• Journal of Korean Society of Steel Construction
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• v.21 no.4
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• pp.433-442
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• 2009

In this paper, new three-dimensional vibration data for the solid cylinders of the N-sided polygonal cross-section with V-notches or sharp cracks are presented, and a Ritz procedure is employed, which incorporates a mathematically complete set of algebraic-trigonometric polynomials in conjunction with an admissible set of edge functions that explicitly model the tri-axial stress singularities that exist along a terminus edge of the V-notch. Convergence studies demonstrate the necessity of adding the edge functions to achieve the accurate frequencies and mode shapes of N-sided polygonal cylindrical solids with stress singularities.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.12
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• pp.75-81
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• 2004

AE-CORDIC improves the CORDIC operation speed with a rotation direction pre-computation algorithm. Its CORDIC iteration stages consist of non-predictable rotation direction states and predictable rotation stages. The non-predictable stages are replaced with lookup-table which has smaller hardware size than CORDIC iteration stages. The predictable stages can determine rotation direction with the input angle and simple encoder. In this paper, a rotation direction pre-computation algorithm with input angle encoder is proposed. and AE-CORDIC which have optimized Lookup-table is compared with the P-CORDIC algorithm. Hardware size, delay, and SQNR of the AE-CORDIC are verified with Samsung 0.18㎛ technology and Synopsys design compiler when input angle bit length is 16.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.47-64
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• 2015

This paper presents the effect of hybridization material on variation of critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the principle of virtual displacement; the formulation is based on a new trigonometric shape function of displacement taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

• Journal of Power Electronics
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• v.15 no.1
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• pp.131-145
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• 2015

The voltage-source inverters (VSI) supplying a motor drive are prone to open transistor faults. To address this issue in fault-tolerant drives applicable to electric vehicles, a new open transistor fault diagnosis (FD) method is presented in this paper. According to the proposed method, in order to define the FD index, the phase angle of the converter output current is estimated by a simple trigonometric function. The proposed FD method is adaptable, simple, capable of detecting multiple open switch faults and robust to load operational variations. Keeping the FD in mind as a mandatory part of the fault tolerant control algorithm, the FD block is applied to a five-phase converter supplying a multiphase fault-tolerant PM motor drive with non-sinusoidal unbalanced current waveforms. To investigate the performance of the FD technique, the fault-tolerant sliding mode control (SMC) of a five-phase brushless direct current (BLDC) motor is developed in this paper with the embedded FD block. Once the theory is explained, experimental waveforms are obtained from a five-phase BLDC motor to show the effectiveness of the proposed FD method. The FD algorithm is implemented on a field programmable gate array (FPGA).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.11
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• pp.5347-5356
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• 2011

In this paper, we compared various shear deformation functions for modelling anti-symmetric composite sandwich plates discretized by a mixed finite element method based on the Lagrangian/Hermite interpolation functions. These shear deformation theories uses polynomial, trigonometric, hyperbolic and exponential functions through the thickness direction, allowing for zero transverse shear stresses at the top and bottom surfaces of the plate. All shear deformation functions are compared with other available analytical/3D elasticity solutions, As a result, reasonable accuracy for investigated problems are predicted. Particularly, The present results show that the use of exponential shear deformation theory provides very good solutions for composite sandwich plates.

• Steel and Composite Structures
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• v.30 no.6
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.101-101
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• 2020

Traditional stochastic simulation of hydroclimatological variables often underestimates the variability and correlation structure of larger timescale due to the difficulty in preserving long-term memory. However, the Long Short-Term Memory (LSTM) model illustrates a remarkable long-term memory from the recursive hidden and cell states. The current study, therefore, employed the LSTM model in stochastic generation of hydrologic and climate variables to examine how much the LSTM model can preserve the long-term memory and overcome the drawbacks of conventional time series models such as autoregressive (AR). A trigonometric function and the Rössler system as well as real case studies for hydrological and climatological variables were tested. Results presented that the LSTM model reproduced the variability and correlation structure of the larger timescale as well as the key statistics of the original time domain better than the AR and other traditional models. The hidden and cell states of the LSTM containing the long-memory and oscillation structure following the observations allows better performance compared to the other tested conventional models. This good representation of the long-term variability can be important in water manager since future water resources planning and management is highly related with this long-term variability.

• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.1-18
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• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• School Mathematics
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• v.15 no.1
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• pp.159-177
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• 2013

This study is a case study of STEAM education. We have developed teaching and learning materials, suggested teaching method, and analysed the result for exploring the potential and effect of STEAM. The content of this study is based on the history of mathematics. Science (S) is related to the 24 divisions of the year, the height of the sun, the movement of heavenly bodies. Technology (T) is related to the exploration with graphic calculators. Engineering (E) is related to design sundial and research on the design principles. Art (A) is related to literature review about mathematical history, the understanding of the value of the mathematics. Mathematics (M) is related to the trigonometric functions. We have considered that Project-Based Learning is proper teaching and learning for STEAM education, we have designed the STEAM PBL and analysed the results focused on the developing integrative knowledge, mathematical attitude including mathematical value, the competencies of 21 century. The result of this study is as follows. We find that STEAM education activates students' collaboration, communication skills and improves representation and critical thinking skills. Also STEAM education makes positive changes of students' mathematical attitudes including the values of the mathematics.