• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.12 s.255
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• pp.1588-1595
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• 2006

The stabilities of a pinned-pinned straight pipe conveying fluid are investigated by complexification-averaging method. The flow is assumed to vary harmonically about a constant mean velocity. Instability conditions of a governing equation are analytically obtained about parametric primary, secondary and combination resonances. The resulted stability conditions show that instabilities exist when the frequency of flow fluctuation is close to one and two times the natural frequency or to the sum of any two natural frequencies. In case that the fluctuated flow frequency is close to the difference of two natural frequencies, instabilities does not exist.

• Journal of Korean Society of Steel Construction
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• v.12 no.6
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• pp.737-748
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• 2000

This paper presents a numerical analysis procedure and a characteristics for dynamic of cylindrical panels. The panels with simply-simply or simply-clamped edge supports are subjectes to circumferential compressive or flexural stresses. The differential equations governing vibration and dynamic for these panels are derived by using the fundamental differential equation of the Love-Timoshenko and are solved numerically by the Galerkin method. The panel with simply-clamped edge supports is used a trigonometric function or an eigen function of a beam as a trial function and the effects of trial functions on numerical solutions are displayed. Numerical results are presented to demonstrate the effects of the flexural parameters in natural frequencies and coefficients of critical buckling, and some typical mode shapes of vibration and buckling are also presented.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.2
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• pp.134-148
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• 2011

In general, forces acting on aerospace structures can be divided into two categories-a) conservative forces and b) nonconservative forces. Aeroelastic effects occur due to highly flexible nature of the structure, coupled with the unsteady aerodynamic forces, causing unbounded static deflection (divergence) and dynamic oscillations (flutter). Flexible wing panels subjected to jet thrust and missile type of structures under end rocket thrust are nonconservative systems. Here the structural elements are subjected to follower kind of forces; as the end thrust follow the deformed shape of the flexible structure. When a structure is under a constant follower force whose direction changes according to the deformation of the structure, it may undergo static instability (divergence) where transverse natural frequencies merge into zero and dynamic instability (flutter), where two natural frequencies coincide with each other resulting in the amplitude of vibration growing without bound. However, when the follower forces are pulsating in nature, another kind of dynamic instability is also seen. If certain conditions are satisfied between the driving frequency and the transverse natural frequency, then dynamic instability called 'parametric resonance' occurs and the amplitude of transverse vibration increases without bound. The present review paper will discuss the aeroelastic behaviour of aerospace structures under nonconservative forces.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.10
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• pp.140-147
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• 1998

The dynamic behavior of elastically restrained beams under the action of distributed tangential forces is investigated in this paper. The beam, which is fixed at one end, is assumed to rest on an intermediate spring support. The governing equations of motion are derived from the energy expressions, and the finite element formulation is employed to calculate the critical distributed tangential force. Jump phenomena for the critical distributed tangential force and instability types are presented for various spring stiffnesses and support positions. Stability maps are generated by performing parametric studies to show how the distributed tangential forces affect the frequencies and the stability of the system considered. Through the numerical simulations, the following conclusioils are obtained: (i) Only flutter type instability exists for the dimensionless spring stiffness K $\leq$ 97, regardless of the position of the spring support. (ii) For the dimensionless spring stiffness K $\leq$ 98, the transition from flutter to divergence occurs at a certain position of the spring support, and the transition position moves from the free end to the free end of the beam as the spring stiffness increases. (iii) For K $\leq$ 10$^{6}$ the support condition can be regarded as a rigid support condition.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.481-500
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• 2007

The dynamic instability of doubly curved panels, subjected to non-uniform tensile in-plane harmonic edge loading $P(t)=P_s+P_d\;{\cos}{\Omega}t$ is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to simple resonances in parametrically excited doubly curved panels. Analytical expressions for the instability regions are obtained at ${\Omega}={\omega}_m+{\omega}_n$, (${\Omega}$ is the excitation frequency and ${\omega}_m$ and ${\omega}_n$ are the natural frequencies of the system) by using the method of multiple scales. It is shown that, besides the principal instability region at ${\Omega}=2{\omega}_1$, where ${\omega}_1$ is the fundamental frequency, other cases of ${\Omega}={\omega}_m+{\omega}_n$, related to other modes, can be of major importance and yield a significantly enlarged instability region. The effects of edge loading, curvature, damping and the static load factor on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which the curved panels cannot become dynamically unstable. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.

• Tribology and Lubricants
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• v.30 no.3
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• pp.131-138
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• 2014

This study investigates the effects of the slopes of the rotational axis and bearing preloads on the natural frequencies and onset speeds of the instability of a rotor supported on gas foil bearings (GFBs). The predictive model for the rotating system consists of a rigid rotor supported on two gas foil journal bearings (GFJBs) and a pair of gas foil thrust bearings (GFTBs). Each GFJB supports approximately half the rotor weight. As the slope of the rotational axis increases from $0^{\circ}$(horizontal rotor operation) to $90^{\circ}$(vertical rotor operation), the applied load on the GFJB owing to the rotor weight decreases. The predictions show that the natural frequency and onset speed of instability decrease significantly with an increase in the slope of the rotational axis. In a parametric study, the nominal radial clearance and preload for the GFJB were changed. In general, a decrease in the nominal radial clearance lead to an increase in the natural frequency and onset speed of instability. For constant assembly clearance, the decrease in the preload changed the natural frequency and onset speed of instability with insignificant improvements in the rotordynamic stability. The present predictions can be used as design guidelines for GFBs for oil-free high-speed rotating machinery with improved rotordynamic performance.

• Wind and Structures
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• v.8 no.1
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• pp.1-12
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• 2005

A simplified analysis able to point out the most relevant geometrical and aerodynamic parameters that can influence the flutter of long span modern bridges is the aim of the paper. With this goal, by using a continuous model of the suspension bridge and by a quasi stationary approach, a simple formula of the combined vertical/torsional flutter wind speed is given. A good agreement is obtained comparing the predictions from the proposed formula with the flutter speeds of three modern suspension or cable stayed bridges: the Great Belt East Bridge, the Akashi and Normandie bridges. The paper ends with some comments and comparisons with the well known Selberg formula.

• Journal of Power Electronics
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• v.14 no.6
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• pp.1208-1216
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• 2014

Mismatch between switching frequency and circuit parameters often occurs in industrial applications, which would lead to instability phenomena. The bifurcation behavior of $V^2$ controlled buck converter is investigated as the pulse width modulation period is varied. Nonlinear behavior is analyzed based on the monodromy matrix of the system. We observed that the stable period-1 orbit was first transformed to the period-2 bifurcation, which subsequently changed to chaos. The mechanism of the series of period-2 bifurcations shows that the characteristic eigenvalue of the monodromy matrix passes through the unit circle along the negative real axis. Resonant parametric perturbation technique has been applied to prevent the onset of instability. Meanwhile, the extended stability region of the converter is obtained. Simulation and experimental prototypes are built, and the corresponding results verify the theoretical analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1034-1039
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• 1992

Time Delay Controller(TDC) is a model following controller which uses input and output values and state variables to estimate additional quantity of dynamics due to external disturbances and/or model parameters variation at some past instant. TDC is very robust against parametric uncertainty whil it is not robust against unmodeled dynamics even showing instability. To solve this problem a stability anlysis is performed and a compensation technique using reduced order observer, Anti-Filtering Compensator(AFC), is proposed for a case in which the high order kinown dynamics is deliberately ignored. If the ignored dynamics causes instability of the TDC control system, AFC is shown to be indispensible fot a stable implementation of TDC.