• 전기의세계
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• v.30 no.11
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• pp.728-733
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• 1981

Most of real world systems are highly non-linear. But due to difficulties in analyzing and dealing with it, only the linear system theory is well estabilished. Bilinear system where state and control are linear but not linear jointly is introduced. Here shows that optimal state estimation of stochastic bilinear system requirs infinite dimensional filter, thus onesub-optimal estimator for this system is suggested.

• Journal of KSNVE
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• v.10 no.2
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• pp.291-298
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• 2000

This paper intends to provide an analytic vibrational model of non-circular cutting by a lathe and to investigate its stability criteria. A single degree-of-freedon model based on the orthogonal cutting theory has the characteristics of parametric excitation due to the nonlinear cutting force that changes periodically its direction as well as its magnitude. The Floquet theory has been applied to investigate the stability of the linearized system and the stability diagrams have been obtained with respect to the ovality, the cut velocity and the cut depth. Also nonlinear analysis has been performed to verify the linear analysis and compare the results with those from circular cutting. Results show that a critical cut depth is decreased as the ovality is increased while a critical cut velocity is increased as the ovality is increased. Also, a good agreement in critical conditions has been observed between the linear and nonlinear analyses for the ovality less than 2%. Accordingly, the linear analysis can be said to be applicable for most practical oval cuttings whose ovality are much less than 2%.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.7-14
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• 2000

Nowadays, the viscous damper using high viscosity oil was much to be used for engine shafting system to reduce the excessive additional stress by torsional vibration. In general, it was assumed that the viscous damper could be modelled having only damping coefficient, that is to say, whose stiffness be ignored. But it is found that there exists a jump phenomenon, as a kind of non-linear vibration, in the actual engine shafting system with a damper of high viscosity. Therefore the damper ring and the casing are modelled as two mass elastic system with a complex viscosity. Also, to analyze a non-linear phenomenon, it is assumed that the viscous damper has a linear stiffness coefficient in proportion to the angular amplitude and a non-linear stiffness coefficient in proportion to cube of the angular amplitude. For the analysis, Quasi-Newton method with BFGS(Broyden-Fletcher-Goldfarb-Shanno) formula is used. Both calculated and measured values are provided in this paper which confirm the possibility of applying non-linear theory to engine shafting system with viscous damper.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.495-510
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• 2015

Free vibration of non-uniform embedded nanoplates based on classical (Kirchhoff's) plate theory in conjunction with nonlocal elasticity theory has been studied. The nanoplate is assumed to be rested on two-parameter Winkler-Pasternak elastic foundation. Non-uniform material properties of nanoplates have been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinates. Detailed analysis has been reported for all possible casesof such variations. Trial functions denoting transverse deflection of the plate are expressed in simple algebraic polynomial forms. Application of the present method converts the problem into generalised eigen value problem. The study aims to investigate the effects of non-uniform parameter, elastic foundation, nonlocal parameter, boundary condition, aspect ratio and length of nanoplates on the frequency parameters. Three-dimensional mode shapes for some of the boundary conditions have also been illustrated. One may note that present method is easier to handle any sets of boundary conditions at the edges.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1955-1959
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• 2005

This paper presents a systematic analysis and a simple design of a robust adaptive control law for a class of non linear systems with modeling errors and a time-delay input. The theory for designing a robust adaptive control law based on input- output feedback linearization of non linear systems with uncertainties and a time-delay in the manipulated input by the approach of parameterized state feedback control is presented. The main advantage of this method is that the parameterized state feedback control law can effectively suppress the effect of the most parts of nonlinearities, including system uncertainties and time-delay input in the pp-coupling perturbation form and the relative order of non linear systems is not limited.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.152-153
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• 2007

industrial site has led to a growing concern for harmonic distortion and the resulting impacts on system equipment and operation. Harmonic current is generated by the operation of non-linear load, it means that voltage and current waveforms exhibit a non-linear relationship. Harmonics cause increase losses in the customer and utility power system components. This paper describes application of instantaneous active and reactive theory for the compensation of harmonic currents in three-phase non-linear load.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.713-722
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• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.