• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.491-505
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• 2022

This paper is concerned with singularly perturbed convection-diffusion parabolic partial differential equations which have time-delayed. We used the Crank-Nicolson(CN) scheme to build a fitted operator to solve the problem. The underling method's stability is investigated, and it is found to be unconditionally stable. We have shown graphically the unstableness of CN-scheme without fitting factor. The order of convergence of the present method is shown to be second order both in space and time in relation to the perturbation parameter. The efficiency of the scheme is demonstrated using model examples and the proposed technique is more accurate than the standard CN-method and some methods available in the literature, according to the findings.

• Wind and Structures
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• 제26권3호
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• pp.147-161
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• 2018

For wind engineering applications downbursts are, presently, almost exclusively modeled, both experimentally and numerically, as transient impinging momentum jets (IJ), even though that model contains none of the physics of real events. As a result, there is no connection between the IJ-simulated downburst wind fields and the conditions of formation of the event. The cooling source (CS) model offers a significant improvement since it incorporates the negative buoyancy forcing and baroclinic vorticity generation that occurs in nature. The present work aims at using large-scale numerical simulation of downburst-producing thunderstorms to develop a simpler model that replicates some of the key physics whilst maintaining the relative simplicity of the IJ model. Using an example of such a simulated event it is found that the non-linear scaling of the velocity field, based on the peak potential temperature (and, hence, density) perturbation forcing immediately beneath the storm cloud, produces results for the radial location of the peak radial outflow wind speeds near the ground, the magnitude of that peak and the time at which the peak occurs that match well (typically within 5%) of those produced from a simple axi-symmetric constant-density dense source simulation. The evolution of the downdraft column within the simulated thunderstorm is significantly more complex than in any axi-symmetric model, with a sequence of downdraft winds that strengthen then weaken within a much longer period (>17 minutes) of consistently downwards winds over almost all heights up to at least 2,500 m.

• Structural Engineering and Mechanics
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• 제66권6호
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• pp.729-736
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• 2018

This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

• Journal of Power Electronics
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• 제15권6호
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• pp.1547-1558
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• 2015

A predictive functional control (PFC) scheme for permanent magnet synchronous motor (PMSM) servo systems is proposed in this paper. The PFC-based method is first introduced in the control design of speed loop. Since the accuracy of the PFC model is influenced by external disturbances and speed detection quantization errors of the low distinguishability optical encoder in servo systems, it is noted that the standard PFC method does not achieve satisfactory results in the presence of strong disturbances. This paper adopted the Kalman filter to observe the load torque, the rotor position and the rotor angular velocity under the condition of a limited precision encoder. The observations are then fed back into PFC model to rebuild it when considering the influence of perturbation. Therefore, an improved PFC method, called the PFC+Kalman filter method, is presented, and a high performance PMSM servo system was achieved. The validity of the proposed controller was tested via experiments. Excellent results were obtained with respect to the speed trajectory tracking, stability, and disturbance rejection.

• 한국해양공학회지
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• 제22권4호
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• pp.14-19
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• 2008

This paper proposes a mixed $H_2/H_{\infty}$ optimal PID controller with a genetic algorithm based on the dynamic model of a brushless direct current (BLDC) motor and applies it to speed control. In the dynamic model of the BLDC motor with perturbation, the proposed controller guarantees arobust and optimal tracking performance to the desired speed of the BLDC motor. A genetic algorithm was used to obtain parameters for the PID controller that satisfy the mixed $H_2/H_{\infty}$ constraint. To implement the proposed controller, a control system based on PIC18F4431 was developed. Numerical and experimental results are shown to prove that the performance of the proposed controller was better than that of the optimal PID controller.

• 한국소음진동공학회논문집
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• 제26권7호
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• pp.795-805
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• 2016

Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

• 대한기계학회논문집
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• 제12권4호
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• pp.694-704
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• 1988

본 연구에서는 현장에서 흔히 수행되는 가공 후(post-process) 측정만을 이용 한 단일절삭(single-pass)으로써 공작물이 원하는 일정한 직경을 유지할 수 있다는 것 을 실험을 통해 검증해 보이고자 한다. 이와 같은 방식은 이미 보오링 작업 중 보오 링바의 노출 길이 변화에 따른 가공면의 내경 오차를 없애주기 위한 방법으로써 제시 된 바 있다. 즉 반복 최소 자승법(recursive least squares)으로 미리 가정된 절삭 조건과 공작물 처짐 사이의 관계식과 관련된 계수를 가공 후에 가공 공작물의 표면 측 정으로 매 번보정(update)시켜 줌으로써 일정 직경을 얻기위한 절삭조건을 결정하고자 한다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.291-300
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• 1998

This paper demonstrates how ambient vibration measurements at a limited number of locations can be effectively utilized to estimate parameters of a finite element model of a large-scale structural system involving a large number of elements. System identification using ambient vibration measurements presents a challenge requiring the use of special identification techniques, which ran deal with very small magnitudes of ambient vibration contaminated by noise without the knowledge of input farces. In the present study, the modal parameters such as natural frequencies, damping ratios, and mode shapes of the structural system were estimated by means of appropriate system identification techniques including the random decrement method. Moreover, estimation of parameters such as the stiffness matrix of the finite element model from the system response measured by a limited number of sensors is another challenge. In this study, the system stiffness matrix was estimated by using the quadratic optimization involving the computed and measured modal strain energy of the system, with the aid of a sensitivity relationship between each element stiffness and the modal parameters established by the second order inverse modal perturbation theory. The finite element models thus identified represent the actual structural system very well, as their calculated dynamic characteristics satisfactorily matched the observed ones from the ambient vibration test performed on a large-scale structural system subjected primarily to ambient wind excitations. The dynamic models identified by this study will be used for design of an active mass damper system to be installed on this structure fer suppressing its wind vibration.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 하계학술대회 논문집 B
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• pp.817-819
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• 1995

Applied by periodic Stimulating Currents in Bonhoeffer-Van der Pol(BVP) model, chaotic and periodic phenomena occured at specific conditions. The conditions of the chaotic motion in BVP comprised 0.7182< $A_{1}$ <0.792 and 1.09< $A_{1}$ <1.302 proved by the analysis of phase plane, bifurcation diagram, and lyapunov exponent. To control the chaotic motion, two methods were suggested by the first used the amplitude parameter $A_{1}$,$A_{1}={\varepsilon}((x-x_{s})-(y-y_{s}))$ and the second used the temperature parameter c, c=c$(1+ {\eta}cos{\Omega}t)$ which the values of $\eta$, ${\Omega}$ varied respectlvly, and $x_{s}$, $y_{s}$ are the periodic signal. As a result of simulating these methods, the chaotic phenomena was controlled with the periodic motion of periodisity. The feasibilities of the chaotic and the periodic phenomena were analysed by phase plane and lyapunov exponent.

• Structural Engineering and Mechanics
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• 제80권6호
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• pp.727-736
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• 2021

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.