• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.37-52
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• 2005

We consider the existence of solutions of viscoelastic degenerate problem of Kirchhoff type with nonlinear boundary damping and memory term. Moreover, we consider the uniform decay of the energy for the problem.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.80-89
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• 1992

This paper deals with the open boundary problems, and two numerical schemes are used for the implementation of open boundary condition. One is to add the artificial damping term to dynamic free-surface boundary condition. Determination of suitable damping coefficient and the damping cone is the most important in this scheme. The other scheme is a modified Orlanski's method. This will be useful for the problems with unidirectional waves. A few typical free-surface wave problems are modeled for the numerical test. Method of solution is fundamental source-distribution method and the fully nonlinear boundary conditions are applied. The computed results are compared with those of others for the proof of practicality of these schemes.

• 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.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.85-97
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• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.1
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• pp.1-9
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• 2003

An active control of the lateral vibration of a translating tensioned Euler-Bemoulli beam is investigated. The dynamics of the translating tensioned beam is represented by a non-linear hyperbolic partial differential equation. A right boundary control law based upon the Lyapunov's second method is derived. The transverse motion of the translating tensioned beam is controlled by a time-varying external force besides a passive damping applied at the right boundary. Exponential stability of the closed loop system is proved. Simulation results demonstrate the effectiveness of the proposed controller.

• Journal of the Korean Society for Heat Treatment
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• v.8 no.3
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• pp.197-204
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• 1995

In recent work, we reported that a hot-rolled Fe-18wt%Mn alloy exhibited high damping capacity as well as excellent mechanical properties. It was also proposed that damping capacity of the alloy was proportional to the ${\gamma}/{\varepsilon}$ boundary area. In the present study, the effects of homogenization(12hrs at $1100^{\circ}C$) and solution treatment(1hr at $1050^{\circ}C$ before air cooling) on damping capacity and mechanical properties were investigated for as-cast and heat treated Fe-18wt%Mn alloy. The specimen subjected to both homogenization and solution treatment was found to show superior damping capacity and mechanical properties to the as-cast state due to removal of segregation and increase in ${\gamma}/{\varepsilon}$ boundary area.

• Journal of the Korean Society of Propulsion Engineers
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• v.9 no.4
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• pp.9-15
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• 2005

A linear acoustic analysis is performed to explore the characteristics of acoustic damping by a gas-liquid scheme coaxial injector in a liquid rocket engine. The injector can play a role of acoustic resonator. Acoustic-damping characteristics of half-wave resonator are compared with those of quarter-wave resonator. Various effects of the boundary absorption coefficient, injector length and sound speed in combustion chamber and resonator are investigated. As a result, short tuning length of resonator and low sound speed of the medium have a favorable effect on acoustic damping. As the boundary absorption coefficient decreases, the tuning range of the resonator length becomes narrower.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.5
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• pp.545-565
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• 2018

A numerical code is developed based on potential flow theory to investigate nonlinear sloshing in rectangular Liquefied Natural Gas (LNG) tanks under forced excitation. Using this code, internal free-surface elevation and sloshing loads on liquid tanks can be obtained both in time domain and frequency domain. In the mathematical model, acceleration potential is solved in the calculation of pressure on tanks and the artificial damping model is adopted to account for energy dissipation during sloshing. The Boundary Element Method (BEM) is used to solve boundary value problems of both velocity potential and acceleration potential. Numerical calculation results are compared with published results to determine the efficiency and accuracy of the numerical code. Sloshing properties in partially filled rectangular and membrane tank under translational and rotational excitations are investigated. It is found that sloshing under horizontal and rotational excitations share similar properties. The first resonant mode and excitation frequency are the dominant response frequencies. Resonant sloshing will be excited when vertical excitation lies in the instability region. For liquid tank under rotational excitation, sloshing responses including amplitude and phase are sensitive to the location of the center of rotation. Moreover, experimental tests were conducted to analyze viscous effects on sloshing and to validate the feasibility of artificial damping models. The results show that the artificial damping model with modifying wall boundary conditions has better applicability in simulating sloshing under different fill levels and excitations.

• Journal of Ocean Engineering and Technology
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• v.25 no.1
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• pp.8-13
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• 2011

A compact array system of small buoys is used for wave energy extraction. To evaluate the performance of this system, hydrodynamic analysis is carried out in regular waves using the higher order boundary element method. The motion response of each buoy is calculated considering hydrodynamic interactions caused by other buoys. The effect of energy extraction device is modeled as a linear damping load. The efficiencies of energy conversion are compared using the various sizes and arrangements of the array system and the damping coefficients for energy extraction. The increase in size or the packing ratio of the system gives better efficiency. However, the wave condition and the cost for the system should be considered to optimize performance from the perspective of engineering and economics. The proposed nondimensionalized damping coefficient for energy extraction is 0.1~0.5.

• 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.