• East Asian mathematical journal
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• v.34 no.1
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• 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.28 no.3
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• pp.339-345
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchho type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1137-1152
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• 2005

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

• Journal of Radiation Protection and Research
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• v.32 no.4
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• pp.190-193
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• 2007

The objective of this study is to recommend the radiation protection design parameters from the shielding point of view for concrete wall between the decay tank room and the primary pump room in TRIGA Mark-II Research Reactor Facility. The shield design for this concrete wall has been performed with the help of Point-kernel Shielding Code Micro-Shield 5.05 and this design was also validated based on the measured dose rate values with Radiation Survey Meter (G-M Counter) considering the ICRP-60 (1990) recommendations for occupational dose rate limit ($10{\mu}Sv/hr$). The recommended shield design parameters are: (i) thickness of 114.3 cm Ilmenite-Magnetite Concrete (IMC) or 129.54 cm Ordinary Reinforced Concrete (ORC) for concrete wall A (ii) thickness of 66.04 cm Ilmenite-Magnetite Concrete (IMC) or 78.74 cm Ordinary Reinforced Concrete (ORC) for concrete wall B and (iii) door thickness of 3.175 cm Mild Steel (MS) on the entrance of decay tank room. In shielding efficiency analysis, the use of I-M concrete in the design of this concrete wall shows that it reduced the dose rate by a factor of at least 3.52 times approximately compared to ordinary reinforced concrete.

• East Asian mathematical journal
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• v.32 no.1
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• pp.117-128
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.455-466
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• 2013

In recent years, many countries have added railway noise to the issues covered by noise regulations. It is known that the rail is the dominant source of rolling noise at frequency range of 500Hz-2000Hz for the conventional speeds (<160km/h). One of the effective ways to reduce noise from railway track is using a rail vibration absorber. To study the acoustic performance of rail absorber, the decay rates of vibration have long been used by researcher. In this paper, A FE model of a periodic supported rail with infinite element in ABAQUS is developed to study the acoustic performance of the rail absorber. To compute the decay rates, acceleration responses along the rail transferred to MATLAB to obtain response levels in frequency domain and then by processing the response levels, the decay rates obtained for each1/3octav band. Continous rail absorber is represented by a steel layer and an elastomer layer. The decay rates for conventional rail and rail with one-side absorber and also, the rail with two side absorber are obtained and compared. Then, to improve the system of rail absorber, a steel plate with elastomer layer is added to bottom of the rail foot. The vertical decay rate results show that the decay rate of rail vibration along the track is significantly increased around the tuned frequency of the absorber and thus the rail vibration energy is substantially reduced in the corresponding frequency region and also effective in rail noise reduction.

• Bulletin of the Korean Chemical Society
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• v.17 no.11
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• pp.1000-1004
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• 1996

A random walk simulation was used to determine the triplet exciton density and annihilation rate for a two dimensional lattice of naphthalene choleic acid with small amount of β-methylnaphthalene (BMN). The results demonstrate that energy transfer efficiency (α) increases as density increases and the annihilation begins to become significant at triplet exciton densities higher then 10-3/sites. Another simulation was carried out to determine annihilation rate and unimolecular decay rate in the absence of BMN. The results indicate that the annihilation rate is equal to the unimolecular decay rate at the density of 1.2×10-3/sites.

• Journal of Environmental Health Sciences
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• v.23 no.4
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• pp.57-66
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• 1997

Successful energy conservation and good indcfor air quality (IAQ) are highly dependent on ventilation system. Air filtration is a primary solution of indoor air control strategies in terms of reducing energy consumption and improving ihdoor air quality. A conventional system with bypass filter, as it is called variable-air-volume/bypass filtration system (VAV/BPFS), is a variation of the conventional variable air volume (VAV) systems, which is designed to eliminate indoor air pollutant and to save energy. Bypass filtration system equipped with a high-efficiency particulate filter and carbon absorbent provides additional cleaned air into indoor environments and maintain good IAQ for human health. The objectives of this research were to compare the relative total decay rate of indoor air pollutant concentrations, and to develop a mathematical model simulating the performance of VAV/BPFS. All experiments were performed in chamber under the controlled conditions. The specific conclusions of this research are: 1. The VAV/BPFS system is more efficient than the VAV system in removing indoor air pollutant concentration. The total decay rates of aerosol, and total volatile organic compound (TVOC) for the VAV/BPFS system were higher than those of the conventional VAV system. 2. IAQ model predictions of each pollutant agree closely with the measured values. 3. According to IAQ model evaluation, reduction of outdoor supply air results in decreased dilution removal rate and on increased bypass filtration removal rate with the VAV/BPFS. As a results, we recommends the VAV/BPFS as an alternative to conventional VAV systems.

• 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.