• Smart Structures and Systems
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• v.26 no.3
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.11
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• pp.5379-5388
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• 2012

In fuzzy modeling for nonlinear process, the fuzzy rules are typically formed by selection of the input variables, the number of space division and membership functions. The Generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, complex nonlinear process can be modeled by generating the fuzzy rules by means of fuzzy division of input space. Therefore, in this paper, rules of non-fuzzy inference systems are generated by partitioning the input space in the scatter form using HCM clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of HCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the consequence parameters of each rule are identified by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process. Through this experiment, we showed that high-dimensional nonlinear systems can be modeled by a very small number of rules.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.3 s.43
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• pp.33-42
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• 2005

Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the $2^{nd}\;or\;3^{rd}$ order nonlinearity is dominant.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-11
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• 2014

In this paper, we show that general nonlinear switched systems are asymptotically controllable if and only if there exist control-Lyapunov functions for their relaxation systems. If the switching signal is dependent on the time, then the control-Lyapunov functions are continuous. And if the switching signal is dependent on the state, then the control-Lyapunov functions are $C^1$-smooth. We obtain the results from the viewpoint of control system theory. Our approach is based on the relaxation theorems of differential inclusions and the classic Lyapunov characterization.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.247-259
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• 2011

In this paper, the $(\frac{G'}{G})$-expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• Smart Structures and Systems
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• v.26 no.6
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• pp.797-807
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• 2020

Due to the influence of nonlinearity and time-variation, it is difficult to establish an accurate model of concrete frame structures that adopt active controllers. Fuzzy theory is a relatively appropriate method but susceptible to human subjective experience to decrease the performance. This paper proposes a novel artificial intelligence based EBA (Evolved Bat Algorithm) controller with machine learning matched membership functions in the complex nonlinear system. The proposed affine transformed membership functions are adopted and stabilization and performance criterion of the closed-loop fuzzy systems are obtained through a new parametrized linear matrix inequality which is rearranged by machine learning affine matched membership functions. The trajectory of the closed-loop dithered system and that of the closed-loop fuzzy relaxed system can be made as close as desired. This enables us to get a rigorous prediction of stability of the closed-loop dithered system by establishing that of the closed-loop fuzzy relaxed system.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.557-570
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• 2023

The conceptions of generalized b-metric spaces or G_b-metric spaces and a generalized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ω_b(𝓗, 𝜃, s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of 𝓗-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.55-61
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• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.135-145
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• 1995

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.