• Journal of Institute of Convergence Technology
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• v.4 no.2
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• pp.17-21
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• 2014

This paper presents the effects of the time delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a time delay model. In this paper, the time delay is considered as the computational time delay that is assumed to be as much as the sampling time. As the time delay increases, the maximal available stiffness of a virtual wall model is reduced reversely. The relation among the time delay and the maximum available stiffness, the mass and the damper of the haptic device are analyzed using the MATLAB simulation.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.233-245
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• 2013

Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1712-1717
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• 1997

Stability and accuracy for the trapezoidal rule of the Newmark time integration method are analyzed when variable time step sizes are adopted. A new analytic approach to stability and accuracy analysis is also proposed for time integration methods with variable time step sizes. The trapezoidal rule with variable time step sizes has the "actual" unconditional stability which is the same as that of the method with constant time step sizes. However, the method with variable time step sizes is first-order accurate while the method with constant time step sizes is second-order accurate. accurate.

• Advances in nano research
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• v.13 no.2
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• pp.113-120
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• 2022

In this paper, a finite element (FE) simulation has been developed in order to examine the nonlinear stability of reinforced sandwich beams with graphene oxide powders (GOPs). In this regard, the nonlinear stability curves have been obtained asuming that the beam is under compressive loads leading to its buckling. The beam is considered to be a three-layered sandwich beam with metal core and GOP reinforced face sheets and it is rested on elastic substrate. Moreover, a higher-order refined beam theory has been considered to formulate the sandwich beam by employing the geometrically perfect and imperfect beam configurations. In the solving procedure, the utalized finite element simulation contains a novel beam element in which shear deformation has been included. The calculated stability curves of GOP-reinforced sandwich beams are shown to be dependent on different parameters such as GOP amount, face sheet thickness, geometrical imperfection and also center deflection.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.57-60
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• 1993

This study suggests a dynamic braking control algorithm in order to improve the transient stability of a multimachine power system. Dynamic braking control has been known as an effective method by which transient stability of power systems could be improved. Under the context, the study suggests a modified MRVM which possibly handles more rapid on-line computation through the improvement of the conventional MRVM(Model Referenced Velocity Matching). In order to resolve the phenomenon of stability recovery hinderance due to the prolonged dynamic braking control under the stable equilibrium state and chattering problem, the study also composes an algorithm in such a way that dynamic braking control could be prohibited by setting-up absolute stability region, Lastly, a comparison with the results derived from the application of the conventional control technique to the model power system is made in order to prove the superiority of the suggested control technique.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.453-460
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• 2022

It is essential for geotechnical engineers to conduct studies and make predictions about the stability of slopes, since collapse of a slope may result in catastrophic events. The Gaussian process regression (GPR) approach was carried out for the purpose of predicting the factor of safety (FOS) of the slopes in the study that was presented here. The model makes use of a total of 327 slope cases from Iran, each of which has a unique combination of geometric and shear strength parameters that were analyzed by PLAXIS software in order to determine their FOS. The K-fold (K = 5) technique of cross-validation (CV) was used in order to conduct an analysis of the accuracy of the models' predictions. In conclusion, the GPR model showed excellent ability in the prediction of FOS of slope stability, with an R² value of 0.8355, RMSE value of 0.1372, and MAPE value of 6.6389%, respectively. According to the results of the sensitivity analysis, the characteristics (friction angle) and (unit weight) are, in descending order, the most effective, the next most effective, and the least effective parameters for determining slope stability.

• Structural Engineering and Mechanics
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• v.87 no.4
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• pp.363-373
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• 2023

Since the first family of structure-dependent methods can simultaneously integrate unconditional stability and explicit formulation in addition to second order accuracy, it is very computationally efficient for solving inertial problems except for adopting auto time-stepping techniques due to no nonlinear iterations. However, an unusual stability property is first found herein since its unconditional stability interval is drastically different for zero and nonzero damping. In fact, instability might occur for solving a damped stiffness hardening system while an accurate result can be obtained for the corresponding undamped stiffness hardening system. A technique of using a stability factor is applied to overcome this difficulty. It can be applied to magnify an unconditional stability interval. After introducing this stability factor, the formulation of this family of structure-dependent methods is changed accordingly and thus its numerical properties must be re-evaluated. In summary, a large stability factor can result in a large unconditional stability interval but also lead to a large relative period error. As a consequence, a stability factor must be appropriately chosen to have a desired unconditional stability interval in addition to an acceptable period distortion.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.93-114
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• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Nuclear Engineering and Technology
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• v.54 no.7
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• pp.2427-2434
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• 2022

Series of unequal quantity Nd/Ce co-doped ceramic nuclear waste forms, (Gd, Nd)₂(Zr, Ce)₂O₇, were prepared to tailor its ordered pyrochlore or disordered fluorite structure. The phase transition, microtopography, and elemental composition of the ceramic samples were systematically investigated, especially the effect of order-disorder structure on the chemical stability. It was confirmed that unequal quantity of Nd/Ce could synchronously replace the Gd/Zr-sites of Gd₂Zr₂O₇. And the phase transition of order-disorder structure could be successfully tailored by regulating the average cationic radius ratio of (Gd, Nd)₂(Zr, Ce)₂O₇ series. The elements of Gd, Nd, Zr, and Ce are uniformly distributed in the ordered or disordered structures. The MCC-1 leaching results showed that (Gd, Nd)₂(Zr, Ce)₂O₇ pyrochlore ceramic nuclear waste forms had excellent chemical stability, whose elements' normalized leaching rates were as low as 10^-4-10^-7 g·m^-2·d^-1 after 7 days. In particular, the chemical stability of disordered structure was superior to that of ordered structure. It was proposed that the force constant and the closest packing were changed with the structure transformation resulting the chemical stability difference.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.394-400
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• 2008

This paper presents an analytical method to investigate the stability of FDBs (fluid dynamic bearings) considering the tilting motion. The perturbed equations of motion are derived with respect to translational and tilting motion for the general rotor-bearing system with five degrees of freedom. The Reynolds equations and their perturbed equations are solved by using the FEM in order to calculate the pressure, load capacity, and the stiffness and damping coefficients. This research introduces the radius of gyration to the equations of notion in order to express the mass moment of interia with respect to the critical mass. Then the critical mass of FDBs is determined by solving the eigenvalue problem of the linear equations of motion. This research is numerically validated by comparing the stability chart of FDBs with the time response of the whirl radius obtained from the direct integration of the equations of motion. This research shows that the tilting motion is one of the major design considerations to determine the stability of rotating system. It also shows that the stability of FDBs considering only translation is overestimated in comparison with the stability of FDBs considering both translational and tilting motion.