• Structural Engineering and Mechanics
• /
• v.43 no.5
• /
• pp.561-582
• /
• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• Journal of the Korean Society of Propulsion Engineers
• /
• v.10 no.2
• /
• pp.1-14
• /
• 2006

Present study examines the numerical issues of cell structure simulation for various regimes of detonation phenomena ranging from weakly unstable to highly unstable detonations. Inviscid fluid dynamics equations with $variable-{\gamma} $ formulation and one-step Arrhenius reaction model are solved by a MUSCL-type TVD scheme and 4th order accurate Runge-Kutta time integration scheme. A series of numerical studies are carried out for the different regimes of the detonation phenomena to investigate the computational requirements for the simulation of the detonation wave cell structure by varying the reaction constants and grid resolutions. The computational results are investigated by comparing the solution of steady ZND structure to draw out the minimum grid resolutions and the size of the computational domain for the capturing cell structures of the different regimes of the detonation phenomena.

• Bulletin of the Korean Chemical Society
• /
• v.8 no.3
• /
• pp.168-170
• /
• 1987

The reaction between 1-benzyl-3-carbamoyl-1,4-dihydropyridine (BNAH) 1 and various 1-arylpyridinium salts 2, and the reaction between 1-(4-methylphenyl)-1,4-dihydropyridine 4b and 1-aryl-3-carbamoylpyridinium (1-arylnicotinamide) salts 5 were carried out. The extents of reaction in equilibrium were estimated by nmr integration data. The equilibrium constants for the reactions, K, and the standard Gibbs free energy changes for the reduction of the pyridinium salts to the corresponding 1,4-dihydropyridines ${\Delta}G^{\circ}'$ were evaluated. The Hammett plot of log K for the reaction between 1 and 2, and ${\Delta}G^{\circ}'$ against ${\sigma}_p$ of the substituents in 1-aryl moiety shows linear correlation with the reaction constant ${\rho}$ of 9.4 (for log K vs ${\sigma}_p$) and -54.5 KJ/mole (for ${\Delta}G^{\circ}'$ vs ${\sigma}_p$). It was found that 1-aryl-1,4-dihydropyridines have much higher reducing power than the corresponding 1-aryl-1,4-dihydronicotinamides, and the power is affected greatly by the electron-withdrawing ability of the substituents in aryl group. The reactions were utilized for preparation of 1,4-dihydropyridines bearing highly electron-withdrawing groups such as 4-nitrophenyl and 2,4-dinitrophenyl, which could not be obtained by conventional dithionite reduction of the corresponding pyridinium salts due to the base-labile nature of the salts.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.3 no.2
• /
• pp.87-96
• /
• 1999

To analyze the dynamic behavior of structure, direct integration and mode superposition may be utilized in time domain analysis. As finite number of frequencies can give relatively exact solutions, mode superposition is preferable in analyzing structural behavior. In non-linear analysis, however, mode superposition is seldom used since time-varying element stiffness changes stiffness matrix, and the change of stiffness matrix leads to the change of essential constants - natural frequencies and mode shapes. In spite of these difficulties, there are some attempts to adopt mode superposition because of low cost compared to direct integration, but the result is not satisfactory. In this paper, a method using mode superposition in non-linear analysis is presented by separating local element stiffness from global stiffness matrix with the difference between linear and non-linear restoring forces to the external force vectors included. Moreover, the hysteresis model changing with the relative deformation in each floor makes it possible to analyze non-linear behavior of structure. The proposed algorithm is applied to shear beam model and the maximum displacement is compared with the result using direct integration method.

• Journal of Biomedical Engineering Research
• /
• v.16 no.2
• /
• pp.223-230
• /
• 1995

This study investigates a combined mathematical model for the quantitative estimation of regional myocardial blood flow in experimental canine coronary artery occlusion and in patients with ischemic myocardial diseases using Rb-82 dynamic myocardial positron emission tomography. The coronary thrombosis was induced using the new catheter technique by narrowing the lumen of coronary vessel gradually, which finally led to partial obstruction of coronary artery. Thirty four Rb-82 dynamic myocardial PET scans were performed sequentially for each experiment using our 5, 10 and 20 second acquisition protocol, respectively, and six to seven regions of interest were drawn on each transaxial slices, one on left ventricular chamber for input function and the others on normal and decreased perfusion myocardial segments for the flow estimation in those regions. Two compartment model and graphical analysis method have been applied to the measured sets of regional PET data, and the rate constants of influx to myocardial tissue were calculated for regional myocardial flow estimates with the two parameter fits of raw data by the Levenberg-Marquardt method. The results showed that, (I) two compartment model suggested by Kety-Schmidt, with proper modification of the measured data and volume of distribution, could be used for the simple estimation of regional myocardial blood flow, (2) the calculated regional myocardial blood flow estimates were dependent on the selection of input function, which reflected partial volume effect and left ventricular wall motion in previously used graphical analysis, and (3) mathematically fitted input and tissue time activity curves were more suitable than the direct application of the measured data in terms of convergence.

• Structural Engineering and Mechanics
• /
• v.53 no.3
• /
• pp.537-573
• /
• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.3
• /
• pp.311-319
• /
• 2003

This paper aims at investigating the exact dynamic response of the system undergoing a exponential impact force from the viewpoints of conservations of momentum and energy. The midpoint method applied in the Newmark's family algorithm is found to be identical to the case of the application of the trapezoidal method which provides conservations of momentum and energy. For the linear impact force the mid point, the trapezoidal and the (n+1) point method exactly meet the conservation characteristics independent of the size of integration interval. On the other hand, constants for the dynamic motion resulting from the nonlinear impact are underestimated or overestimated by these method mentioned above. To overcome this indispensible error, the Simpson 1/3 method as one of multi step methods whose advantages is to use longer time interval with the same number of evaluation functions is adopted for the exact conservations of momentum and energy. Moreover, the suggested method is expected to expand the similar algorithm for the general dynamic motion including finite rotations.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.5
• /
• pp.531-542
• /
• 2011

The time-dependent temperature distribution across the section in bridges is determined on the basis of the three-dimensional finite element analyses and numerical time integration in this study. The material properties which change with time and thermal stress of concrete are taken into account to effectively trace the early-age structural responses. Since the temperature distribution is nonlinear and depends upon many material constants such as the thermal conductivity, specific heat, hydration heat of concrete, heat transfer coefficients and solar radiation, three representative influencing factors of the construction season, wind velocity and bridge pavement are considered at the parametric studies. The validity of the introduced numerical model is established by comparing the analytical predictions with results from previous analytical studies. On the basis of parametric studies for four different bridge sections, it is found that the creep deformation in concrete bridges must be considered to reach more reasonable design results and the temperature distribution proposed in the Korean bridge design specification need to be improved.

• Journal of the Korean Ceramic Society
• /
• v.43 no.6 s.289
• /
• pp.362-368
• /
• 2006

Epitaxial $Ba_{0.5}Sr_{0.5}TiO_3$ (BSTO) thin films have been grown on TiN buffered Si (001) substrates by Pulsed Laser Deposition (PLD) method and the effects of substrate temperature and oxygen partial pressure during the deposition on their dielectric properties and crystallinity were investigated. The crystal orientation, epitaxy nature, and microstructure of oxide thin films were investigated using X-Ray Diffraction (XRD) and Transmission Electron Microscopy (TEM). Thin films were prepared with laser fluence of $4.2\;J/cm^2\;and\;3\;J/cm^2$, repetition rate of 8 Hz and 10 Hz, substrate temperatures of $700^{\circ}C$ and ranging from $350^{\circ}C\;to\;700^{\circ}C$ for TiN and oxide respectively. BSTO thin-films were grown on TiN-buffered Si substrates at various oxygen partial pressure ranging from $1{\times}10^{-4}$ torr to $1{\times}10^{-5}$ torr. The TiN buffer layer and BSTO thin films were grown with cube-on-cube epitaxial orientation relationship of $[110](001)_{BSTO}{\parallel}[110](001)_{TiN}{\parallel}[110](001)_{Si}$. The crystallinity of BSTO thin films was improved with increasing substrate temperature. C-axis lattice parameters of BSTO thin films, calculated from XRD ${\theta}-2{\theta}$ scans, decreased from 0.408 m to 0.404 nm and the dielectric constants of BSTO epitaxial thin films increased from 440 to 938 with increasing processing oxygen partial pressure.

• Journal of Korean Society of Environmental Engineers
• /
• v.28 no.5
• /
• pp.487-493
• /
• 2006

Reductive dechlorination of chlorophenols by nickel coated iron was investigated to understand the feasibility of using Ni/Fe for the in situ remediation of contaminated groundwater. Zero Valent Iron(ZVI) was amended with Ni(II) ions to form bimetal(Ni/Fe). Dechlorination of five chlorophenol compounds and formation of intermediates were examined using Ni/Fe. Rate constant for each reaction pathway was quantified by the numerical integration of a series of differential rate equation. Experimental results showed that the sequence of hydrodechlorination rate constant was in the order of 2-CP>4-CP>2,4-DCP>2,4,6-TCP>2,6-DCP. The hydrodechlorination pathways for the conversion of each chlorophenol compound involves a full dechlorination to phenol via both concerted and stepwise mechanisms. Reaction pathways and corresponding kinetic rate constants were suggested based on the experiments and numerical simulations.