• Journal of computational fluids engineering
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• v.14 no.4
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• pp.41-47
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• 2009

An immersed boundary method(IBM, Kim et al.(2001)) for simulating flows over complex geometries is applied to computation of three-dimensional Floquet stability of a periodic wake. Floquet stability analysis is employed to extract different modes of three-dimensional instability. To verify the present method, a fully-resolved Floquet stability calculation for flow past a circular cylinder is considered. There are two different instability modes with long(mode A) and short (mode B) spanwise wavelengths for the periodic wake of a circular cylinder. The critical Reynolds number and the most unstable spanwise wavelengths of modes A and B are computed using the present method, and compared with other authors' results currently available.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.8
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• pp.734-741
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• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.10 s.241
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• pp.1321-1328
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• 2005

Based upon the Floquet theory, the complex modal solution for general rotor systems with periodically time-varying parameters is newly derived. The complete modal response can be obtained from the orthonormality condition between the time-variant eigenvectors and the corresponding adjoint vectors. The harmonic solutions such as the response and directional special a patterns are then derived in terms of harmonic modes whose coefficients are obtained from the modal analysis. The stability analysis by the Floquet's transition matrix and the eigen-analysis is also performed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.267-268
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• 2013

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.877-882
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• 2005

Dynamic stability of an axially accelerating beam stucture is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively targe unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• Journal of KSNVE
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• v.9 no.6
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• pp.1157-1165
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• 1999

Dynamic stability of a flying structure undertaking constnat and pulsating thrust force is investigated in this paper. The equations of motion of the structure, which is idealized as a free-free beam, are derived by using the hybrid variable method and the assumed mode method. The structural system includes a directional control unit to obtain the directional stability. Unstable regions due to periodically pulsating thrust forces are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the constant force, the location of gimbal, and the frequency of pulsating force. The validity of the diagrams are confirmed by direct numerical simulations of the dynamic system.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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• pp.1053-1059
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• 2005

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.1
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• pp.40-46
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• 2011

This paper is to investigate the effects of the asymmetrical support stiffness on the stability of a supercritical driveshaft with asymmetrical shaft stiffness and anisotropic bearings. The equations of motion is derived for a system including a rigid disk, a massless flexible asymmetric shaft, anisotropic bearings and a support beam. The Floquet theory is applied to perform the stability analysis with the variation of the support stiffness, the shaft asymmetry, the shaft damping and the shaft speed. The results show that the asymmetric support stiffness is closely related to the stability caused by primary resonance as well as the supercritical operation. First, the stiffness variation can stabilize the system around primary resonance by weakening the parametric resonance from the shaft asymmetry. Second, it also improve the stability characteristics at a supercritical operation when the support stiffness is not so high relative to the shaft stiffness.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.185.1-185.1
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• 2005

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.62-70
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• 2010

Secondary instability in the flow past two square cylinders in side-by-side arrangements is numerically studied by using a Floquet analysis. The distance between the neighboring faces of the two cylinders (G) is the key parameter which affects the secondary instability under consideration. In this paper, we present the critical Reynolds number for the secondary instability and the corresponding spanwise wave number of the most unstable (or least stable) wave for each G. Our results would shed light on a complete understanding of the onset of secondary instability in the presence of two side-by-side square cylinders.