• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.41-50
• /
• 2019

This paper is dealt with one-dimensional elliptic jumping problem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic boundary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the elliptic eigenvalue problem and Leray-Schauder degree theory.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.321-338
• /
• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Smart Structures and Systems
• /
• v.15 no.2
• /
• pp.409-424
• /
• 2015

Structural nonlinearity is a common phenomenon encountered in engineering structures under severe dynamic loading. It is necessary to localize and identify structural nonlinearities using structural dynamic measurements for damage detection and performance evaluation of structures. However, identification of nonlinear structural systems is a difficult task, especially when proper mathematical models for structural nonlinear behaviors are not available. In prior studies on nonparametric identification of nonlinear structures, the locations of structural nonlinearities are usually assumed known and all structural responses are measured. In this paper, an identification algorithm is proposed for locating and identifying model-free structural nonlinearities and systems using incomplete measurements of structural responses. First, equivalent linear structural systems are established and identified by the extended Kalman filter (EKF). The locations of structural nonlinearities are identified. Then, the model-free structural nonlinear restoring forces are approximated by power series polynomial models. The unscented Kalman filter (UKF) is utilized to identify structural nonlinear restoring forces and structural systems. Both numerical simulation examples and experimental test of a multi-story shear building with a MR damper are used to validate the proposed algorithm.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.5 no.4
• /
• pp.87-100
• /
• 1995

In order to control systems which contain nonlinearities of uncertainties, control strategies must deal with the effects of them. Since most of control methods based on system mathematical models have been mainly developed focused on stability robustness against nonlinearities or uncertainties under the assumption that controlled systems are linear time invariant, they have certain amount of limitations to smartly improve the transient responses of systems disturbed by nonlinearities or uncertainties. In this paper, a nonlinear fuzzy PID control method is suggested which can stably improve the transient responses of systems disturbed by nonlinearities, as well as systems whose mathematical characteristics are not perfectly known. Although the derivation process is based on the design process similar to general fuzzy logic controller, resultant control law has analytical forms with time varying PID gains rather than linguistic forms, so that implementation using common-used versatile microprocessors cna be achieved easily and effectively in real-time control aspect.

• Journal of Advanced Marine Engineering and Technology
• /
• v.23 no.4
• /
• pp.583-592
• /
• 1999

In order to control systems which contain nonlinearities control strategies must deal with the effects of them. Since most of control methods based on system mathematical models have been mainly developed focused on stability robustness against nonlinearities or uncertainties under the assumption that controlled systems are linear time invariant they have certain amount of limita-tions to smartly improve control perfomances of systems disturbed by nonlinearities or uncertainties. In this paper the fuzzy PID control law is suggested which can improve control performances of the nonlinear heavy load hydraulic systems disturbed by nonlinearities and uncertainties. Although the derivation process is based on the design process similar to general fuzzy logic con-troller resultant control law has analytical forms with time varying PID gains rather than linguis-tic forms so that implementation using commn-used versatile microprocessors can be achieved easily and effectively in real-time control aspect.

• Journal of Institute of Control, Robotics and Systems
• /
• v.22 no.6
• /
• pp.477-482
• /
• 2016

This paper presents a simple approximation-based design approach for consensus tracking of heterogeneous second-order nonlinear systems under a directed network. All nonlinearities of followers are assumed to be unknown and non-identical. In the controller design procedure, graph-independent error surfaces are used and an unimplementable intermediate controller for each follower is designed at the first design step. Then, by adding and subtracting a graph-based term at the second step, the actual controller for each follower is designed by using one neural network employed to estimate a lumped and distributed nonlinearity. Therefore, the proposed local controller for each follower has a simpler structure than existing approximation-based consensus tracking controllers for multi-agent systems with unmatched nonlinearities.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.11a
• /
• pp.341-344
• /
• 2006

A study for the nonlinear analysis of segmentally erected curved PSC(prestressed concrete) cable-stayed bridge considering the effects due to large deflections is presented. Various case studies regarding the effects of the material nonlinearities and the geometric nonlinearities on the behavior of segmentally erected curved PSC cable-stayed bridge are conducted. The numerical results on the bridge which has relatively low stress profile through the bridge deck section like the example herein show that the geometric nonlinearities has more significant effects on the structural behavior than the material nonlinearities.

• Current Optics and Photonics
• /
• v.1 no.1
• /
• pp.60-64
• /
• 2017

We have considered optical nonlinearities of coupled quantum dots theoretically, where an exciton dipole-dipole interaction is mediated between the adjacent large and small quantum dots. For increasing a pump pulse area in resonance with the large quantum dot exciton the induced nonlinear refractive index of the small quantum dot exciton has been obtained. As the exciton dipole-dipole interaction depends on the relative orientation of two exciton dipoles, the optical nonlinearities for the directions parallel and perpendicular to the coupling axis of the two quantum dots are compared. The directional imbalance of optical nonlinearities in coupled quantum dots can be utilized for a polarization phase modulator by controlling a pump pulse area and propagation length.

• Journal of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.691-699
• /
• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• Journal of Ocean Engineering and Technology
• /
• v.4 no.2
• /
• pp.185-185
• /
• 1990