• Earthquakes and Structures
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• v.16 no.1
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• pp.55-67
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• 2019

The finite solutions of deflection and the corresponding in-plane stress values of the graded sandwich shallow shell structure are computed in this research article via a higher-order polynomial shear deformation kinematics. The shell structural equilibrium equation is derived using the variational principle in association with a nine noded isoprametric element (nine degrees of freedom per node). The deflection values are computed via an own customized MATLAB code including the current formulation. The stability of the current finite element solutions including their accuracies have been demonstrated by solving different kind of numerical examples. Additionally, a few numerical experimentations have been conducted to show the influence of different design input parameters (geometrical and material) on the flexural strength of the graded sandwich shell panel including the geometrical configurations.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.586-592
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• 1999

We investigate the characteristic of 소데 responses of the Manabe standard form which is used recently for design of the controller. We obtain some theorems and these theorems have the properties of the relationship between the roots of the polynomial and the stability indices which are used for the Manabe standard form. The Manabe standard form has the following properties: The sum of the squal to zero, the sum of the reciprocal of the squared roots is greater than zero and the parameter $\tau$ is the negative value of the sum of the reciprocal of the roots. We compare the step responses of the Manabe standard form with those of the ITAE form, the dead beat response and Bessel forms. We choose the 6th order closed loop polynomial and keep the same settling time for the four forms. Under these conditions we find that the Manabe standard form have faster 90% rising time than the Bessel and dead beat response. We see that the ITAE, bessel and dead beat responses have some overshoot, whereas the Manabe standard form has none. We also compare the Manabe form with the other three forms for the controller design using the pole assignment technique. If the open loop transfer function is a type-1 system (transfer functions having one integrator), then, for the closed loop system associated with the open loop transfer function, the steady state error of the unit ramp input is obtained in terms of the parameter $\tau$ of the Manabe standard form.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.5
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• pp.321-328
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• 2017

In this study, vortex tube system model is developed to predict the temperature of the hot and the cold sides. The vortex tube model is developed based on the system identification method, and the model utilized in this work to design the vortex tube is ARX type (Auto-Regressive with eXtra inputs). The derived polynomial model is validated against experimental data to verify the overall model accuracy. It is also shown that the derived model passes the stability test. It is confirmed that the derived model closely mimics the physical behavior of the vortex tube from both the static and dynamic numerical experiments by changing the angles of the low-temperature side throttle valve, clearly showing temperature separation. These results imply that the system identification based modeling can be a promising approach for the prediction of complex physical systems, including the vortex tube.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2005.11a
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• pp.159-162
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• 2005

Recently, due to rapid developments of wireless communication and digital TV, modern society needs to process of aquisition, storage and transmission of much information. So the importance of signal processing is increasing and various digital filters are used in the two-dimensional signal such as image. And kinds of these digital filters are IIR(infinite impulse response) filter and FIR(finite impulse response) filter. And FIR filter which has the phase linearity, the easiness of creation and stability is applied to many fields. In design of this FIR filter, flatness property is a important factor in pass-band and stop-band. In this paper, we designed a 2-D Circular FIR filter using the Bernstein polynomial, it is presented flatness property in pass-band and stop-band. And we simulated the designed filter with noisy test image and compared the results with existing methods.

• Journal of KSNVE
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• v.5 no.4
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• pp.565-575
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• 1995

Gearboxes are often used in the petrochemical and electrical power plants to transmit mechanical power between two branches of a machinery train rotating at different speeds. When the gearboxes are connected with rotors supported by journal bearings, bearing loads vary in magnitude and direction with rotor speed and torque transmitted by the gearboxes. In this study, dynamic characteristics of the system which consists of gearboxes and a rotor supported by journal bearings are investigated analytically and experimentally by employing the polynomial transfer matrix method and modal analysis under different speeds and torque levels. Journal bearing loads due to the transmitted torque are claculated analytically and the stiffness and damping coefficient of the journal bearings are obtained using finite element method. Comparison of the analytical and experimental results shows that the cross coupled stiffness coefficients increase with increasing rotor speed, while the cross coupled damping coefficients decrease. This generates the oil whirl instability in the journal bearings. As the transmitted torque level goes up, the stiffness coefficients of the journal bearing and the first horizontal natural frequency increase. High levels of the transmitted torque produce high bearing stiffness since the contact loads of the mating gear teeth increase. The logarithmic decrement, which is a stability indicator, is shown to decrease with increasing speed and decreasing torque. Thus, at the low torque level, the system become unstable even at the low shaft speed.

• Journal of Sensor Science and Technology
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• v.29 no.5
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• pp.303-311
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• 2020

Nondispersive infrared CO₂ gas sensor was developed after the simulation of optical cavity structure and assembling the optical components: IR source, concave reflectors, Fresnel lens, a hollow disk, and IR detectors. By placing a hollow disk in front of reference IR detector, the output voltages are almost constant value, near to 70.2 mV. The absorbance of IR light, F_a, shows the second order of polynomial according to ambient temperatures at 1,500 ppm. The differential output voltages and the absorbance of IR light give a higher accuracy in estimations of CO₂ concentrations with less than ± 1.5 % errors. After implementing the parameters that are dependent upon the ambient temperatures in microcontroller unit (MCU), the measured CO₂ concentrations show high accuracies (less than ± 1.0 %) from 281 K to 308 K and the time constant of developed sensor is about 58 sec at 301 K. Even though the estimation errors are relatively high at low concentration, the developed sensor is competitive to the commercial product with a high accuracy and the stability.

• 한국방재학회:학술대회논문집
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• 2011.02a
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• pp.198-198
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• 2011

The numerical simulation of dam break problem suffers from several challenges in terms of accuracy, stability, and versatility of the simulation algorithm since the water flow is generally discontinuous and presents abrupt variations. Thus, to obtain stable and accurate solutions, flow models for this purpose require numerical schemes provided with shock-capturing properties, and with the ability to work with flexible two-dimensional meshes. In this context, SU/PG method(Hughes and Brooks, 1979) is excellent candidate for the solution of the dam break problem. The weak formulation of the equations and the discontinuous polynomial basis lead to an accurate representation of bore waves(shocks). Furthermore, the discretization of the domain in finite elements is extremely effective in modeling complex geometries. In this study, a finite element model based on the SU/PG scheme is developed to solve shallow water equations and the model is applied to dam break problem. It is found that the present model accurately captures the bore wave that propagates downstream while spreading laterally and the depression wave that moves upstream. Furthermore, the propagation and formation of water surface profile compared favorably with those obtained by the previously published results.