• Title/Summary/Keyword: Functions of matrices

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Semi-analytical Annular Mindlin Plate Element for Out-of-plane Vibration Analysis of Thick Disks (두꺼운 디스크의 면외 진동 해석을 위한 준-해석적 환상 민드린 평판 요소)

  • Kim, Chang-Boo;Cho, Hyeon Seok;Beom, Hyeon Gyu
    • Journal of the Korean Society for Railway
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    • v.15 no.6
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    • pp.588-596
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    • 2012
  • This paper presents a new semi-analytical annular Mindlin plate element with which out-of-plane natural vibration of thick disks can be analyzed simply, efficiently, and accurately through FEM by including effects of rotary inertia and transverse shear deformation. Using static deformation modes which are exact solutions of equilibrium equations of annular Mindlin plate, the element interpolation functions, stiffness and mass matrices corresponding to each number of nodal diameters are derived. The element is capable of representing out-of-plane rigid-body motions exactly and free from shear locking. Natural frequencies of uniform and multi-step disks with or without concentric ring support are analyzed by applying the presented element. Such results are compared with theoretical predictions of previous works or FEA results obtained by using two-dimensional shell element to investigate the convergence and accuracy of the presented element.

The Finite Element Formulation and Its Classification of Dynamic Thermoelastic Problems of Solids (구조동역학-열탄성학 연성문제의 유한요소 정식화 및 분류)

  • Yun, Seong-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.13 no.1
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    • pp.37-49
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    • 2000
  • This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.

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Phenyl modified silica sol-gel films for photonics (Photonic 재로로서 페닐실리카 코팅막의 특성)

  • Ahn, Bok-Yeop;Seok, Sang-Il;Kim, Joo-Hyeun;Lim, Mi-Ae
    • Proceedings of the Materials Research Society of Korea Conference
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    • 2003.11a
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    • pp.131-131
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    • 2003
  • The advent of photonic technologies in the field of communications and data transmission has been heavily increasing the demand in integrated optical (IO) circuits capable of accomplishing not only simple tasks like signal, but also more sophisticated functions like all-optical signal routing or active multiplexing/demultiplexing. In the last decade, sol-gel technology has been widely used to prepare optical materials. Sol-gel processes show many promises for the development of low-loss, high-performance glass integrated optical circuits. However, crack formation is likely to occur during heat treatment in thick gel films. In order to overcome the critical thickness limitation, the organic-modified silicate has been widely used. In this case coating matrices have been prepared from the organo-silanes of T structures, acidic catalyst and the as-prepared gel films have been heat-treated below 200$^{\circ}C$ to avoid the crack formation and the degradation of organic components. However, the films prepared in the acidic condition and the low heat temperature make the films contain high OH groups which is the major optical loss function. In this work, C$\sub$6/H$\sub$5/SiO$\sub$1.5/ films were prepared on silicon substrate by sol-gel method using base catalyst in a PTMS/NH$_4$OH/H$_2$O/C$_2$H$\sub$5/OH system. The sol showed spinable viscosity at 50 wt% of solid content, and neglectable viscosity change with time. The films were crack-free and transparent after curing at 450 $^{\circ}C$, and highly condensed to minimize OH content in C$\sub$6/H$\sub$5/SiO$\sub$1.5/ networks. The effects of heat treatment of the films are characterized on the critical thickness, the chemical composition and the refractive indices by means of SEM, FT-IR, TGA, prism coupler, respectively.

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Classification of Mental States Based on Spatiospectral Patterns of Brain Electrical Activity

  • Hwang, Han-Jeong;Lim, Jeong-Hwan;Im, Chang-Hwan
    • Journal of Biomedical Engineering Research
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    • v.33 no.1
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    • pp.15-24
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    • 2012
  • Classification of human thought is an emerging research field that may allow us to understand human brain functions and further develop advanced brain-computer interface (BCI) systems. In the present study, we introduce a new approach to classify various mental states from noninvasive electrophysiological recordings of human brain activity. We utilized the full spatial and spectral information contained in the electroencephalography (EEG) signals recorded while a subject is performing a specific mental task. For this, the EEG data were converted into a 2D spatiospectral pattern map, of which each element was filled with 1, 0, and -1 reflecting the degrees of event-related synchronization (ERS) and event-related desynchronization (ERD). We evaluated the similarity between a current (input) 2D pattern map and the template pattern maps (database), by taking the inner-product of pattern matrices. Then, the current 2D pattern map was assigned to a class that demonstrated the highest similarity value. For the verification of our approach, eight participants took part in the present study; their EEG data were recorded while they performed four different cognitive imagery tasks. Consistent ERS/ERD patterns were observed more frequently between trials in the same class than those in different classes, indicating that these spatiospectral pattern maps could be used to classify different mental states. The classification accuracy was evaluated for each participant from both the proposed approach and a conventional mental state classification method based on the inter-hemispheric spectral power asymmetry, using the leave-one-out cross-validation (LOOCV). An average accuracy of 68.13% (${\pm}9.64%$) was attained for the proposed method; whereas an average accuracy of 57% (${\pm}5.68%$) was attained for the conventional method (significance was assessed by the one-tail paired $t$-test, $p$ < 0.01), showing that the proposed simple classification approach might be one of the promising methods in discriminating various mental states.

Buckling of thick deep laminated composite shell of revolution under follower forces

  • Khayat, Majid;Poorveis, Davood;Moradi, Shapour;Hemmati, Mona
    • Structural Engineering and Mechanics
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    • v.58 no.1
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    • pp.59-91
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    • 2016
  • Laminated composite shells are commonly used in various engineering applications including aerospace and marine structures. In this paper, using semi-analytical finite strip method, the buckling behavior of laminated composite deep as well as thick shells of revolution under follower forces which remain normal to the shell is investigated. The stiffness caused by pressure is calculated for the follower forces subjected to external fibers in thick shells. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness-shear flexibility. Displacements and rotations in the middle surface of shell are approximated by combining polynomial functions in the meridional direction as well as truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of loads direction will be derived for each strip of the shell. Assembling of these matrices results in global load stiffness matrix which may be un-symmetric. Upon forming linear elastic stiffness matrix called constitutive stiffness matrix, geometric stiffness matrix and load stiffness matrix, the required elements for the second step analysis which is an eigenvalue problem are provided. In this study, different parameter effects are investigated including shell geometry, material properties, and different boundary conditions. Afterwards, the outcomes are compared with other researches. By considering the results of this article, it can be concluded that the deformation-dependent pressure assumption can entail to decrease the calculated buckling load in shells. This characteristic is studied for different examples.

Analysis of Microstrip Single Line, Unmitered Bend and Coupled Line Using the Multiport Network Model (Multiport network model을 이용한 마이크로스트립 단일선로;직각벤드 및 결합선로의 해석)

  • Yun, Young;Chun, Joong-Chang;Park, Wee-Sang
    • The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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    • v.6 no.3
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    • pp.80-90
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    • 1995
  • The scattering parameters of a microstrip single line, a right-angle bend and a coupled line are calculated using the multiport network model for the frequency range from 1 to 18 GHz. The single line is analyzed using the planar waveguide model. The right-angle bend is broken into two rectangular segments, and each segment is analyzed in a similar fashion as the single line. Impedance matrices corresponding to the two segments are combined by the segmentation method. In the analysis of elec- tromagnetic coupling of the coupled line, a new method is employed resulting in much less computation time than those previous methods involving Green's functions. A good agreement between the numerical results for the three structures and those from SuperCompact reveals the usefulness of the multiport network medel in analyzing complicated mirostrip single and coupled line discontinuities.

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Prediction of the Transmission Loss of Rectangular Lined Plenum Chamber by the Rayleigh-Ritz Method (Rayleigh-Ritz 방법에 의한 흡음재가 부착된 직방형 소음기의 전달 손실 예측)

  • Kim, Hoi-Jeon;Ih, Jeong-Guon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.869-872
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    • 2005
  • The purpose of this study is on the prediction of the acoustic performance of the lined rectangular plenum chamber which can be used in the HVAC systems. The lined plenum chamber is modeled as a piston driven rectangular tube without mean flow and the acoustic pressure in the lined chamber is obtained by superposing the three dimensional pressure due to each of uniformly and harmonically fluctuating pistons. The arbitrary locations of inlet/outlet ports as well as the acoustic higher order modes generated at the area discontinuities of the port chamber interfaces are taken into consideration. The four-pole parameters can be derived by imposing the proper boundary conditions on each inlet and outlet ports. The lining material on the internal wall is assumed to be a bulk-reacting model. A single weak variation statement which satisfies the fluctuating rigid piston condition and the pressure and displacement continuity condition at the interface between the lining material and the airway was developed. The set of cosine functions were used as the admissible function when applying the Rayleigh-Ritz method. Computed results are compared with those predicted by using the locally-reacting lining material and experimental results, respectively. There are a good agreement shown between the results by the Rayleigh-Ritz method and the experiment results. The derived transfer matrices can be easily combined with other four-pole parameters of different types of mufflers for the calculation of the whole system performance.

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Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants (상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동)

  • Noh Hyuk-Chun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.291-302
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    • 2005
  • Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

A Study of Dynamic Behavior of Track and Train Interaction on Rail Open Gap (레일 개구부에서의 궤도-차량 상호작용에 대한 연구)

  • Kang, Yun Suk;Kang, Young Jong;Yang, Shin Chu;Cho, Sun Kyu;Han, Sang Yun
    • Journal of Korean Society of Steel Construction
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    • v.19 no.4
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    • pp.345-355
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    • 2007
  • During winter, the CWR (continuous welded rail) may be broken when a temperature drop below the neutral level changes the axial force, causing tensile fracture and creating a rail gap. The passage of a train on a rail with an open gap may lead to very costly derailments. In this paper, the use of a track-and-train-coupled model whose rail has an open gap is proposed for dynamic interaction analysis. Linear track and train systems were coupled in this study by a nonlinear Herzian contact spring, and the complete system matrices of the total track-train system were constructed. Moreover, the interaction phenomenon considering the presence of an open gap in the rail was toughly defined by assigning the irregularity functions between the two sides of the gap. Time history analysis, which has an iteration scheme such as the Newmark-$\beta$ method (based on the Modified Newton-Raphson methods), was conducted to solve the nonlinear equation. .Finally, numerical studies were conducted to assess the effect of the various parameters of the system when applied to various speeds, open-gap sizes, and support stiffnesses of the rail.

Free Vibration of Tapered Tube (선형변단면관(線形變斷面管)의 자유진동)

  • Lee, Yong Woo;Min, Kyung Ju
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.11 no.4
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    • pp.45-54
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    • 1991
  • The closed forms of mass matrix with rotational inertia matrix are developed for free vibration analysis in space structures containing linearing tapered members with cross section of thin-walled tube. The exact displacement functions are used for formulating mass matrix. The very small slopes of the tapered member are used in usual practice, such that the series expansion forms of these are also developed to avoid numerical failure in vibration analysis. Significant improvements of accuracy and efficiency of free vibration analysis are achieved by using the mass matrices developed in this study. Frequencies of free vibration of tapered members are compared with solutions based upon stepped representation of beam element.

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