• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1165-1176
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• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1557-1569
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• 2011

In this paper, we consider the oscillation of the following certain second order nonlinear differential equations $(r(t)(x^{\prime}(t))^{\alpha})^{\prime}+q(t)x^{\beta}(t)=0$>, where ${\alpha}$ and ${\beta}$ are ratios of positive odd integers. New oscillation theorems are established, which are based on a class of new functions ${\Phi}={\Phi}(t,s,l)$ defined in the sequel. Also, we establish some interval oscillation criteria for this equation.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.29-40
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• 2016

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.581-589
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• 2009

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term and forcing term: $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+q(t)f(x(t))=0$$. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity. And, as a consequence, our results apply to wider classes of nonlinear differential equations. Some illustrative examples are considered.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.875-882
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• 2014

In this paper, we propose a new parameter estimation method that can deal with the data of multiple time intervals simultaneously. If there are common modes in the multiple time intervals, it is possible to create a new polynomial by summing the coefficients of the prediction error polynomials of each time interval. By calculating the roots of the new polynomial, it is possible to estimate the common modes that exist in each time interval. The accuracy of the proposed parameter estimation method has been proven by using appropriate test signals.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1017-1030
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• 2012

We consider forced second order differential equation with $p$-Laplacian and nonlinearities given by a Riemann-Stieltjes integrals in the form of $$(p(t){\phi}_{\gamma}(x^{\prime}(t)))^{\prime}+q_0(t){\phi}_{\gamma}(x(t))+{\int}^b_0q(t,s){\phi}_{{\alpha}(s)}(x(t))d{\zeta}(s)=e(t)$$, where ${\phi}_{\alpha}(u):={\mid}u{\mid}^{\alpha}\;sgn\;u$, ${\gamma}$, $b{\in}(0,{\infty})$, ${\alpha}{\in}C[0,b)$ is strictly increasing such that $0{\leq}{\alpha}(0)<{\gamma}<{\alpha}(b-)$, $p$, $q_0$, $e{\in}C([t_0,{\infty}),{\mathbb{R}})$ with $p(t)>0$ on $[t_0,{\infty})$, $q{\in}C([0,{\infty}){\times}[0,b))$, and ${\zeta}:[0,b){\rightarrow}{\mathbb{R}}$ is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unifies, and improves many existing results in the literature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.476-476
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• 2009

Periodic vortex separations generate periodic vertical forces acting on a trailing edge of an airfoil. When a natural frequency of the trailing edge of the airfoil is close to a vortex shedding frequency, an amplitude of the edge oscillation becomes maximal; it makes intensive noise called singing. Motion of the trailing edge may also feedback to the vortex shedding so that self-sustained oscillation appear, and a resonant frequency is locked in some interval of the speed of the incident flow. In this study, a theoretical model is proposed and applied for modeling an airfoil singing. Results are compared with experimental measurements which are carried out in an anechoic wind tunnel.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.115-121
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• 2010

Periodic vortex separations generate periodic vertical forces acting on a trailing edge of an airfoil. When a natural frequency of the trailing edge of the airfoil is close to a vortex shedding frequency, an amplitude of the edge oscillation becomes maximal; it makes intensive noise called singing. Motion of the trailing edge may also feedback to the vortex shedding so that self-sustained oscillation appears, and a resonant frequency is locked in some interval of the speed of the incident flow. In this study, a theoretical model is proposed and applied for modeling an airfoil singing. Results are compared with experimental measurements which are carried out in an anechoic wind tunnel.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.5
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• pp.343-348
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• 2013

When a natural frequency of the trailing edge of a wing is close to a vortex shedding frequency, an amplitude of the edge oscillation becomes maximal; it makes intensive noise called singing. Motion of the trailing edge may also feedback to the vortex shedding so that self-sustained oscillation appears, and a resonant frequency is locked in some interval of the speed of the incident flow. In this study, we first evaluate main features of oscillating characteristics of the wing. Second we simulate fluid-structure interaction of the wing with a flap using a commercial code, ANSYS-CFX, and investigate lift characteristics in a frequency domain.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.1
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• pp.13-17
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• 2006

In this paper, the RCF(Resistive Companion Form) analysis method which is used to analyze small signal stability problems of non-continuous systems including switching devices. The RCF analysis method is mathematically rigorous and computes eigenvalue of the system periodic transition matrix based on discrete system analysis method. As an effect of switching operations, the eigenvalues of the systems are changed and newly unstable oscillation modes may be occurred. As an illustrating example, the oscillation modes of the system with different switching time intervals are computed exactly by the RCF analysis method and the results show that ON/OFF time intervals of switching equipments are important factors to make the system stable or unstable. This result shows that the RCF analysis method is very powerful to analyze small signal stability problems of power systems including switching devices such as FACTS equipments.