• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1991.04a
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• pp.153-158
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• 1991

Recently, demands on light weight, high strength, and low noise or vibration have led to the design of complicated structural systems. Although finite elements [1], mode synthesis [2], and statistical energy analysis [3] can be used to compute the dynamic response of such systems, the structural complexity has made the interpretation of the results of such analysis difficult. Many researchers in dynamic analysis have sought to further develop existing theories or develop alternate methods to obtain greater insight in the behavior of large massive primary systems (P systems) with connected light secondary systems (S systems). Some recent research includes work by Sackman and Kelly [4], Sackman et al.[5], Der Kiureghian et al.[6], and Igusa and Der Kiureghian [7-9] who have combined mode synthesis concepts, matrix algebraic theory, and perturbation methods for characterizing weakly-coupled structural systems. A major limitation of these works are that they are limited to lumped mass S systems. In this paper, the general ideas in the Refs.[4-9] are used to study continuous S systems and the method to reduce the complexity, studied in the works by Igusa, Achenbach, and Min [10,11], is developed into the frequency window method.

• Journal of Astronomy and Space Sciences
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• v.12 no.2
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• pp.244-255
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• 1995

The success of a satellites mission is largely depended upon the choice of an appropriate orbit. In the case of a remote sensing satellite which observes the Earth, there exits an optimum solar elevation angle depending on the mission. Therefore a sun-synchronous orbit is suitable for a remote sensing mission. The second-order theory for secular perturbation due to non-symmetric geopotential was described. To design a sun-synchronous orbit, a constraint condition on regression of node was derived. A algorithm to determine the altitude and the inclination was introduced using this constraint condition. As practical examples, the altitudes and the inclinations of four remote sensing satellites were calculated. The ground tracks obtained by the orbit propagator were used to verify the resulting sun-synchronous orbital elements.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.87-103
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• 2015

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake's length and thickness on the critical buckling load.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.1-8
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• 2003

Satellite formation flying is the placing micro-satellites with the same mission into nearby orbits to form a cluster. Clohessy-Wiltshire equations are used to describe the relative motion and control strategies between satellites within a cluster, which are known as Hill's equations. Even though Hill's equations are powerful in determining initial conditions for the satellite formation flying, they can not accurately express the relative motion under J2 perturbation. Some methods have been developed for the determination of initial conditions to avoid limits of Hill's equation. This paper gives a new method of determining initial conditions using mean elements. For this research mean elements were transformed to osculating elements using Brouwer's theory and the orbit was propaeated with the consideration of J2-J8 to get a relative position. The results show that satellites within a cluster are maintained in the desired boundary for long period and the method is effective on a fuel saving for satellite formation flying.

• Wind and Structures
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• v.7 no.4
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• pp.265-280
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• 2004

This paper presents some fundamental results on the dynamics of the periodic Karman wake behind a circular cylinder. The wake is treated like a dynamical system. External forcing is then introduced and its effect investigated. The main result obtained is the following. Perturbation of the wake, by controlled cylinder oscillations in the flow direction at a frequency equal to the Karman vortex shedding frequency, leads to instability of the Karman vortex structure. The resulting wake structure oscillates at half the original Karman vortex shedding frequency. For higher frequency excitation the primary pattern involves symmetry breaking of the initially shed symmetric vortex pairs. The Karman shedding phenomenon can be modeled by a nonlinear oscillator. The symmetrical flow perturbations resulting from the periodic cylinder excitation can also be similarly represented by a nonlinear oscillator. The oscillators represent two flow modes. By considering these two nonlinear oscillators, one having inline shedding symmetry and the other having the Karman wake spatio-temporal symmetry, the possible symmetries of subsequent flow perturbations resulting from the modal interaction are determined. A theoretical analysis based on symmetry (group) theory is presented. The analysis confirms the occurrence of a period-doubling instability, which is responsible for the frequency halving phenomenon observed in the experiments. Finally it is remarked that the present findings have important implications for vortex shedding control. Perturbations in the inflow direction introduce 'control' of the Karman wake by inducing a bifurcation which forces the transfer of energy to a lower frequency which is far from the original Karman frequency.

• Structural Engineering and Mechanics
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• v.66 no.6
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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.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.547-558
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• 2007

This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.461-468
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• 2020

The improvements of the DeCART/MUSAD code system for uncertainty analysis of HTGR neutronic parameters are presented in this paper. The function for quantifying an uncertainty of critical-spectrumweighted few group cross section was implemented using the generalized adjoint B₁ equation solver. Though the changes between the infinite and critical spectra cause a considerable difference in the contribution by the graphite scattering cross section, it does not significantly affect the total uncertainty. To reduce the number of iterations of the generalized adjoint transport equation solver, the generalized adjoint B₁ solution was used as the initial value for it and the number of iterations decreased to 50%. To reflect the implicit uncertainty, the correction factor was derived with the resonance integral. Moreover, an additional correction factor for the double heterogeneity was derived with the effective cross section of the DH region and it reduces the difference from the complete uncertainty. The code system was examined with the MHTGR-350 Ex.II-2 3D core benchmark. The k_eff uncertainty for Ex.II-2a with only the fresh fuel block was similar to that of the block and the uncertainty for Ex.II-2b with the fresh fuel and the burnt fuel blocks was smaller than that of the fresh fuel block.

• Journal of The Korean Astronomical Society
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• v.47 no.3
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• pp.87-98
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• 2014

We develop a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is implemented based on the smoothed particle hydrodynamics. The initial displacement and velocity of simulation particles are calculated according to second-order Lagrangian perturbation theory using the power spectra of dark matter and baryonic matter. The initial background temperature is given by Recfast and the temperature uctuations at the initial particle position are assigned according to the adiabatic model. We use a time-limiter scheme over the individual time steps to capture shock-fronts and to ease the time-step tension between the shock and preshock particles. We also include the astrophysical gas processes of radiative heating/cooling, star formation, metal enrichment, and supernova feedback. We test the code in several standard cases such as one-dimensional Riemann problems, Kelvin-Helmholtz, and Sedov blast wave instability. Star formation on the galactic disk is investigated to check whether the Schmidt-Kennicutt relation is properly recovered. We also study global star formation history at different simulation resolutions and compare them with observations.

• Nuclear Engineering and Technology
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• v.44 no.1
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• pp.43-52
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• 2012

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.