• Title/Summary/Keyword: Linear perturbation theory

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Stochastic free vibration analysis of smart random composite plates

  • Singh, B.N.;Vyas, N.;Dash, P.
    • Structural Engineering and Mechanics
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    • v.31 no.5
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    • pp.481-506
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    • 2009
  • The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

Torque Sensorless Decentralized Position/Force Control for Constrained Reconfigurable Manipulator via Non-fragile H Dynamic Output Feedback

  • Zhou, Fan;Dong, Bo;Li, Yuanchun
    • Journal of Electrical Engineering and Technology
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    • v.13 no.1
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    • pp.418-429
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    • 2018
  • This paper studies the decentralized position/force control problem for constrained reconfigurable manipulator without torque sensing. A novel joint torque estimation scheme that exploits the existing structural elasticity of the manipulator joint with harmonic drive model is applied for each joint module. Based on the estimated joint torque and dynamic output feedback technique, a decentralized position/force control strategy is presented. In order to solve the problem of controller parameter perturbation, the non-fragile robust technique is introduced into the dynamic output feedback controller. Subsequently, the stability of the closed-loop system is proved using the Lyapunov theory and linear matrix inequality (LMI) technique. Finally, two 2-DOF constrained reconfigurable manipulators with different configurations are applied to verify the effectiveness of the proposed control scheme in numerical simulation.

Robust Decoupling Control of Ship Propulsion System with CPP (CPP를 갖는 선박 추진 시스템의 강인한 Decoupling 제어)

  • 김영복;변정환
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.9
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    • pp.33-42
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    • 1998
  • If a ship diesel engine is operated by consolidated control with Controllable Pitch Propeller(CPP), the minimum fuel consumption is achieved together with the demanded ship speed. For this, it is necessary that the ship is operated on the ideal operating line which satisfies the minimum fuel consumption and that the pitch angle of CPP and throtle valve angle are controlled simultaneously. In this point of view, this paper presents a controller design method for a ship propulsion system with CPP based on the decoupling control theory. To do this, Linear Matrix Inequality(LMI) approach is introduced for the control system to satisfy the given $H_\infty$ control performance and robust stability in the presence of physical parameter perturbations. The validity and applicability of this approach are illustrated by simulation in the all operating ranges.

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Wave Resistance of a Ship at Low Froude Numbers (비 Froude수에 있어서 선체의 조파저항)

  • 김인철
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.17 no.2
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    • pp.109-113
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    • 1981
  • Most existing theories on ship waves and wave resistance are based on the perturbation of the flow field by a small pararr.eter which specifies the slenderness of the ship hull. Since however, ship hulls in practice are neither so slender nor thin enough to secure the validity of the linearized theory, the agreen:ent between the theoretical prediction and the experimental result is not generally satisfactory. The author pointed out that the contribution by the non-linear term in the free surface condition can be represented by sorr.e source distribution over the still water plane. This paper leads to a forrr.ula for the wave resistance of not slender ships at low Froude nurr.bers. and deals with the asynptotic expression. As a nurr.erical example, the wave resistance of Wigley model is calculated, and the result is compared with experimental values. It is concluded that the wave resistance coefficient varies in the rate of Fn6 at low speed limit in general. A comparison with the result derived from the linearized free surface condition shows that the non-linearity of the free surface is irr portant at low speed.

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Determination of Reactivity by MO Theory (ⅩⅧ). An Intermolecular Perturbation Study of the Acid-Catalyzed Hydrolysis of Diformamide$^*$

  • Kwun, Oh-Cheun
    • Bulletin of the Korean Chemical Society
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    • v.1 no.3
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    • pp.109-112
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    • 1980
  • Ultraviolet spectrophotometric investigations were carried out on monoalkylbenzene-iodine systems in carbon tetrachloride. The results reveal the formation of one-to-one molecular complexes. On the basis of the equilibrium constants for these complexes of representative monosubstituted benzenes, the following order of increasing stability is obtained: i-propyl- ${\Delta}$H, ${\Delta}$G and ${\Delta}$S for the interaction of a number of monoalkyl substituted benzenes with iodine have been determined. In general, it can be said that as ${\Delta}$H becomes increasingly negative, corresponding decreases in the ${\Delta}$G and the ${\Delta}$S values are observed, and these variations are linear. The thermodynamic constants become increasingly negative with increasing monoalkyl substitution of the aromatic donor nucleus. The complex bond is therefore weak, and its formation is accompanied by relatively small entropy changes. Thus, analysis of these findings is discussed.

Locating a weakened interface in a laminated elastic plate

  • Zhu, J.;Yang, J.S.;Chen, W.Q.
    • Structural Engineering and Mechanics
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    • v.41 no.6
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    • pp.751-758
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    • 2012
  • We study thickness-shear (TSh) free vibrations of an unbounded, laminated elastic plate with three layers of different materials. One of the two interfaces is slightly weakened as described by the shear-lag model that allows the displacement to be discontinuous across the interface. A frequency equation is obtained from the linear theory of elasticity. A perturbation solution of the frequency equation is obtained from which the frequency shifts of TSh modes due to the weakened interface can be calculated. It is shown that the frequency shifts of TSh modes of different orders are different, and they satisfy different conditions when different interfaces are weakened. These conditions are obtained which can potentially be used as criteria for determining specifically which interface is weakened.

Smart tracking design for aerial system via fuzzy nonlinear criterion

  • Wang, Ruei-yuan;Hung, C.C.;Ling, Hsiao-Chi
    • Smart Structures and Systems
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    • v.29 no.4
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    • pp.617-624
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    • 2022
  • A new intelligent adaptive control scheme was proposed that combines the control based on interference observer and fuzzy adaptive s-curve for flight path tracking control of unmanned aerial vehicle (UAV). The most important contribution is that the control configurations don't need to know the uncertainty limit of the vehicle and the influence of interference is removed. The proposed control law is an integration of fuzzy control estimator and adaptive proportional integral (PI) compensator with input. The rated feedback drive specifies the desired dynamic properties of the closed control loop based on the known properties of the preferred acceleration vector. At the same time, the adaptive PI control compensate for the unknown of perturbation. Additional terms such as s-surface control can ensure rapid convergence due to the non-linear representation on the surface and also improve the stability. In addition, the observer improves the robustness of the adaptive fuzzy system. It has been proven that the stability of the regulatory system can be ensured according to linear matrix equality based Lyapunov's theory. In summary, the numerical simulation results show the efficiency and the feasibility by the use of the robust control methodology.

Adaptive Chaos Control of Time-Varying Permanent-Magnet Synchronous Motors (시변 영구자석형 동기 전동기의 적응형 카오스 제어)

  • Jeong, Sang-Chul;Cho, Hyun-Cheol;Lee, Hyung-Ki
    • Journal of the Institute of Convergence Signal Processing
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    • v.9 no.1
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    • pp.89-97
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    • 2008
  • Chaotic behavior in motor systems is undesired dynamics in real-time implementation since the speed is oscillated in a wide range and the torque is changed by a random manner. We present an adaptive control approach for time-varying permanent-magnet synchronous motors (PMSM) with chaotic phenomenon. We consider that its parameters are changed randomly within certain bounds. First, a nonlinear system model of a PMSM is transformed to derive a nominal linear control strategy. Then, an auxiliary control for compensating real-time control error occurred by system perturbation due to parameter change is designed by using Lyapunov stability theory. Numerical simulation is accomplished for evaluating its efficiency and reliability comparing with the traditional control method. Additionally, we test our control method in real-time motor experiment including a PSoC based drive system to demonstrate its practical applicability.

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Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core

  • Kamran Foroutan;Liming Dai
    • Steel and Composite Structures
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    • v.48 no.3
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    • pp.335-351
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    • 2023
  • This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

THE NEW HORIZON RUN COSMOLOGICAL N-BODY SIMULATIONS

  • Kim, Ju-Han;Park, Chang-Bom;Rossi, Graziano;Lee, Sang-Min;Gott, J. Richard III
    • Journal of The Korean Astronomical Society
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    • v.44 no.6
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    • pp.217-234
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    • 2011
  • We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using $6000^3$ = 216 billions and $7210^3$ = 374 billion particles, spanning a volume of $(7.200\;h^{-1}Gpc)^3$ and $(10.815\;h^{-1}Gpc)^3$, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to $1.25{\times}10^{11}h^{-1}M_{\odot}$, allowing to resolve galaxy-size halos with mean particle separations of $1.2h^{-1}$Mpc and $1.5h^{-1}$Mpc, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the CDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z = 0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.