• Journal of Biosystems Engineering
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• v.41 no.3
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• pp.170-176
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• 2016

Purpose: This study aimed to improve the method for determining the position of the center of gravity for agricultural tractors. Methods: The proposed method uses trigonometric functions and coordinate transformation. Data were measured according to the ISO 789-6 test procedures for the center of gravity of agricultural tractors. The height calculated using the proposed method was compared with that determined from an AutoCAD drawing. To find the center of gravity of the tractor, the algorithm for finding the intersection of the two lines was used. Results: The vertical height from the ground to the center of gravity is 682.06 mm. The vertical coordinates obtained from the calculation and the drawing were the same. Conclusions: The developed method uses trigonometric and polar coordinate transformation. The method was compared and verified with the AutoCAD drawing results. The results indicate that users can apply this developed method instead of the plotting method which is an inconvenient and time-consuming. Further, users can program Microsoft Excel to easily determine the vertical coordinate. In addition, researchers will propose this method to the ISO as a standard method for determining the center of gravity in accordance with ISO 789-6.

• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• The KSFM Journal of Fluid Machinery
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• v.18 no.6
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• pp.71-75
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• 2015

The flow and noise characteristics of the regenerative blower are evaluated experimentally. To decrease the noise of regenerative blower at a high frequency, we arrange the impeller vanes unevenly by special formula. The uneven pitch formular consists of the combination of trigonometric function. The magnitude of degree between each vanes and the control parameters of trigonometric functions are main design parameters for the uneven pitch. The flow characteristics of even and uneven impellers are tested by the fan tester and compared each results. The efficiency of a blower is calculated by the axial power using a dynamo system. The noise property of designed impeller is measured in an anechoic room. In this study, we certify that the uneven pitch impeller is effective in the noise reduction at a high frequency.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.121-123
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• 2015

We report our measurements of the trigonometric distance and proper motion of IRAS 20056+3350, obtained from the annual parallax of $H_2O$ masers. Our distance of $D=4.69^{+0.65}_{-0.51}kpc$, which is 2.8 times larger than the near kinematic distance adopted in the literature, places IRAS 20056+3350 at the leading tip of the Local arm and proximal to the Solar circle. We estimated the proper motion of IRAS 20056+3350 to be (${\mu}_{\alpha}cos{\delta}$, ${\mu}_{\delta}$) = ($-2.62{\pm}0.33$, $-5.65{\pm}0.52$) $mas\;yr^{-1}$ from the group motion of $H_2O$ masers, and use our results to estimate the angular velocity of Galactic rotation at the Galactocentric distance of the Sun, ${\Omega}_0=29.75{\pm}2.29km\;s^{-1}kpc^{-1}$, which is consistent with the values obtained for other tangent points and Solar circle objects.

• The Journal of Information Technology
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• v.8 no.3
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• pp.1-10
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• 2005

Cosine and Sine function is widely used for the arithmetic, translation, object drawing, Simulation and etc. of Computer Graphics in Natural Science and Engineering. In general, Cordic Algorithm is effective method since it has relatively small size and simple architecture on trigonometric function generation. However profitably it has those merits, the problem of operation speed is occurred. In graphic display system, the operation result of object drawing is quantized and has the condition that is satisfied with rms error less than 1. So in this paper, the proposed generator is composed of partition operation at each ${\pi}/4$ and basic Cosine, Sine function generator in the range of $0{\sim}{\pi}/4$ using the lower order of Tayler's series in an acceptable error range, that enlarge the range of $0{\sim}2{\pi}$ according to a definition of the trigonometric function for the purpose of having a high speed Cosine, Sine function generation. And, division operator using code partition for divisor three is proposed, the proposed function generator has high speed operation, but it has the problems in the other application parts with accurate results, is need to increase the speed of the multiplication.

• Steel and Composite Structures
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• v.18 no.2
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• pp.409-423
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• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• Wind and Structures
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• v.28 no.1
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• pp.19-30
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• 2019

This article present the free vibration analysis of simply supported perfect and imperfect (porous) FG beams using a high order trigonometric deformation theory. It is assumed that the material properties of the porous beam vary across the thickness. Unlike other theories, the number of unknown is only three. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the beams are simply supported the Navier's procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature.

• Advances in materials Research
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• v.12 no.2
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• pp.161-177
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• 2023

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

• Journal of The Korean Association of Information Education
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• v.21 no.2
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• pp.199-208
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• 2017

The present study investigates the potential of an educational programming game as a strategy for enhancing effective domains of mathematics curriculum, which has been criticized as a problem of education in Korea. The process of programming Fortress, an educational game, in conjunction with the lesson on the trigonometric function as part of the middle school mathematics curriculum, was designed for instruction and learning, and its effectiveness was tested. The study was conducted using a nonequivalent pretest-posttest experimental design. Research procedures included the following steps: (1) both the experimental and the comparison groups participated in four classes to understand and apply the concept of the trigonometric function, and (2) the experimental group participated in Fortress game programming activities using Scratch, which was designed in this study, while the comparison group participated in solving a real-life trigonometric problem - calculating the height of a building using the concept of trigonometry. The results of the t-test showed that students' interest and perceived value of the mathematics curriculum were significantly higher in the experimental group than in the comparison group. However, the results of analysis of covariance (ANCOVA) using pretest scores of the interest and perceived value showed the influence of pretest scores on posttest scores for the interest level, although the effect of the experiment on the perceived value of the mathematics curriculum was more significant.

• Journal of Veterinary Clinics
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• v.22 no.2
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• pp.79-83
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• 2005

Six dogs including 4 dogs living in different geographic locations of Kangwon province and 2 client-owned dogs were used to determine the periodicity of microfilariae of D. immitis using a trigonometric model. The calculated periodicity index was ranged from 25.6 to $95.5\%$ with mean of $57.6\%$, and the estimated hour of peak was approximately 21:00 hrs (range, 20:04-21:29 hrs) and minimum counts at 09:00 hrs (range, 08:04 - 09:29 hrs). Correlation coefficient between the observed and the expected count from the model varies depending on dogs, ranging from 6.4 to $49.2\%$. Based on this study, the periodicity of microfilariae of D. immitis was considered as nocturnally sub-periodic for all dogs employed. This result is in consistent with previous report in peak hour but different in minimal hour, indicating that further studies on the periodicity need to be performed to better understanding the dynamics of the periodicity and to help practitioners in the choice of the time for examination of the dogs.