• Korean Journal of Mathematics
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• v.17 no.3
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

• East Asian mathematical journal
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• v.34 no.5
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• pp.651-660
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• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

• Journal of Ocean Engineering and Technology
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• v.30 no.6
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• pp.458-467
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• 2016

In this paper, a strongly coupled method for investigating the interaction between a cable and tow-fish is presented. The nodal position finite element method was utilized to analyze the nonlinear cable dynamics, and 6DOF equations of motion were employed to describe the 3D rigid body motion of the tow-fish. Combining cable and tow-fish systems into a single formulation allowed the two nonlinear systems to be strongly coupled into a unified nonlinear system. This strongly coupled system was numerically integrated in the time domain using a predictor/multi-corrector Newmark algorithm. To demonstrate the validity, efficacy, and applicability of the current approach, two different scenarios (virtual and sea trial) were simulated, and the simulation results were validated using the physical plausibility and the sea trial test.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.171-178
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• 2017

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.187-193
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• 2003

In this paper, a systematic design method of the intelligent PAM fuzzy controller for nonlinear systems using the efficient tools-Linear Matrix Inequality and the intelligent digital redesign is proposed. In order to digitally control the nonlinear systems, the TS fuzzy model is used for fuzzy modeling of the given nonlinear system. The convex representation technique also can be utilized for obtaining TS fuzzy models. First, the analog fuzzy-model-based controller is designed such that the closed-loop system is globally asymptotically stable in the sense of Lyapunov stability criterion. The simulation results strongly convince us that the proposed method has great potential in the application to the industry.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.157-160
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• 1999

A prediction method of conditional event matching pre-diction (EMP) for a purpose of predicting nonlinear phenomena of insulator pollution was proposed in this paper. The EMP was used if the conditional probability for increase of insulator pollution exceeded a threshold value. A performance of the EMP was strongly related to selection of database of events and a closeness function. By use of the prediction of the insulator pollution based on the conditional EMP, reliable decision making for the washing timing of the polluted insulators was e-valuated based on actual data in Kasatsu substation, Japan.

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.255-270
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• 2006

In this paper, a design method of nonlinear autopilot for ship-to-ship missiles is proposed. Ship-to-ship missiles have strongly coupled dynamics through roll, yaw, and pitch channel in comparison with general STT type missiles. Thus it becomes difficult to employ previous control design method directly since we should find three different solutions for each control fin deflection and should verify the stability for more complicated dynamics. In this study, we first propose a control loop structure for roll, yaw, and pitch autopilot which can determine the required angles of all three control fins. For yaw and pitch autopilot design, missile model is reduced to a minimum phase model by applying a singular perturbation like technique to the yaw and pitch dynamics. Based on this model, a multi-input multi-output (MIMO) nonlinear autopilot is designed. And the stability is analyzed considering roll influences on dynamic couplings of yaw and pitch channel as well as the aerodynamic couplings. Some additional issues on the autopilot implementation for these coupled missile dynamics are discussed. Lastly, 6-DOF (degree of freedom) numerical simulation results are presented to verify the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1169-1172
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• 1996

A time-optimal control law for quick, strongly nonlinear systems has been developed and demonstrated. This procedure involves the utilization of neural networks as state feedback controllers that learn the time-optimal control actions by means of an iterative minimization of both the final time and the final state error for the known and unknown systems with constrained inputs and/or states. The nature of neural networks as a parallel processor would circumvent the problem of "curse of dimensionality". The control law has been demonstrated for a velocity input type motor identified by a genetic algorithm called GENOCOP.