• 제목/요약/키워드: Differential Transform Method

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Characteristic equation solution of nonuniform soil deposit: An energy-based mode perturbation method

  • Pan, Danguang;Lu, Wenyan;Chen, Qingjun;Lu, Pan
    • Geomechanics and Engineering
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    • 제19권5호
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    • pp.463-472
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    • 2019
  • The mode perturbation method (MPM) is suitable and efficient for solving the eigenvalue problem of a nonuniform soil deposit whose property varies with depth. However, results of the MPM do not always converge to the exact solution, when the variation of soil deposit property is discontinuous. This discontinuity is typical because soil is usually made up of sedimentary layers of different geologic materials. Based on the energy integral of the variational principle, a new mode perturbation method, the energy-based mode perturbation method (EMPM), is proposed to address the convergence of the perturbation solution on the natural frequencies and the corresponding mode shapes and is able to find solution whether the soil properties are continuous or not. First, the variational principle is used to transform the variable coefficient differential equation into an equivalent energy integral equation. Then, the natural mode shapes of the uniform shear beam with same height and boundary conditions are used as Ritz function. The EMPM transforms the energy integral equation into a set of nonlinear algebraic equations which significantly simplifies the eigenvalue solution of the soil layer with variable properties. Finally, the accuracy and convergence of this new method are illustrated with two case study examples. Numerical results show that the EMPM is more accurate and convergent than the MPM. As for the mode shapes of the uniform shear beam included in the EMPM, the additional 8 modes of vibration are sufficient in engineering applications.

Nanostructured Hydroxyapatite for Biomedical Applications: From Powder to Bioceramic

  • Eslami, Hossein;Tahriri, Mohammadreza;Moztarzadeh, Fathollah;Bader, Rizwan;Tayebi, Lobat
    • 한국세라믹학회지
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    • 제55권6호
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    • pp.597-607
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    • 2018
  • In this study, a wet chemical method was used to synthesize nanostructured hydroxyapatite for biomedical applications. Diammonium hydrogen phosphate and calcium nitrate 4-hydrate were used as starting materials with a sodium hydroxide solution as an agent for pH adjustment. Scanning electron microscopy, transmission electron microscopy, Fourier-transform infrared spectroscopy, differential thermal analysis, thermal gravimetric analysis, atomic absorption spectroscopy, and ethylenediaminetetraacetic acid (EDTA) titration analysis were used to characterize the synthesized powders. Having been uniaxially pressed, the powders formed a disk-like shape. The sinterability and electrical properties of the samples were examined, and the three-point bending test allowed for the measurement of their mechanical properties. Sedimentation analysis was used to analyze the slurry ability of hydroxyapatite. As in-vitro biological properties of the samples, biocompatibility and cytotoxicity were assessed using osteoblast-like cells and the L929 cell line, respectively. Solubility was assessed by employing a simulated body fluid.

점진원모델을 사용한 층상지반에서의 깊이에 따른 지반운동 특성 변화연구 (A Study on the Depth Dependent Characteristics of Earthquake Ground Motions in a Layered Ground Medium Using Point Source Models)

  • 고현무;김재관;권기준
    • 대한토목학회논문집
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    • 제14권3호
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    • pp.453-462
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    • 1994
  • 다층 탄성반무한체에서 지진파장의 깊이에 따른 변화특성을 propagator matrix와 경사계단함수(ramp function) 형상의 단층이동함수(fault slip function)를 갖는 점진원 모델을 사용하여 연구하였다. 본 논문에서 지반은 수평방향으로 평행하고 각층에서는 재료특성이 균일한 지층으로 구성된 반무한체로서 모델링되었다. 각 층에서 지진운동의 지배편미분방정식의 해를 구하기 위해서 Fourier Hankel 변환기법이 적용되었다. 층상지반아래 반무한체에 있는 연직 dip-slip 및 주향이동(strike slip) 점진원에 의한 각층경계에서의 가속도와 변위의 시간이력과 주파수내용을 개발한 해석프로그램에 의하여 계산하였고 그 특성을 논의하였다.

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Aerodynamic stability analysis of geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction

  • Xu, Yun-ping;Zheng, Zhou-lian;Liu, Chang-jiang;Wu, Kui;Song, Wei-ju
    • Wind and Structures
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    • 제26권6호
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    • pp.355-367
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    • 2018
  • This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

환원된 산화그래핀/젤라틴 복합필름의 합성과 분석 (Synthesis and Characterization of Reduced Graphene Oxide/Gelatin Composite Films)

  • Chen, Guangxin;Qiao, Congde;Xu, Jing;Yao, Jinshui
    • 폴리머
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    • 제38권4호
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    • pp.484-490
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    • 2014
  • Reduced graphene oxide (RGO) was fabricated using gelatin as a reductant, and it could be stably dispersed in gelatin solution without aggregation. A series of RGO/gelatin composite films with various RGO contents were prepared by a solution-casting method. The structure and thermal properties of the RGO/gelatin composite films were characterized by UV-vis spectroscopy, Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), differential scanning calorimeter (DSC) and thermal gravimetric analysis (TGA). The addition of RGO enhances the degree of crosslinking of gelatin films and decreases the swelling ability of the gelatin films in water, indicating that RGO/gelatin composite films have a better wet stability than gelatin films. The glass transition temperature ($T_g$) of gelatin films is also increased with the incorporation of RGO. The presence of RGO slightly increases the degradation temperature of gelatin films due to the very low content of RGO in the composite films. Since gelatin is a natural and nontoxic biomacromolecule, the RGO/gelatin composite films are expected to have potential applications in the biomedical field.

적외선 광학렌즈 제작을 위한 GeSe의 벌크 제작 및 특성 연구 (A Study on the Properties and Fabrication of Bulk Forming GeSe Based Chalcogenide Glass for Infrared Optical Lens)

  • 배동식;여종빈;박정후;이현용
    • 한국전기전자재료학회논문지
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    • 제26권9호
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    • pp.641-645
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    • 2013
  • Chalcogenide glass has superior property of optical transmittance in the infrared region. Glass made using Ge-Se how many important optical applications. We have determined the composite formular of $Ge_{0.25}Se_{0.75}$ to be the GeSe chalcogenide glass composition appropriate for IR lenses. Also, the optical, thermal and physical characteristics of chalcogenide glass depended on the composition ratio. GeSe bulk sample is produced using the traditional melt-quenching method. The optical, structural, thermal and physical properties of the compound were measured by using Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), Differential scanning calorimeter (DSC), and Scanning electron microscope (SEM) respectively.

Non-stationary mixed problem of elasticity for a semi-strip

  • Reut, Viktor;Vaysfeld, Natalya;Zhuravlova, Zinaida
    • Coupled systems mechanics
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    • 제9권1호
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    • pp.77-89
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    • 2020
  • This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

PTCA와 BTCA를 이용한 면셀룰로오스의 에스테르 가교화에 대한 pH 영향(I) (Effect of pH on the Ester-crosslinking of Cotton Cellulose with PTCA and BTCA(I))

  • Chan-Min, Lee;Chul-Ho, Choi
    • 한국염색가공학회지
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    • 제9권5호
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    • pp.30-41
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    • 1997
  • A purpose of this research is to prove unknown relation -ship between finish bath pH and crosslinking. In pursuit of these goals, we have treated 100% cotton broad cloth with PTCA and BTCA at different pH values. They were used with H$_{3}$PO$_{4}$, NaH$_{2}$PO$_{2}$, NaH$_{2}$PO$_{4}$, Na$_{2}$HPO$_{4}$, Na$_{3}$PO$_{4}$, catalysts to produce nonformaldehyde fabrics finishes. Treatments were applied to all cotton fabrics using a parletry-cure process. For the fully understood on the relationship of finish bath pH effect and cotton cellulose esterification, the relative concentrations of chemical species were calculated from ionization constants. The effect of pH on the cotton cellulose ester was investigated using Fourier transform infrared spectra, the surface area measurement by BET method and wrinkle recovery analysis. Results of differential FT-IR spectra and their relative concentration analysis were compared with those of catalyst treated controls. FT-IR and wrinkle recovery data indicated that the esterfication by polycarboxylic acids is pridependent. A similar phenomenon also occurred when a phosphate or hypophosphite was used. Therefore, it is necessary to choose the optimum pH range of a finishing bath in order to achieve the most effective esterification.

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Effect of Copper Substitution on Structural and Magnetic Properties of NiZn Ferrite Nanopowders

  • Niyaifar, Mohammad;Shalilian, Hoda;Hasanpour, Ahmad;Mohammadpour, Hory
    • Journal of Magnetics
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    • 제18권4호
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    • pp.391-394
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    • 2013
  • In this study, nickel-zinc ferrite nanoparticles, with the chemical formula of $Ni_{0.3}Zn_{0.7-x}Cu_xFe_2O_4$ (where x = 0.1- 0.6 by step 0.1), were fabricated by the sol-gel method. The effect of copper substitution on the phase formation and crystal structure of the sample was investigated by X-ray diffraction (XRD), thermo-gravimetry (TG), differential thermal analysis (DTA), Fourier transform infrared spectrometry (FT-IR), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The XRD result shows that due to the reduction of Zn content,the crystallite size of the sample increased. The results of the vibration sample magnetometer (VSM) exhibit an increase in saturation magnetization value (Ms) for samples with x ${\leq}$ 0.3 and a linear decrease for samples with x > 0.3. The variation of saturation magnetization and coercivity of the samples were then studied.

Influence of Amorphous Polymer Nanoparticles on the Crystallization Behavior of Poly(vinyl alcohol) Nanocomposites

  • Lee, Kyung-Jin;Lee, Ji-Hye;Hong, Jin-Yong;Jang, Jyong-Sik
    • Macromolecular Research
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    • 제17권7호
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    • pp.476-482
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    • 2009
  • The crystallization behavior of poly(vinyl alcohol) (PVA) in the presence and absence of polypyrrole nanoparticles (PPy NPs) was investigated in terms of the heterogeneous nucleation effect of PPy NPs using FTIR, X-ray diffraction, differential scanning calorimeter and polarized optical microscope analysis. PPy NPs were prepared by dispersion polymerization method stabilized by PVA in aqueous solution. A polymer nanocomposite with uniform dispersity could be readily obtained due to the enhanced compatibility between the filler and matrix. Compared with the PPy NP-absent PVA, the PPy NP/PVA nanocomposite exhibited an enhanced degree of crystallinity. The degree of crystallinity increased up to 17% at the PPy NP concentration of 1 wt%, compared to the pristine PVA. The PPy NP acted as an effective nucleating agent during the crystallization process, thereby enhancing the degree and rate of crystallization. The kinetics study of the crystallization also revealed the decreased value of the Avrami coefficient in the case of the PPy NP/PVA nanocomposite.