• Steel and Composite Structures
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• 제26권1호
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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.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Bulletin of the Korean Chemical Society
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• 제7권4호
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• pp.262-266
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• 1986

A multi-reference many-body perturbation theory (MRMBPT) method is critically tested in second order by comparing with the corresponding configuration interaction (CI) calculations. Excitation energies of the four-valence-electron states of transition metal atoms and ions are used for the comparison. The agreement between the second order MRMBPT and CI calculations is very reasonable, confirming the reliability of the second order MRMBPT method. The reliability of calculations with the present second order MRMBPT method was only been inferred empirically in the past since most results have been gauged by the agreement with experiment and/or with other MRMBPT calculations based upon different sets of orbitals and configuration spaces. The present MRMBPT method appears to be an efficient ab initio multi-reference method for the calculation of electron correlation effects in atoms and molecules, and it is shown how MRMBPT can be used to estimate core-core and core-valence correlation effects which are often omitted in CI calculations because too many configurations and correlating electrons are involved.

• 대한조선학회논문집
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• 제58권6호
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• pp.348-357
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• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• International Journal of Computer Science & Network Security
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• 제23권10호
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• pp.81-88
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• 2023

In the present scenario, enormous amounts of data are produced every second. These data also contain private information from sources including media platforms, the banking sector, finance, healthcare, and criminal histories. Data mining is a method for looking through and analyzing massive volumes of data to find usable information. Preserving personal data during data mining has become difficult, thus privacy-preserving data mining (PPDM) is used to do so. Data perturbation is one of the several tactics used by the PPDM data privacy protection mechanism. In Perturbation, datasets are perturbed in order to preserve personal information. Both data accuracy and data privacy are addressed by it. This paper will explore and compare several perturbation strategies that may be used to protect data privacy. For this experiment, two perturbation techniques based on random projection and principal component analysis were used. These techniques include Improved Random Projection Perturbation (IRPP) and Enhanced Principal Component Analysis based Technique (EPCAT). The Naive Bayes classification algorithm is used for data mining approaches. These methods are employed to assess the precision, run time, and accuracy of the experimental results. The best perturbation method in the Nave-Bayes classification is determined to be a random projection-based technique (IRPP) for both the cardiovascular and hypothyroid datasets.

• Bulletin of the Korean Chemical Society
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• 제20권11호
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• pp.1281-1287
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• 1999

The low-lying electronic states of diazirine and 3,3'-dimethyldiazirine have been studied by high level ab initio quantum chemical methods. The equilibrium geometries of the ground state and the first excited singlet and triplet states have been optimized using the Hartree-Fock (HF) and complete active space SCF (CASSCF) methods, as well as using the Møller-Plesset second order perturbation (MP2) theory and the single configuration interaction (CIS) theory. It was found that the first excited singlet state is of 1 B1 symmetry resulting from the n- π* transition, while the first excited triplet state is of 3 B2 symmetry resulting from the π- π* transition. The harmonic vibrational frequencies have been calculated at the optimized geometry of each electronic state, and the scaled frequencies have been compared with the experimental frequencies available. The adiabatic and vertical transition energies from the ground electronic state to the low-lying electronic states have been estimated by means of multireference methods based on the CASSCF wavefunctions, i.e., the multiconfigurational quasidegenerate second order perturbation (MCQDPT2) theory and the CASSCF second-order configuration interaction (CASSCF-SOCI) theory. The vertical transition energies have also been calculated by the CIS method for comparison. The computed transition energies, particularly by MCQDPT2, agree well with the experimental observations, and the electronic structures of the molecules have been discussed, particularly in light of the controversy over the existence of the so-called second electronic state.

• Structural Engineering and Mechanics
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• 제27권3호
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• 전산구조공학
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• 제7권3호
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• pp.115-122
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• 1994

불확정 구조계획의 선형 고유치 문제는 재료정수나 경게조건 및 외부하중 등에 결정론적으로 사용할 수 없는 확률량을 포함하고 있다. 변동량을 내포한 고유치 문제의 해석은 기대치에 대한 지배 방정식과 변동량 결정방정식을 고려해야 한다. 비선형성이 심한 구조계를 선형화할 대 일차 및 이차 변동값을 반영함으로 고유치의 정도를 향상시킬 수 있다. 매개변수에 불확정성을 포함한 고유치 문제는 최적설계 정식화에서 변동된 값을 고료해 줌으로 신뢰성 있는 설계가 된다. 최적설계 알고리즘 중에는 목적함수와 제한 조건식의 설계 민감도를 요한다. 이차 기울기에 근거를 둔 최적설계 수행시에 변동량에 고려하여 제한식으로 설정하고, 설계 민감도를 구할 수 있는 방법을 제시하였다.

• 천문학회지
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• 제40권2호
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• pp.49-60
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• 2007

This paper deals with the theory for rotational motion of a two-layer Earth model (an inelastic mantle and liquid core) including the dissipation in the mantle-core boundary(CMB) along with tidal effects produced by Moon and Sun. An analytical solution being derived using Hori's perturbation technique at a second order Hamiltonian. Numerical nutation series will be deduced from the theory.

• Advances in aircraft and spacecraft science
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• 제4권5호
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.