• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.27-34
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• 2013

In this paper, we consider the Duffing type p-Laplacian equation with multiple deviating arguments of the form $$({\varphi}_p(x^{\prime}(t)))^{\prime}+Cx^{\prime}(t)+go(t,x(t))+\sum_{k=1}^ngk(t,x(t-{\tau}_k(t)))=e(t)$$. By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation. Moreover, an example is given to illustrate the effectiveness of our results.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 합동 추계학술대회 논문집 정보 및 제어부문
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• pp.15-17
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• 2001

This paper deals with a design problem of a switching-type fuzzy-model-based controller for a nonlinear system. Takagi-Sugeno(TS) fuzzy model and duffing forced-oscillation system are employed in designing the switching-type fuzzy controller. Finally, we analyze the stability of the global system controlled by the proposed controller.

• 한국전자통신학회논문지
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• 제7권5호
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• pp.1073-1078
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• 2012

본 논문에서는 MEMS에서 비선형적인 특성을 확인하기 위하여 Duffing 방정식을 가지는 MEMS 시스템을 제안하고 여기에 다른 종류의 비선형 항을 삽입하였을 때의 비선형 현상을 분석하였다. 검증 방법으로 파라미터 변화에 의한 카오스 운동이 있음을 시계열 데이터, 위상 공간, 전력 스펙트럼을 통하여 확인하였다.

• 한국전자통신학회논문지
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• 제9권6호
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• pp.711-717
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• 2014

행복은 사회학과 심리학에서 주된 관심사로 연구되어 왔다. 본 논문에서는 Spring-Damper-Mass 시스템과 등가적으로 구성할 수 있는 새로운 2차계로 구성한 행복 모델을 제안하여 Duffing 방정식과 동일한 형태의 2차원 모델로 구성한다. Duffing 방정식에 비선형 항을 추가하고 행복 현상이 나타날 수 있는 외부 신호로서 주기적인 정현파와 가우시안 백색 잡음을 인가하였다. 그런 후 새로운 행복 모델에서 파라미터 변화에 따라 랜덤 운동, 주기 운동, 카오스 운동이 있음을 확인하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.35.6-35
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• 2002

$\textbullet$ The duffing forced oscillation system. $\textbullet$ The picture is result of the computer simulation. $\textbullet$ Control input of the PWM controller. $\textbullet$ The solid line type is resulted by digital controller. $\textbullet$ The dotted line type is resulted by analogue controller.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• 한국세라믹학회지
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• 제31권10호
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• pp.1133-1140
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• 1994

Nonlinear resonance characteristics of transverse type-PZT ceramic resonator were investigated, and their nonlinear coefficients were calculated using the nonlinear theory proposed by Duffing. Resonance characteristics of sample showed nonlinearity by the thermal effects due to driving current. Nonlinear coefficients greatly affected by sample dimension, however comparing with respect to current density, it was almost constant. Nonlinear coefficients were not changed as driving current increased upto 40 mA/$\textrm{cm}^2$, when $\alpha$ and $\beta$ was 920 and -10.6, respectively, while nonlinear coefficients exponentially increased beyond the current density of 40 mA/$\textrm{cm}^2$. Nonlinear coefficients were slightly increased as temperature increased.

• 한국공간구조학회논문집
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• 제20권4호
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• pp.149-158
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• 2020

The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.

• Advances in nano research
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• 제16권3호
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• pp.231-249
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• 2024

When the amplitude of the vibrations is equivalent to that clearance, the vibrations for small amplitudes will really be significantly nonlinear. Nonlinearities will not be significant for amplitudes that are rather modest. Finally, nonlinearities will become crucial once again for big amplitudes. Therefore, the concrete panel system may experience a big amplitude in this work as a result of the high temperature. Based on the 3D modeling of the shell theory, the current work shows the influences of the von Kármán strain-displacement kinematic nonlinearity on the constitutive laws of the structure. The system's governing Equations in the nonlinear form are solved using Kronecker and Hadamard products, the discretization of Equations on the space domain, and Duffing-type Equations. Thermo-elasticity Equations. are used to represent the system's temperature. The harmonic solution technique for the displacement domain and the multiple-scale approach for the time domain are both covered in the section on solution procedures for solving nonlinear Equations. An effective data-driven solution is often utilized to predict how different systems would behave. The number of hidden layers and the learning rate are two hyperparameters for the network that are often chosen manually when required. Additionally, the data-driven method is offered for addressing the nonlinear vibration issue in order to reduce the computing cost of the current study. The conclusions of the present study may be validated by contrasting them with those of data-driven solutions and other published articles. The findings show that certain physical and geometrical characteristics have a significant effect on the existing concrete panel structure's susceptibility to temperature change and GPL weight fraction. For building construction industries, several useful recommendations for improving the thermo-mechanics' behavior of structural concrete panels are presented.