• Title/Summary/Keyword: cosine equation

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Instability caused by interaction between a rotating disk and a mass-spring-damper system (회전원판과 스프링-댐퍼를 가진 질점계의 상호작용에 의한 불안정성)

  • Kim, C.B;Han, D.H
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.12
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    • pp.2038-2046
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    • 1997
  • In this paper the instability of the system which has a disk and a mass-spring-damper system interacting through a medium having stiffness and damping is analyzed. To solve the equations of motion of this systme, it is assumed that the solution consists of the eigenfunctions which are the products of the Bessel functions and sine or cosine functions. The former represents the radial characteristics of the disk and the latter represents the circumferential characteristics. Using this assumed solution and the orthogonality of the eigenfunctions, the equations of motion can be transformed into a set of equations of motion with variables dependent only on the time. After this set is changed to the state equation, the eigenvalue problem can be made. Once the eigenvalues are calculated according to the angular velocity of the disk, the dynamic characteristics ofthis system is obtained. Because the thickness of the disk and the element characteristics of the mass-spring-damper system have important effects on the stability of the system, it will be understood how these factors affect the system and then a method to ameliorate the stability of the system with a disk will be presented.

Still Image Watermarking in the DCT Domain Using the Human Visual System (DCT 영역에서의 인간의 시각적 특성을 이용한 정지 영상 워터마킹 방법)

  • Kwon O-Hyung;Park Rae-Hong
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.30 no.12C
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    • pp.1214-1221
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    • 2005
  • In this paper, we propose a digital watermarking method for still images, in which the human visual system (HVS) is used in the discrete cosine transform (DCT) domain. The modulation transfer function (MTF) of the HVS model is employed to increase the invisibility of the inserted watermark in images. The proposed watermarking method is shown to be robust to several common image processing techniques, including lowpass filtering and cropping. Also, using the energy relationship of the DCT, we derive the equation that directly computes the watermark weighting factor in the DCT domain for the specified peak signal to noise ratio (PSNR) of the still image and the length of watermark to be inserted. The difference between desired PSNR and PSNR in spatial domain is within 0.07dB for the 7 test images.

Molecular Dynamics Simulation Studies of Physico Chemical Properties of Liquid Pentane Isomers

  • 이승구;이송희
    • Bulletin of the Korean Chemical Society
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    • v.20 no.8
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    • pp.897-904
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    • 1999
  • We have presented the thermodynamic, structural and dynamic properties of liquid pentane isomers - normal pentane, isopentane, and neopentane - using an expanded collapsed atomic model. The thermodynamic properties show that the intermolecular interactions become weaker as the molecular shape becomes more nearly spherical and the surface area decreases with branching. The structural properties are well predicted from the site-site radial, the average end-to-end distance, and the root-mean-squared radius of gyration distribution func-tions. The dynamic properties are obtained from the time correlation functions - the mean square displacement (MSD), the velocity auto-correlation (VAC), the cosine (CAC), the stress (SAC), the pressure (PAC), and the heat flux auto-correlation (HFAC) functions - of liquid pentane isomers. Two self-diffusion coefficients of liquid pentane isomers calculated from the MSD's via the Einstein equation and the VAC's via the Green-Kubo relation show the same trend but do not coincide with the branching effect on self-diffusion. The rotational re-laxation time of liquid pentane isomers obtained from the CAC's decreases monotonously as branching increases. Two kinds of viscosities of liquid pentane isomers calculated from the SAC and PAC functions via the Green-Kubo relation have the same trend compared with the experimental results. The thermal conductivity calculated from the HFAC increases as branching increases.

Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates

  • Alazwari, Mashhour A.;Daikh, Ahmed Amine;Eltaher, Mohamed A.
    • Advances in nano research
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    • v.12 no.2
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    • pp.117-137
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    • 2022
  • Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.

Static and stress analyses of bi-directional FG porous plate using unified higher order kinematics theories

  • Mohamed, Salwa;Assie, Amr E.;Mohamed, Nazira;Eltaher, Mohamed A.
    • Steel and Composite Structures
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    • v.45 no.3
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    • pp.305-330
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    • 2022
  • This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

A Study on the Construction of the Automatic Extracts and Summaries - On the Basis of Scientific Journal Articles - (자동 발췌문/요약 시스템 구축에 관한 연구 - 학술지 논문기사를 중심으로 -)

  • Lee Tae-Young
    • Journal of the Korean Society for Library and Information Science
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    • v.39 no.3
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    • pp.139-163
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    • 2005
  • Various corpus-based approaches, rhetorical roles of discourse structure, and unifications of similar sentences were applied to construct the automatic Ext/Sums(extracts and summaries). Rhetorical roles of sentences like objective, method, background, result, conclusion, etc. for making elastic Ext/Sums were established and extraction engines according to respective role were prepared. The $90\%$ of Success rate in extracting the important sentences of sample articles was accomplished. Rearranging the selected sentences, it used unification of similar sentences using the cosine coefficient equation, deletion of unnecessary modification and insertion clauses, junction of short sentences, and connection of sentences able to link. They suggest the methods applying rhetorical roles of sentences, meaning and signature of noun and verb in clauses, and cue words and location will be researched to construct the more effective Ext/Sums.

The Study of Fisheye Lens for the Causes of Rapid Illumination Drop and the Ways to Correct on an Image Sensor due to an Ultra Wide Angle of View (어안렌즈 시야각의 광각화에 따른 조도저하의 원인과 개선방안에 관한 연구)

  • Rim, Cheon-Seog
    • Korean Journal of Optics and Photonics
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    • v.23 no.5
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    • pp.179-188
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    • 2012
  • Lenses with an ultra wide angle of view are usually called fisheye lenses since a fish can see an ultra wide panoramic view under water. As the angle of view for these kinds of lenses reaches a wide angle, the illumination on an image sensor is reduced by a rapid drop. In this paper, we discuss the causes and the ways to correct for a rapid drop. First, it is treated for the sign convention of directional cosine vectors and normal vectors on the curved surface by means of analytic geometry. And, from the fundamental discussion for these vectors, the rapid illumination drop is numerically analyzed for various kinds of causes by utilizing geometrical optics and radiometry as well as Fresnel equations derived from electromagnetic boundary conditions. As a result, we are able to get the full understanding for the rapid illumination drop and to propose ways to correct effects due to an wide angle of view.

Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects

  • Eltaher, Mohamed A.;Omar, Fatema-Alzahraa;Abdalla, Waleed S.;Kabeel, Abdallah M.;Alshorbagy, Amal E.
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.141-151
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    • 2020
  • This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

Identification of Nonstationary Time Varying EMG Signal in the DCT Domain and a Real Time Implementation Using Parallel Processing Computer (DCT 평면에서의 비정상 시변 근전도 신호의 인식과 병렬처리컴퓨터를 이용한 실시간 구현)

  • Lee, Young-Seock;Lee, Jin;Kim, Sung-Hwan
    • Journal of Biomedical Engineering Research
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    • v.16 no.4
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    • pp.507-516
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    • 1995
  • The nonstationary identifier in the DCT domain is suggested in this study for the identification of AR parameters of above-lesion upper-trunk electromyographic (EMG) signals as a means of developing a reliable real time signal to control functional electrical stimulation (FES) in paraplegics to enable primitive walking. As paraplegic shifts his posture from one attitude to another, there is transition period where the signal is clearly nonstationary. Also as muscle fatigues, nonstationarities become more prevalent even during stable postures. So, it requires a develpment of time varying nonstationary EMG signal identifier. In this paper, time varying nonstationary EMG signals are transformed into DCT domain and the transformed EMG signals are modeled and analyzed in the transform domain. In the DCT domain, we verified reduction of condition number and increment of the smallest eigenvalue of input correlation matrix that influences numerical properties and mean square error were compared with SLS algorithm, and the proposed algorithm is implemented using IMS T-805 parallel processing computer for real time application.

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