• Advances in aircraft and spacecraft science
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• v.2 no.2
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• pp.199-215
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• 2015

This study focuses on the limit cycle oscillations (LCOs) of cantilever swept-back wings containing a cubic nonlinearity in an incompressible flow. The governing aeroelastic equations of two degrees-of-freedom swept wings are derived through applying the strip theory and unsteady aerodynamics. In order to apply strip theory, mode shapes of the cantilever beam are used. The harmonic balance method is used to calculate the frequencies of LCOs. Linear flutter analysis is conducted for several values of sweep angles to obtain the flutter boundaries.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• Wind and Structures
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• v.7 no.4
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• pp.251-264
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• 2004

The effects of a class of nonlinear Tuned Mass Dampers on the aeroelastic behavior of SDOF systems are investigated. Unlike classical linear TMDs, nonlinear constitutive laws of the internal damping acting between the primary oscillator and the TMD are considered, while the elastic properties are keept linear. The perturbative Multiple Scale Method is applied to derive a set of bifurcation equations in the amplitude and phase and a parametric analysis is performed to describe the postcritical scenario of the system. Both cubic- and van der Pol-type dampings are considered and the dependence of the limit-cycle amplitudes on the system parameters is studied. These new results, compared with the previously obtained bifurcation scenario of a SDOF aeroelastic oscillator equipped with a linear TMD, show a detrimental effect on the maximum limit-cycle amplitude reduction of the nonlinear TMD. However, the analyses evidence that in the parameter region away from the perfect tuning condition the nonlinear connection can be used to tune the system with an enhancement of the limit-cycle amplitude reduction.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.447-470
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• 2016

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of a swept aircraft wing with cubic restoring moments in the pitch degree of freedom is investigated. The unsteady aerodynamic loading applied on the wing is modeled by using the strip theory. The harmonic balance method is used to calculate the LCO frequency and amplitude for the swept wing. Finally the super and subcritical Hopf bifurcation diagrams are plotted. It is concluded that the type of bifurcation and turning point location is sensitive to the system parameters such as wing geometry and sweep angle.

• Journal of KSNVE
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• v.8 no.6
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• pp.1144-1149
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• 1998

A two degree-of-freedom model of suspended cables is studied for forced resonant response. The method of averaging is used to obtain first-order approximations to the response of the system. A bifurcation analysis of the averaged system is performed in the case of 2-to-1 internal resonance. Nonlinear coupled-mode motions are found to bifurcate from single-mode responses and further bifurcate to limit cycle motions via Hopf bifurcations. The limit cycle solutions undergo period doubling bifurcations to chaos.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.05a
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• pp.240-243
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• 2003

Combustion instability phenomena have been observed in various different combustion systems. For each specific combustion system, pressure fluctuations measured during high frequency combustion instability presented many different characteristics. High frequency instability occurring in a lean premixed gas turbine combustor mar be dominantly affected by a nonlinear relation between pressure oscillations and heat release rate fluctuations, and gas dynamics plays a crucial role in determining an amplitude of a limit cycle for a liquid rocket thrust chamber. Combustion instability phenomena manifest their inherent nonlinear characteristics. One is a limit cycle and the other bifurcation described by nonlinear time series analysis.

• Interaction and multiscale mechanics
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• v.4 no.4
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• pp.291-311
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• 2011

To simulate the self excited torsional vibrations of rotating drill strings (DSs) in vertical bore-holes, the nonlinear wave models of homogeneous and sectional torsional pendulums are formulated. The stated problem is shown to be of singularly perturbed type because the coefficient appearing before the second derivative of the constitutive nonlinear differential equation is small. The diapasons ${\omega}_b\leq{\omega}\leq{\omega}_l$ of angular velocity ${\omega}$ of the DS rotation are found, where the torsional auto-oscillations (of limit cycles) of the DS bit are generated. The variation of the limit cycle states, i.e. birth (${\omega}={\omega}_b$), evolution (${\omega}_b<{\omega}<{\omega}_l$) and loss (${\omega}={\omega}_l$), with the increase in angular velocity ${\omega}$ is analyzed. It is observed that firstly, at birth state of bifurcation of the limit cycle, the auto-oscillation generated proceeds in the regime of fast and slow motions (multiscale motion) with very small amplitude and it has a relaxation mode with nearly discontinuous angular velocities of elastic twisting. The vibration amplitude increases as ${\omega}$ increases, and then it decreases as ${\omega}$ approaches ${\omega}_l$. Sectional drill strings are also considered, and the conditions of the solution at the point of the upper and lower section joints are deduced. Besides, the peculiarities of the auto-oscillations of the sectional DSs are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.7 s.250
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• pp.671-681
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• 2006

This study focuses on the development of numerical procedure to analyze the nonlinear combustion instabilities in liquid rocket engine. Nonlinear behaviors of acoustic instabilities are characterized by the existence of limit cycle in linearly unstable engines and nonlinear or triggering instability in linearly stable engines. To discretize convective fluxes with high accuracy and robustness, approximated Riemann solver based on characteristics and Euler-characteristic boundary conditions are employed. The present procedure predicts well the transition processes from initial harmonic pressure disturbance to N-like steep-fronted shock wave in a resonant pipe. Longitudinal pressure oscillations within the SSME(Space Shuttle Main Engine) engine have been analyzed using the pressure-sensitive time lag model to account for unsteady combustion response. It is observed that the pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.58-61
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• 2015

Combustion instability in solid rocket motors is a long-term open problem since the first rockets were used. Based on the numerous previous studies, it is known that the limit cycle amplitude is one of the key characteristics of the nonlinear combustion instability in solid rocket motors. Flandro's extended energy balance corollary, aims to predict the limit cycle amplitude of complex, nonlinear pressure oscillations for rockets or air-breathing engines, and leads to a precise assessment of nonlinear combustion instability in solid rocket motors. However, based on the comparison with experimental data, it is revealed that the Flandro's method cannot accurately describe such a complex oscillatory pressure. Thus in this work we make modifications of the nonlinear term in the nonlinear wave equations which represents the interaction of different modes. Through this modified method, a numerical simulation of the cylindrical solid rocket has been carried out, and the simulated result consists well with the experimental data. It means that the added coefficient makes the nonlinear wave growth equations describe the experimental data better.

• Bulletin of the Korean Chemical Society
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• v.26 no.4
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• pp.543-547
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• 2005

The Belousov-Zhabotinskii system measured by a Pt electrode is investigated under external electrode current constraint. A dynamical analysis of the electrode reaction phase has been made by means of a linearized stability criterion valid for three-variable system. It turns out that limit cycle oscillatory regime and dynamical behaviors of the electrode reaction phase have been degenerated under periodical electrode current.