• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1434-1439
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• 2008

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.103-120
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• 2002

A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.2
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• pp.179-184
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• 2005

First lactation records (174) of Jersey${\times}$Sahiwal and Holstein Friesian${\times}$Sahiwal half breds under 9 sires maintained at Chandra Shekher Azad University of Agriculture and Technology, Kanpur, Uttar Pradesh, India from 1975-1983, were used to estimate the genetic parameters and to predict herd life milk yield and average milk yield per day of herd life from first lactation traits. The traits included were: age at first calving, first service period, first lactation period, first calving interval, first lactation milk yield, milk yield per day of first calving interval, herd life milk yield, herd life and average milk yield per day of herd life. Most of the production and reproduction traits were found to have positive and significant correlations between them on genetic as well as phenotypic scales. Total twelve regression equations were fitted. The prediction equation of herd life milk yield in both the genetic groups showed linear relationship with AFC, FSP, FLP, FLMY and MY/DCI and was apparent and significant. Similarly, polynomials for milk yield per day of herd life for J${\times}$S and HF${\times}$S half breds also showed linear trend, which was found highly significant. The highest and lowest $R^2$ values were found for FCI and AFC, respectively.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.485-498
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• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.8
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• pp.693-700
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• 2016

In this paper, it is represented that equations for design of linear interferometer antenna when the 3 dB beamwidth is only region of interest. Using the equations, relationships between angle measurement ambiguity and element antenna spacings are described. And then, operating frequency, angle measurement accuracy, beamwidth, correct measurement probability are calculated for five antennas interferometer to measure azimuth and elevation angle. The interferometer antenna was designed and fabricated using the calculated parameters. The angle measurement accuracy were $0.01^{\circ}$ and $0.016^{\circ}$ for azimuth and elevation axes with 99 % probability of doing measurements correctly which means that ambiguous solution did not occur more than 1 % of the time. These results validated the equations and design procedures.

• Journal of the Korean Chemical Society
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• v.7 no.4
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• pp.238-244
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• 1963

Linear relationships between thermodynamic parameters, ,${\Delta}{\Delta}H^{\neq}=a{\sigma}+b{\Delta}{\Delta}S^{\neq}$, and $\Delta{\Delta}F^\neq=a\sigma+(b-T)\Delta{\Delta}S^\neq$, which were derived in the previous report have been tested with 57 reactions from literature. Linearities of plots $\Delta{\Delta}H^\neq-a\sigma$ vs. $\Delta{\Delta}S^\neq$ were generally good and the average correlation coefficient was 0.983 and the average of standard deviations from regression lines was 0.11. For 15 out of 57 reactions, Hammett plots were unsatisfactory and most of the reaction did not satisfy the Leffler equation. The general applicability of the new equations has been confirmed by the analysis of each reaction for which existing equations failed to correlate.

• Journal of the Earthquake Engineering Society of Korea
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• v.21 no.1
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• pp.1-9
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• 2017

The scale of disaster and damage witnessed in the 2004 Indian Ocean Tsunami and the 2011 Great East Japan Tsunami has motivated researchers in developing foolproof disaster mitigation techniques for safety of coastal communities. This study focuses on developing tsunami hazard map by numerical modeling at Imwon Port to minimize losses of human beings and property damage when a real tsunami event occurs. A hazard map is developed based on inundation maps obtained by numerical modeling of 3 past and 11 virtual tsunami cases. The linear shallow-water equations with manipulation of frequency dispersion and the non-linear shallow-water equations are employed to obtain inundation maps. The inundation map gives the maximum extent of expected flooded area and corresponding inundation depths which helps in identifying vulnerable areas for unexpected tsunami attacks. The information can be used for planning and developing safety zones and evacuation structures to minimize damage in case of real tsunami events.