• Journal of Ocean Engineering and Technology
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• v.24 no.1
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• pp.34-38
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• 2010

An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.46-51
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• 2004

Natural frequencies of the transverse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.10a
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• pp.152-157
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• 2003

Natural frequencies of the transνerse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.572-577
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• 1992

In this paper, the optimal homing guidance problem is investigated for the general missile/target models described in the state-space. The closed-form solution of the optimal guidance law derived, and its asymptotic properties are studied as the time-to-go goes to infinity or zero. Futhermore, several approximate solutions of the optimal guidance law are suggested for real-time applications.

• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.39-47
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• 2000

Bifurcation intability modes of axially compressed circular cylindrical shell are investigated in the limit of zero thickness (i.e., h (thickness) ${\rightarrow}$ 0) analytically, adopting the general stability theory developed by Triantafyllidis and Kwon (1987) and Kwon (1992). The primary state of the shell is obtained in a closed form using the asymptotic technique, and then the straight-forward bifurcation analysis is followed according to the general stability theory to obtain the bifurcation modes in the limit of zero thickness in a full analytical manner. Hence, the closed form bifurcation solution is obtained. Finally, the result is compared with the classical one.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.277-284
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• 1993

Interfacial surface crack perpendicular to the surface, which is imbedded into bonded quarter planes under single anti-plane shear load is analyzed. The problem is formulated using Mellin transform, form which single Wiener-Hopf equation is derived. By solving the equation stress intensity factor is obtained in closed form. This solution can be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.913-917
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• 1989

In this paper, the selection method of weighting matrices in the discrete-time LQ problem are suggested in order to improve the guaranteed stability margins, i.e. the gain and phase margins. The asymptotic properties of the solution of the algebraic Riccati equations are investigated by using the closed form solution of the difference Riccati equations. It is shown that the solution of the algebraic Riccati equations monotonically increases as the state weighting matrix Q or the control weighting matrix R increase. The increasing rate of the solution is shown to be much less than that of R for large R. It is also proven that the guaranteed stability margins increases as the ratio between Q and R decreases.

• Journal of Communications and Networks
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• v.15 no.5
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• pp.476-485
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• 2013

In this paper, the effective capacity of a multiple-input multiple-output (MIMO) system in two different cases with receive antenna selection (RAS) and transmit antenna selection (TAS) schemes is investigated. A closed-form solution for the maximum constant arrival rate of this network with statistical delay quality of service (QoS) constraint is extracted in the quasi-static fading channel. This study is conducted in two different cases.When channel state information (CSI) is not available at the MIMO transmitter, implementation of TAS is difficult. Therefore, RAS scheme is employed and one antenna with the maximum instantaneous signal to noise ratio is chosen at the receiver. On the other hand, when CSI is available at the transmitter, TAS scheme is executed. In this case, one antenna is selected at the transmitter. Moreover, an optimal power-control policy is applied to the selected antenna and the effective capacity of the MIMO system is derived. Finally, this optimal power adaptation and the effective capacity are investigated in two asymptotic cases with the loose and strict QoS requirements. In particular, we show that in the TAS scheme with the loose QoS restriction, the effective capacity converges to the ergodic capacity. Then, an exact closed-form solution is obtained for the ergodic capacity of the channel here.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.2
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• pp.184-195
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• 1995

A theoretical one-dimensional model for the charging process in stratified thermal storage tanks is established presuming that the fluid ensuing from the tank inlet creates a perfectly mixed, layer above the thermocline. Both the generic and asymptotic closed-form solutions are obtained via the Laplace transformation. The asymptotic solution describes the nature of the charging pertaining to the case of no thermal diffusion, whereas the generic solution is of practical importance to understand the role of operating parameters on the stratification. The present model is validated through comparison with available experimental data, where they agree well with each other within a reasonable limit. An interpretation of the exact solution entails two important features associated with the charging process. The first is that an in-crease in the mixing depth $h_m$ causes a relatively slow temperature rise in the perfectly mixed region, but on the other hand it results in a faster decay of the overall temperature gradient across the thermocline. Next is the predominance of the mixing depth in the presence of the prefectly mixed region. In such a case the effect of the Peclet number is marginal and there-fore the thermal characteristics are solely dependent on the mixing depth paticularly for large $h_m$. The Peclet number affects significantly only for the case without mixing. Variation of the storage efficiency in response to the change in the mass flow rate agrees favorably with the published experimental results, which confirms the utility of the present study.