• Proceedings of the Zoological Society Korea Conference
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• 2003.08a
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• pp.166.2-166
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• 2003

No Abstract, See Full Text

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.215-224
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• 2017

The moment closure method is an approximation method to compute the moments for stochastic models of chemical reaction systems. In this paper, we develop an analytic estimation of errors generated from the approximation of an infinite system of differential equations into a finite system truncated by the moment closure method. As an example, we apply the result to an essential bimolecular reaction system, the dimerization model.

• Journal of Electrical Engineering and Technology
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• v.8 no.2
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• pp.271-281
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• 2013

In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.76.3-76
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• 2002

The purpose of this paper is to present a new nonlinear feedback control called AACC (Augmented automatic choosing control) for nonlinear systems. Generally, it is easy to design the optimal control laws for linear systems, but it is not so for nonlinear systems, though they have been studied for many years. One of most popular and practical nonlinear control laws is synthesized by applying a linearization method by Taylor expansion truncated at the first order and the linear optimal control method. This is only effective in a small region around the steady state point or in almost linear systems. Controllers based on a change of coordinates in differential geometry are effective in wider...

• Steel and Composite Structures
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• v.25 no.5
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• pp.581-591
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• 2017

The dynamic instability of truncated conical shells subjected to dynamic axial load within first order shear deformation theory (FSDT) is examined. The conical shell is made from functionally graded (FG) orthotropic material. In the formulation of problem a dynamic version of Donnell's shell theory is used. The equations are converted to a Mathieu-Hill type differential equation employing Galerkin's method. The boundaries of main instability zones are found applying the method proposed by Bolotin. To verify these results, the results of other studies in the literature were compared. The influences of material gradient, orthotropy, as well as changing the geometric dimensions on the borders of the main areas of the instability are investigated.

• Computational Structural Engineering : An International Journal
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• v.2 no.1
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• pp.43-50
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• 2002

This paper presents a method to predict dynamic responses of floating bodies in the time domain. Because of the frequency-dependence of the radiation wave forces, the memory effect must be taken into account when the responses are evaluated in the time domain. Although the formulations firstly developed by Cummins (1962) have been well-known for this purpose, the effective numerical procedure has not been established yet. This study employs FFT (Fast Fourier Transform) algorithm to evaluate the memory effect function, and the equations of motion of an integro-differential type are solved by Newmark-β method. Numerical examples for a truncated circular cylinder have indicated the effectiveness of the proposed numerical procedure.

• Advances in nano research
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• v.16 no.2
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• pp.201-215
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• 2024

The present research study emphasizes the utilization of mathematical simulation on a nanoelectromechanical systems (NEMS) sensor to facilitate the detection of injuries in players and equipment. Specifically, an investigation is conducted on the thermal buckling behavior of a small-scale truncated conical, cylindrical beam, which is fabricated using porous functionally graded (FG) material. The beam exhibits non-uniform characteristics in terms of porosity, thickness, and material distribution along both radial and axial directions. To assess the thermal buckling performance under various environmental heat conditions, classical and first-order nonlocal beam theories are employed. The governing equations for thermal stability are derived through the application of the energy technique and subsequently numerically solved using the extended differential quadratic technique (GDQM). The obtained results are comprehensively analyzed, taking into account the diverse range of effective parameters employed in this meticulous study.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.213-221
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• 2013

This paper introduces a mesh continuation scheme for a one-dimensional inverse medium problem to reconstruct the spatial distribution of elastic wave velocities in heterogeneous semi-infinite solid domains. To formulate the inverse problem, perfectly-matched-layers(PMLs) are introduced as wave-absorbing boundaries that surround the finite computational domain truncated from the originally semi-infinite extent. To tackle the inverse problem in the PML-truncated domain, a partial-differential-equations(PDE)-constrained optimization approach is utilized, where a least-squares misfit between calculated and measured surface responses is minimized under the constraint of PML-endowed wave equations. The optimization problem iteratively solves for the unknown wave velocities with their updates calculated by Fletcher-Reeves conjugate gradient algorithms. The optimization is performed using a mesh continuation scheme through which the wave velocity profile is reconstructed in successively denser mesh conditions. Numerical results showed the robust performance of the mesh continuation scheme in reconstructing target wave velocity profile in a layered heterogeneous solid domain.

• Steel and Composite Structures
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• v.26 no.6
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• pp.771-791
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• 2018

This paper deals with the low velocity impact response and dynamic stresses of composite sandwich truncated conical shells (STCS) with compressible or incompressible core. Impacts are assumed to occur normally over the top face-sheet and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The displacement fields of core and face sheets are considered by higher order and first order shear deformation theory (FSDT), respectively. Considering continuity boundary conditions between the layers, the motion equations are derived based on Hamilton's principal incorporating the curvature, in-plane stress of the core and the structural damping effects based on Kelvin-Voigt model. In order to obtain the contact force, the displacement histories and the dynamic stresses, the differential quadrature method (DQM) is used. The effects of different parameters such as number of the layers of the face sheets, boundary conditions, semi vertex angle of the cone, impact velocity of impactor, trapezoidal shape and in-plane stresses of the core are examined on the low velocity impact response of STCS. Comparison of the present results with those reported by other researchers, confirms the accuracy of the present method. Numerical results show that increasing the impact velocity of the impactor yields to increases in the maximum contact force and deflection, while the contact duration is decreased. In addition, the normal stresses induced in top layer are higher than bottom layer since the top layer is subjected to impact load. Furthermore, with considering structural damping, the contact force and dynamic deflection decrees.