of suspension bridge. The results show that the empirical formula method in which the limit state function is explicitly represented as a function of variables is only a too conservative estimate for flutter reliability analysis but is not accurate adequately. So it is not suitable for reliability analysis of bridge flutter. The actual flutter reliability analysis should be conducted based on a finite element method in which limit state function is implicitly represented as a function of variables. The proposed M-DRM provide an alternate and efficient way to analyze a much more complicated flutter reliability of long span suspension bridge.

• The Korean Journal of Applied Statistics
• /
• v.36 no.4
• /
• pp.323-335
• /
• 2023

In causal analysis of high dimensional data, it is important to reduce the dimension of covariates and transform them appropriately to control confounders that affect treatment and potential outcomes. The augmented inverse probability weighting (AIPW) method is mainly used for estimation of average treatment effect (ATE). AIPW estimator can be obtained by using estimated propensity score and outcome model. ATE estimator can be inconsistent or have large asymptotic variance when using estimated propensity score and outcome model obtained by parametric methods that includes all covariates, especially for high dimensional data. For this reason, an ATE estimation using an appropriate dimension reduction method and semiparametric model for high dimensional data is attracting attention. Semiparametric method or sparse sufficient dimensionality reduction method can be uesd for dimension reduction for the estimation of propensity score and outcome model. Recently, another method has been proposed that does not use propensity score and outcome regression. After reducing dimension of covariates, ATE estimation can be performed using matching. Among the studies on ATE estimation methods for high dimensional data, four recently proposed studies will be introduced, and how to interpret the estimated ATE will be discussed.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.219-231
• /
• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.211-218
• /
• 2009

We investigate the multiple solutions for a suspending beam equation with jumping nonlinearity crossing three eigenvalues, with Dirichlet boundary condition and periodic condition. We show the existence of at least six nontrivial periodic solutions for the equation by using the finite dimensional reduction method and the geometry of the mapping.

• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.1-24
• /
• 2008

Let $Lu=u_{tt}+u_{xxxx}$ and E be the complete normed space spanned by the eigenfunctions of L. We reveal the existence of six nontrivial solutions of a nonlinear suspension bridge equation $Lu+bu^+=1+{\epsilon}h(x,t)$ in E when the nonlinearity crosses three eigenvalues. It is shown by the critical point theory induced from the limit relative category of the torus with three holes and finite dimensional reduction method.

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.443-468
• /
• 2008

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

• Journal of Industrial Technology
• /
• v.26 no.B
• /
• pp.43-51
• /
• 2006

Through the result of calculating the deviation between the value calculated from two-dimensional number formula, one-dimensional number interpretation, and curving part water surface type calculation method, we could confirmed that the deviation is reduced more than 50% when we use curving part water surface type calculation method. Also it was confirmed that there occurs the reduction rate of maximum 59% as the result of comparing with one-dimensional number interpretation since the reduction rate of safe room height was 20%, in 500 CMS of flood water quantity when we planted the construction of levee by curving part water surface type calculation method. And therefore, we have confirmed that the curving water surface type calculation method can be used as a simple formula in rivers with water quantity less than 500 CMS that flows in and out in Jess than 90 degree angle.