• Title/Summary/Keyword: D-continuous function

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Investigation of 1D sand compression response using enhanced compressibility model

  • Chong, Song-Hun
    • Geomechanics and Engineering
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    • v.25 no.4
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    • pp.341-345
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    • 2021
  • 1D sand compression response to ko-loading experiences volume contraction from low to high effective stress regimes. Previous study suggested compressibility model with physically correct asymptotic void ratios at low and high stress levels and examined only for both remolded clays and natural clays. This study extends the validity of Enhanced Terzaghi model for different sand types complied from 1D compression data. The model involved with four parameters can adequately fit 1D sand compression data for a wide stress range. The low stress obtained from fitting parameters helps to identify the initial fabric conditions. In addition, strong correlation between compressibility and the void ratio at low stress facilitates determination of self-consistent fitting parameters. The computed tangent constrained modulus can capture monotonic stiffening effect induced by an increase in effective stress. The magnitude of tangent stiffness during large strain test should not be associated with small strain stiffness values. The use of a single continuous function to capture 1D stress-strain sand response to ko-loading can improve numerical efficiency and systematically quantify the yield stress instead of ad hoc methods.

Design of Modal Transducer in 2D Structure Using Multi-Layered PVDF Films Based on Electrode Pattern Optimization (다층 압전 필름의 전극 패턴 최적화를 통한 2차원 구조물에서의 모달 변환기 구현)

  • 유정규;김지철;김승조
    • Journal of KSNVE
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    • v.8 no.4
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    • pp.632-642
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    • 1998
  • A method based on finite element discretization is developed for optimizing the polarization profile of PVDF film to create the modal transducer for specific modes. Using this concept, one can design the modal transducer in two-dimensional structure having arbitrary geometry and boundary conditions. As a practical means for implementing this polarization profile without repoling the PVDF film the polarization profile is approximated by optimizing electrode patterns, lamination angles, and poling directions of the multi-layered PVDF transducer. This corresponds to the approximation of a continuous function using discrete values. The electrode pattern of each PVDF layer is optimized by deciding the electrode of each finite element to be used or not. Genetic algorithm, suitable for discrete problems, is used as an optimization scheme. For the optimization of each layers lamination angle, the continuous lamination angle is encoded into discrete value using binary 5 bit string. For the experimental demonstration, a modal sensor for first and second modes of cantilevered composite plate is designed using two layers of PVDF films. The actuator is designed based on the criterion of minimizing the system energy in the control modes under a given initial condition. Experimental results show that the signals from residual modes are successfully reduced using the optimized multi-layered PVDF sensor. Using discrete LQG control law, the modal peaks of first and second modes are reduced in the amount of 12 dB and 4 dB, resepctively.

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CONTACT FORCE MODEL FOR A BEAM WITH DISCRETELY SPACED GAP SUPPORTS AND ITS APPROXIMATED SOLUTION

  • Park, Nam-Gyu;Suh, Jung-Min;Jeon, Kyeong-Lak
    • Nuclear Engineering and Technology
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    • v.43 no.5
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    • pp.447-458
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    • 2011
  • This paper proposes an approximated contact force model to identify the nonlinear behavior of a fuel rod with gap supports; also, the numerical prediction of interfacial forces in the mechanical contact of fuel rods with gap supports is studied. The Newmark integration method requires the current status of the contact force, but the contact force is not given a priori. Taylor's expansion can be used to predict the unknown contact force; therefore, it should be guaranteed that the first derivative of the contact force is continuous. This work proposes a continuous and differentiable contact force model with the ability to estimate the current state of the contact force. An approximated convex and differentiable potential function for the contact force is described, and a variational formulation is also provided. A numerical example that considers the particularly stiff supports has been studied, and a fuel rod with hardening supports was also examined for a realistic simulation. An approximated proper solution can be obtained using the results, and abrupt changes from the contacting state to non-contacting state, or vice versa, can be relieved. It can also be seen that not only the external force but also the developed contact force affects the response.

RESISTANCE ESTIMATION OF A PWM-DRIVEN SOLENOID

  • Jung, H.G.;Hwang, J.Y.;Yoon, P.J.;Kim, J.H.
    • International Journal of Automotive Technology
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    • v.8 no.2
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    • pp.249-258
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    • 2007
  • This paper proposes a method that can be used for the resistance estimation of a PWM (Pulse Width Modulation)-driven solenoid. By using estimated solenoid resistance, the PWM duty ratio was compensated to be proportional to the solenoid current. The proposed method was developed for use with EHB (Electro-Hydraulic Braking) systems, which are essential features of the regenerative braking system of many electric vehicles. Because the HU (Hydraulic Unit) of most EHB systems performs not only ABS/TCS/ESP (Electronic Stability Program) functions but also service braking function, the possible duration of continuous solenoid driving is so long that the generated heat can drastically change the level of solenoid resistance. The current model of the PWM-driven solenoid is further developed in this paper; from this a new resistance equation is derived. This resistance equation is solved by using an iterative method known as the FPT (fixed point theorem). Furthermore, by taking the average of the resistance estimates, it was possible to successfully eliminate the effect of measurement noise factors. Simulation results showed that the proposed method contained a sufficient pass-band in the frequency response. Experimental results also showed that adaptive solenoid driving which incorporates resistance estimations is able to maintain a linear relationship between the PWM duty ratio and the solenoid current in spite of a wide variety of ambient temperatures and continuous driving.

CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION BY INDEPENDENCE PROPERTY OF RANDOM VARIABLES

  • Jin, Hyun-Woo;Lee, Min-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.157-163
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    • 2014
  • Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

A Diffraction Transfer Function Approach to the Calculation of the Transient Field of Acoustic Radiators

  • Lee, Chan-Kil
    • ETRI Journal
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    • v.16 no.1
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    • pp.1-15
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    • 1994
  • A computationally-efficient approach to the calculation of the transient field of an acoustic radiator was developed. With this approach, a planar or curved source, radiating either continuous or pulsed waves, is divided into a finite number of shifted and/or rotated versions of an incremental source such that the Fraunhofer approximation holds at each field point. The acoustic field from the incremental source is given by a 2-D spatial Fourier transform. The diffraction transfer function of the entire source can be expressed as a sum of Fraunhofer diffraction pattern of the incremental sources with the appropriate coordinate transformations for the particular geometry of the radiator. For a given spectrum of radiator velocity, the transient field can be computed directly in the frequency domain using the diffraction transfer function. To determine the accuracy of the proposed approach, the impulse response was derived using the inverse Fourier transform. The results obtained agree well with published data obtained using the impulse response approach. The computational efficiency of the proposed method compares favorably to those of the point source method and the impulse response approach.

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CHARACTERIZATIONS OF GAMMA DISTRIBUTION

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.411-418
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    • 2007
  • Let $X_1$, ${\cdots}$, $X_n$ be nondegenerate and positive independent identically distributed(i.i.d.) random variables with common absolutely continuous distribution function F(x) and $E(X^2)$ < ${\infty}$. The random variables $X_1+{\cdots}+X_n$ and $\frac{X_1+{\cdots}+X_m}{X_1+{\cdots}+X_n}$are independent for 1 $1{\leq}$ m < n if and only if $X_1$, ${\cdots}$, $X_n$ have gamma distribution.

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STATIONARY SOLUTIONS FOR ITERATED FUNCTION SYSTEMS CONTROLLED BY STATIONARY PROCESSES

  • Lee, O.;Shin, D.W.
    • Journal of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.737-746
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    • 1999
  • We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

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Numerical study on the mitigation of rain-wind induced vibrations of stay cables with dampers

  • Li, Shouying;Wu, Teng;Li, Shouke;Gu, Ming
    • Wind and Structures
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    • v.23 no.6
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    • pp.615-639
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    • 2016
  • Although the underlying mechanism of rain-wind induced vibrations (RWIVs) of stay cables has not been fully understood, some countermeasures have been successfully applied to mitigating this kind of vibration. Among these, installing dampers near the bridge deck was widely adopted, and several field observations have shown its effectiveness. In this study, the effectiveness of dampers to RWIVs of stay cables is numerically investigated comprehensively by means of finite difference method (FDM). Based on the free vibration analysis of a taut string, it is found that the 3-points triangle scheme, which can be easily implemented in FDM, can offer an excellent approximation of the concentrated damping coefficient (expressed as a Dirac delta function) at the location where the damper is installed. Then, free vibration analysis of a 3-D continuous stay cable attached with two dampers is carried out to study the relationship of modal damping ratio and damping coefficient of the dampers. The effects of orientation of the dampers and cable sag on the modal damping ratio are investigated in detail. Finally, the RWIV response of a 3-D continuous stay cable attached with two dampers is examined. The results indicate that 0.5% of damping ratio is sufficient to reduce the RWIV vibration of the Cable A20 on the No.2 Nanjing Bridge over Yangtze River.

A Research on 3D Texture Production Using Artificial Intelligence Softwear

  • Ke Ma;Jeanhun Chung
    • International Journal of Internet, Broadcasting and Communication
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    • v.15 no.4
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    • pp.178-184
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    • 2023
  • AI image generation technology has become a popular research direction in the field of AI, which is widely used in the field of digital art and conceptual design, and can also be used in the process of 3D texture mapping. This paper introduces the production process of 3D texture mapping using AI image technology, and discusses whether it can be used as a new way of 3D texture mapping to enrich the 3D texture mapping production process. Two AI deep learning models, Stable Diffusion and Midjourney, were combined to generate high-quality AI textures. Finally, the lmage to material function of substance 3D Sampler was used to convert the AI-generated textures into PBR 3D texture maps. And applied in 3D environment. This study shows that 3D texture maps generated by AI image generation technology can be used in 3D environment, which not only has short production time and high production efficiency, but also has rich changes in map styles, which can be quickly adjusted and modified according to the design scheme. However, some AI texture maps need to be manually modified before they can be used. With the continuous development of AI technology, there will be great potential for further development and innovation of AI-generated image technology in the 3D content production process in the future.