• 대한기계학회논문집B
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• 제27권8호
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• pp.1158-1164
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• 2003

Steady-state structure and acoustic-pressure responses of $H_2$/Air counterflow diffusion flames are studied numerically with a detailed chemistry in view of acoustic instability. The Rayleigh criterion is adopted to judge acoustic amplification or attenuation from flame responses. Steady-state flame structures are first investigated and flame responses to various acoustic-pressure oscillations are numerically calculated in near-equilibrium and near-extinction regimes. The acoustic responses of $H_2$/Air flame show that the responses in near-extinction regime always contribute to acoustic amplification regardless of acoustic-oscillation frequency Flames near extinction condition are sensitive to pressure perturbation and thereby peculiar nonlinear responses occur, which could be a possible mechanism in generating the threshold phenomena observed in combustion chamber of propulsion systems.

• 한국소음진동공학회논문집
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• 제13권4호
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• pp.317-322
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• 2003

Torsional oscillations of a system incorporating a Hooke's joint are investigated by adopting a nonlinear 2-degree-of-freedom model. Linear and Van der Pol transformations are applied to obtain the equations of motion to which the method of averaging can be readily applied. Various subharmonic and combination resonances are identified with the conditions of their occurrences. Applying the method of averaging leads to the reduced amplitude- and phase-equations of motion, of which constant and periodic solutions are obtained numerically. The periodic solution which emerges from Hopf bifurcation point experiences period doubling bifurcation leading to infinite solution rather than chaotic solution.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1455-1460
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• 2000

When a tube is oscillated at a resonant frequency, acoustic variables such as density, velocity, and pressure undergo very large perturbation, often described as nonlinear oscillation. In order to analyze these phenomena, nonlinear governing equation has been drived and solved numerically. Numerical simulations were accomplished to study the effect of the tube shape on the maximum pressure we can obtain. The tubes of cylindrical, conical, and cosine-shape, which have same volume and length, were investigated. Results show that the resonant frequency and patterns of pressure waves strongly depend on not only the tube shape but also the amplitude of driving acceleration. The degree of non-linearity of wave patterns was also measured by the newly defined nonlinear energy ratio of the pressure signals. It was found that the 1/2 cosine-shape tube is more suitable to induce high compression ratio than other shapes.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제2권3호
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• pp.220-226
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• 2002

In this paper, we develop the intelligent digitally redesigned fuzzy controller for nonlinear systems. Takagi-Sugeno (TS) fuzzy model is used to model the nonlinear systems and a continuous-time fuzzy-model-based controller is designed based on the extended parallel-distributed-compensation(EPDC) method . The digital controllers are determined from existing analogue controllers. The proposed method provides an accurate and effective method for digital control of continuous-time nonlinear systems and enables us to efficiently implement a digital controller via the pre-determined continuous-time 75 fuzzy-model-based controller. We have applied the proposed method to the duffing forced oscillation system to show the effectiveness and feasibility of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.461-467
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• 1998

In spite of significant nonlinearities even in the simplest model, some types of steady-state and dynamic behavior common for nonlinear systems have never been associated with distillation columns. In recent years, multiplicity of steady states has been a subject of much research and is now widely accepted. Subsequently, stability of steady states has been explored. Another phenomenon that. although widely observed in chemical reactors, has not been associated with models of distillation columns is the existence of periodic oscillations. In this article we study the steady-state and dynamic behavior of the azeotropic distillation of the ternary homogeneous system methanol-methyl butyrate-toluene. Our simulations reveal nonlinear behavior not reported in earlier studies. Under certain conditions, the open-loop distillation system shows a sustained oscillation associated with branching to periodic solutions. The limit cycles are accompanied by traveling waves inside the column. Significant underdamped oscillations are also observed over a wide range of product rates.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• Smart Structures and Systems
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• 제24권3호
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• pp.303-317
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• 2019

Magneto-rheological fluid (MRF) rotatory dampers are normally used for controlling the constant rotation of machines and engines. In this research, such a device is proposed to act as variable stiffness device to alleviate the rotational oscillation existing in the many engineering applications, such as motor. Under such thought, the main purpose of this work is to characterize the nonlinear torque-angular displacement/angular velocity responses of an MRF based variable stiffness device in oscillatory motion. A rotational hysteresis model, consisting of a rotatory spring, a rotatory viscous damping element and an error function-based hysteresis element, is proposed, which is capable of describing the unique dynamical characteristics of this smart device. To estimate the optimal model parameters, a modified whale optimization algorithm (MWOA) is employed on the captured experimental data of torque, angular displacement and angular velocity under various excitation conditions. In MWOA, a nonlinear algorithm parameter updating mechanism is adopted to replace the traditional linear one, enhancing the global search ability initially and the local search ability at the later stage of the algorithm evolution. Additionally, the immune operation is introduced in the whale individual selection, improving the identification accuracy of solution. Finally, the dynamic testing results are used to validate the performance of the proposed model and the effectiveness of the proposed optimization algorithm.

• 대한수학회논문집
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• 제26권4호
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• pp.695-708
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• 2011

Based on the multiple-time-scale (MTS) method, a general formula has been presented for solving an n-th, n = 2, 3, ${\ldots}$, order ordinary differential equation with strong linear damping forces. Like the solution of the unified Krylov-Bogoliubov-Mitropolskii (KBM) method or the general Struble's method, the new solution covers the un-damped, under-damped and over-damped cases. The solutions are identical to those obtained by the unified KBM method and the general Struble's method. The technique is a new form of the classical MTS method. The formulation as well as the determination of the solution from the derived formula is very simple. The method is illustrated by several examples. The general MTS solution reduces to its classical form when the real parts of eigen-values of the unperturbed equation vanish.

• 한국연소학회지
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• 제22권2호
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• pp.19-26
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• 2017

An experimental study investigates the flame response characteristics of jet-diffusion flame and premixed flame. The experiment was conducted while varying the amplitude. Flame lengths were quantified for OH chemiluminescence measurement and compared with the result of the flame transfer function. Flame length and flame velocity perturbation were normalized and compared with the result of the flame transfer function. The comparison results appear that velocity perturbation and flame length oscillation of premixed flame show linear behaviors on the other hand jet-diffusion flame, amplitudes are more thant 0.20, shows nonlinear behaviors of flame velocity perturbation and flame length oscillation.

• 한국수자원학회논문집
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• 제30권6호
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• pp.753-759
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• 1997

밀도가 변하는 지하수의 흐름과 용질의 수송 현상을 정확히 모델링할 수 있는 수치모델을 개발하였다. 수치모델의 정확도는 이송이 지배적인 경우에 발생하는 수치진동을 피할 수 있어야 얻을 수 있다. 이를 위하여 변분법에 기초한 비선형 수치진동흡수 유한요소법을 적용하였다. 개발된 수치모델은 기존 수치모델들과 달리 확장성이 뛰어나다. 본 수치모델의 정확도를 해석해와 다른 수치모델 결과와 비교하여 평가하였다.