• Advances in materials Research
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• v.12 no.2
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• pp.101-118
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• 2023

The purpose of this paper is to study the effects of magnetic field and gravitational field on fiber-reinforced thermoelastic medium with memory-dependent derivative. Three-phase-lag model of thermoelasticity (3PHL) is used to study the plane waves in a fiber-reinforced magneto-thermoelastic material with memory-dependent derivative. A gravitating magneto-thermoelastic two-dimensional substrate is influenced by both thermal shock and mechanical loads at the free surface. Analytical expressions of the considered variables are obtained by using Laplace-Fourier transforms technique with the eigenvalue approach technique. A numerical example is considered to illustrate graphically the effects of the magnetic field, gravitational field and two types of mechanical loads(continuous load and impact load).

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.469-476
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• 2022

A mathematical model of Lord-Shulman photo-thermal theorem induced by pulse heat flux is presented to study the propagations waves for plasma, thermal and elastic in two-dimensional semiconductor materials. The medium is assumed initially quiescent. By using Laplace-Fourier transforms with the eigenvalue method, the variables are obtained analytically. A semiconductor medium such as silicon is investigated. The displacements, stresses, the carrier density and temperature distributions are calculated numerically and clarified graphically. The outcomes show that thermal relaxation time has varying degrees of effects on the studying fields.

• Structural Engineering and Mechanics
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• v.92 no.1
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• pp.53-64
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• 2024

This paper presents an innovative theoretical and numerical model to predict the lateral-torsional buckling (LTB) of simply supported steel I-beams with external prestressed tendons. The model incorporates an updated prestressing force, accounting for thermal effects and various external loadings. Critical multipliers are determined by solving an eigenvalue problem derived from applying Galërkin's approach to a set of nonlinear equilibrium equations. Validation is carried out through Finite Element Method (FEM) simulations, incorporating a new expression for an equivalent thermal expansion coefficient for the beam-tendon system, addressing both mechanical and thermal deformations. The primary aim is to estimate critical conditions considering material property degradation due to fire. The present results are generally in good agreement with those provided by the literature.

• Journal of the Optical Society of Korea
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• v.18 no.4
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• pp.317-329
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• 2014

In vision measurement systems based on structured light, the key point of detection precision is to determine accurately the central position of the projected laser line in the image. The purpose of this research is to extract laser line centers based on a decision function generated to distinguish the real centers from candidate points with a high recognition rate. First, preprocessing of an image adopting a difference image method is conducted to realize image segmentation of the laser line. Second, the feature points in an integral pixel level are selected as the initiating light line centers by the eigenvalues of the Hessian matrix. Third, according to the light intensity distribution of a laser line obeying a Gaussian distribution in transverse section and a constant distribution in longitudinal section, a normalized model of Hessian matrix eigenvalues for the candidate centers of the laser line is presented to balance reasonably the two eigenvalues that indicate the variation tendencies of the second-order partial derivatives of the Gaussian function and constant function, respectively. The proposed model integrates a Gaussian recognition function and a sinusoidal recognition function. The Gaussian recognition function estimates the characteristic that one eigenvalue approaches zero, and enhances the sensitivity of the decision function to that characteristic, which corresponds to the longitudinal direction of the laser line. The sinusoidal recognition function evaluates the feature that the other eigenvalue is negative with a large absolute value, making the decision function more sensitive to that feature, which is related to the transverse direction of the laser line. In the proposed model the decision function is weighted for higher values to the real centers synthetically, considering the properties in the longitudinal and transverse directions of the laser line. Moreover, this method provides a decision value from 0 to 1 for arbitrary candidate centers, which yields a normalized measure for different laser lines in different images. The normalized results of pixels close to 1 are determined to be the real centers by progressive scanning of the image columns. Finally, the zero point of a second-order Taylor expansion in the eigenvector's direction is employed to refine further the extraction results of the central points at the subpixel level. The experimental results show that the method based on this normalization model accurately extracts the coordinates of laser line centers and obtains a higher recognition rate in two group experiments.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.100-104
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• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.742-747
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• 2012

A modified NDIF method using a sub-domain approach is introduced to extract highly accurate eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex cavities. It was revealed that the solution of the NDIF method is very inaccurate or is not suitable for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave domain into several convex domains. Finally, the validity of the proposed method is verified in two case studies, which indicate that eigenvalues obtained by the proposed method are more accurate compared to the exact method, the NDIF method, or FEM(ANSYS).

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.10
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• pp.988-995
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• 2008

A consensus-based feedback linearization method is proposed to maintain a specified time-varying geometric configuration for formation flying of multiple autonomous vehicles. In this approach, there exists no explicit leader in the team, and the proposed control strategy requires only the local neighbor-to-neighbor information between vehicles. The information flow topology between the vehicles is defined by Graph Laplacian matrix, and the formation flying can be achieved by the proposed feedback linearization with consensus algorithm. The stability analysis of the proposed controller is also performed via eigenvalue analysis for the closed-looop system. Numerical simulation is performed for rotary-wing type micro aerial vehicles to validate the performance of the proposed controller.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.345-355
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• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• Structural Engineering and Mechanics
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• v.75 no.4
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• pp.465-475
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• 2020

The analytical approach for stability and response of iced conductor under uniform wind or turbulent wind is presented in this study. A nonlinear dynamic model is established to describe the motion of iced conductor galloping. In the case of uniform wind, the stability condition is derived by analyzing the eigenvalue associated with linearized matrix; The first order and second order approximation of galloping amplitude are obtained using multi-scale method. However, real wind has random characteristics essentially. To accurately evaluate the performance of the galloping iced conductor, turbulence wind should be described by random processes. In the case of turbulence wind, the Lyapunov exponent is conducted to judge the stability condition; The probability density of displacement is obtained by using the path integral method to predict galloping amplitude. An example is proposed to verify the effectiveness of the previous methods. It is shown that the fluctuating component of wind has little influence on the stability of iced conductor, but it can increase galloping amplitude. The analytical results on stability and response are also verified by numerical time stepping method.