• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.39-53
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• 2023

In this paper, we consider a delayed ratio-dependent predator-prey reaction-diffusion system with homogenous Neumann boundary conditions. We study the existence of nonnegative solutions and the stability of the nonnegative equilibria to the system. In particular, we provide a sufficient condition for the positive equilibrium to be globally asymptotically stable.

• Fire Science and Engineering
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• v.28 no.1
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• pp.20-25
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• 2014

Steel column is very important an structural element in steel framed building and plays a key role in sustataining the applied external load. Generally, the fire resistance performance of steel column has been executed by application of fire standard and vertical furnace having a limitation in height. Therefore, the fire resistance test was conducted with a H-section column having 3500 mm in length and hinge to hinge boundary condition. And the fire protective material derived from the fire test can be applied to any kind of boundary conditions and lengths. However, it is hard to determine the fire resistance. In this paper, to make sure the structural stability of them at high temperature according to various boundary conditions and lengths of H-section column, an analysis was done by using the mechanical properties and an heat transfer theory.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1759-1771
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• 2017

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

• Steel and Composite Structures
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• v.44 no.4
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• pp.503-517
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• 2022

This paper presents the mechanical buckling of bi-directional functionally graded sandwich beams (BFGSW) with various boundary conditions employing a quasi-3D beam theory, including an integral term in the displacement field, which reduces the number of unknowns and governing equations. The beams are composed of three layers. The core is made from two constituents and varies across the thickness; however, the covering layers of the beams are made of bidirectional functionally graded material (BFGSW) and vary smoothly along the beam length and thickness directions. The power gradation model is considered to estimate the variation of material properties. The used formulation reflects the transverse shear effect and uses only three variables without including the correction factor used in the first shear deformation theory (FSDT) proposed by Timoshenko. The principle of virtual forces is used to obtain stability equations. Moreover, the impacts of the control of the power-law index, layer thickness ratio, length-to-depth ratio, and boundary conditions on buckling response are demonstrated. Our contribution in the present work is applying an analytical solution to investigate the stability behavior of bidirectional FG sandwich beams under various boundary conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.41-47
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• 2007

Scattering fields of two dimensional acoustic waves by a circular cylinder are investigated. The present numerical approach for the acoustic scattering problem has difficulties of numerical robustness, long-time stability and suitability of far-field boundary treatments. The time-dependent periodic acoustic source is used to analyze Interference patterns between incident waves and waves reflected by the cylinder. Characteristic boundary algorithms coupled with 4th order Modified-Flux-Approach ENO(essentially non-oscillatory) schemes are employed in generalized coordinates to examine the effect of the wane frequency on the interference patterns. Non-reflecting boundary conditions, which is crustal for accurate computations of aeroacoustic problems, are used not to contaminate scattering fields by reflected waves at the outer boundary. Computed scattering fields show the circumferential acoustic modes generated by interacting between acoustic sources and scattered waves. At a lower frequency, the wave passes almost straight through the cylinder without Interacting with circular cylinder. Simulation results are presented and compared with the analytic solution. Computed RMS-pressure distribution on the cylinder wall is good agreement with exact solution.

• Smart Structures and Systems
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• v.18 no.2
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Journal of the Korean Geotechnical Society
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• v.19 no.2
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• pp.147-157
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• 2003

The characteristics of a rock joint which influence the stability of rock mass structures such as cut slopes and tunnels are largely controlled by the conditions of the rock joint as well as its boundary conditions. The conditions of rock joints comprise asperity strength, roughness, and filling materials. Boundary conditions can be represented by assuming that the deformability(or stiffness) of the rock mass surrounding the joints is modelled by a spring with stiffness. A new direct shear apparatus was developed in this study, which adapts a servo control system using PID algorithm. This apparatus can be used to investigate the various aspects of shear characteristics of the rock joints at conditions of constant normal stress and constant normal stiffness and so on. The test results for saw-cut teeth joints show that shear strength should be evaluated by considering its specific boundary conditions far the design of tunnels and cut slopes.

• Journal of KSNVE
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• v.9 no.4
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• pp.828-834
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• 1999

The paper describes the vibration and the stability of nonuniform tapered beams resting on two-layered elastic foundations. The two-layered elastic foundations are constructed by discributed Winkler springs and shearing layers as ofen used in oil models. Governing equations are derived from energy experssions using Hamilton's Principle. The associated eigenvalue problems are solved to obtain the free vibration frequencies or the buckling loads. Numerical results for the vibration and the stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies and critical forces are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters, and boundary conditions of tapered beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.927-932
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• 2002

The stability ratio and vibrational amplitude of each tube inside a steam generator have different values. We estimate the characteristics of flow-induced vibration for CE type steam generator with various column and row number of the tube. To obtain the thermal-hydraulic data and stability ratio we use the ATHOS3-MODI and PIAT-FEI/TE code respectively. It turns out that the steam generator has a bounded central zone with the distributed values of the stability ratio and the vibrational amplitude, and those values across the zone boundary become decreased.