• East Asian mathematical journal
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• v.32 no.3
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• pp.355-364
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• 2016

In this paper, we study exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Kang [3]. Energy decay rate are obtained by the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• v.30 no.3
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• pp.249-258
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• 2014

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang[14]. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.7 s.112
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• pp.690-696
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• 2006

Thickness of damping layer in sandwich plate needs to be optimized in order to make modal loss factor of the sandwich plate maximum. Since previous studies were interested in noise reductions over high frequency range, the modal properties were derived based on simply supported boundaries. This conventional formula is approximately applicable to other boundary conditions over high frequency range only. The purpose of this study is to propose a method to determine optimum damping layer thickness of sandwich plate for maximum modal damping in low frequency range when the boundary condition is not a simple support. The conventional RKU equation based on simply supported boundary is modified to reflect other boundary conditions and the modified RKU equation is subsequently applied to determine the optimum damping layer thickness for arbitrary conditions. In order to reflect frequency-dependent characteristics of elastic modulus of the damping layer, an iteration method is proposed in determining the modal properties. Test results on sandwich plates for optimum damping layer thickness are compared with predictions by the proposed method and conventional method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.681-689
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• 2014

In this paper, we investigate the influence of boundary dissipations on decay property of the solutions for a semilinear wave equation with damping and memory condition on the boundary using the multiplier technique.

• Structural Engineering and Mechanics
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• v.49 no.3
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• pp.285-296
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• 2014

Material damping affects the dynamic behaviors of engineering structures considerably, but up to till now little research is maintained on influence factors of material damping. Based on the damping-stress function of steel, the material damping of steel beams is obtained by calculating the stress distribution of the beams with an analytical method. Some key influence factors of the material damping, such as boundary condition, amplitude and frequency of excitation, load position as well as the cross-sectional dimension of a steel beam are analyzed respectively. The calculated results show that even in elastic scope, material damping does not remain constant but varies with these influence factors. Although boundary condition affects material damping to some extent, such influence can be neglected when the maximum stress amplitude of the beam is less than the fatigue limit of steel. Exciting frequency, load position and cross-section dimension have great effects on the material damping of the beam which maintain the similar changing trend under different boundary conditions respectively.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.4 no.1
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• pp.22-30
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• 2001

A new concept wave absorber is proposed. It is a net type wave absorber. Its efficiency was reported in another publication. Since it is based on new concept, the traditional wave absorber theory is not applicable. It is modeled by introducing damping terms in linearized free surface boundary conditions in this study. The length and the thickness of the wave absorber are modeled by the length and the coefficient of the damping terms. Series of experiments are carried out to get the data for the coefficients of the damping term. The boundary element method is adopted to solve the system. The predicted wave heights show excellent agreement with those of experiments when the lengths of the incoming waves are within the length of the wave absorber.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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• pp.63-78
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• 1994

This paper deals with the treatment of the open boundary in two-dimensional free-surface wave problems. Two numerical schemes are investigated for the implementation of the open boundary condition. One is to add the artificial damping term to the dynamic free-surface boundary condition, in which the determination of suitable damping coefficient and the damping zone is the most important. The other is a modified Orlanski's method, which is known to be very useful for the uni-directional waves. Using these two schemes, numerical tests have been conducted for a few typical free-surface wave problems. To obtain the numerical solution of the free-surface boundary value problem, the fundamental source-distribution method is used and the fully nonlinear free-surface boundary conditions are applied. The computed results are presented in comparison with those of others for the proof of practicality of these two schemes.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.623-632
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• 1997

In this paper, the nonexistence of the global solutions of semilinear wave equations with damping terms in the boundary conditions is investigated.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.11
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• pp.179-185
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• 2004

The effect of viscous damping on stability of beam resting on an elastic foundation subjected to a dry friction force is analytically studied. The beam resting on an elastic foundation subjected to dry friction force is modeled for simplicity into a beam resting on Kelvin-Voigt type foundation subjected to distributed follower load. In particular, the effects of four boundary conditions (clamped-free, clamped-pinned, pinned-pinned, clamped-clamped) on the system stability are considered. The critical value and instability type of columns on the elastic foundation subjected to a distributed follower load is investigated by means of finite element method for four boundary conditions. The elastic foundation modulus, viscous damping coefficient and boundary conditions affect greatly both the instability type and critical load. Also, the increase of damping coefficient raises the critical flutter load (stabilizing effect) but reduces the critical divergence load (destabilizing effect).

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-206
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• 2014

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation $$u_{tt}-M({\parallel}{\nabla}u{\parallel}^2){\triangle}u+{\alpha}u_t+f(u)=0\;in\;{\Omega}{\times}[0,{\infty}),\\u(x,t)=0\;on\;{\Gamma}_1{\times}[0,{\infty}),\\{\frac{{\partial}u}{\partial{\nu}}}+g(u_t)=0\;on\;{\Gamma}_0{\times}[0,{\infty}),\\u(x,0)=u_0,u_t(x,0)=u_1\;in\;{\Omega}$$ with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some difficulties due to the presence of nonlinear terms $M({\parallel}{\nabla}u{\parallel}^2)$ and $g(u_t)$ by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.