• Structural Engineering and Mechanics
• /
• 제33권1호
• /
• pp.15-30
• /
• 2009

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.

• Korean Journal of Mathematics
• /
• 제16권3호
• /
• pp.389-402
• /
• 2008

We show the existence of at least two solutions for a class of systems of the critical growth nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We first show that the system has a positive solution under suitable conditions, and next show that the system has another solution under the same conditions by the linking arguments.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
• /
• pp.185-189
• /
• 1998

This paper addresses analysis and design of a fuzzy model-based-controller for the control of uncertain SISO nonlinear systems. In the design procedure, we represent the nonlinear system by using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller via parallel distributed compensation and sliding mode control. Unlike other parallel distributed controllers, this globally stable fuzzy controller is designed without finding a common positive definite matrix for a set of Lyapunov equations, and has good tracking performance. The stability analysis is conducted not for the fuzzy model but for the real underlying nonlinear system. Furthermore, the proposed method can be applied to partially known uncertain nonlinear systems. A numerical simulation is performed for the control of an inverted pendulum, to show the effectiveness and feasibility of the proposed fuzzy control method.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권4호
• /
• pp.329-336
• /
• 2011

Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
• /
• pp.357-360
• /
• 2001

In this paper, we study the existence and uniqueness of fuzzy solution for the nonlinear fuzzy differential equations with nonlocal initial condition in E$\sub$N/$\^$2/ by using the concept of fuzzy number of dimension 2 whose values are normal convex upper semicontinuous and compactly supported surface in R$_2$.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 1996년도 추계학술대회 학술발표 논문집
• /
• pp.298-301
• /
• 1996

This paper describes the structure Identification of nonlinear function using Adaptive Neuro-Fuzzy Inference Technique(ANFIS). Nonlinear mapping relationship between inputs and outputs were modeled by Sugeno-Takaki's Fuzzy Inference Method. Specially, the consequent parts were identified using a series of 1st order equations and the antecedent parts using triangular type membership function or bell type ones. According to learning Rules of ANFIS, adjustable parameters were converged rapidly and accurately.

• 한국지능시스템학회논문지
• /
• 제15권5호
• /
• pp.621-625
• /
• 2005

In this paper we study the controllability for the nonlinear fuzzy integro-differential equations on $E_N^n$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in $R^n$. $E_N^n$ the set of all fuzzy numbers in $R^n$ with edges having bases parallel to axis $X_1,\;X_2, ... , X_n$.

• Journal of Mechanical Science and Technology
• /
• 제19권spc1호
• /
• pp.461-472
• /
• 2005

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
• /
• pp.25-28
• /
• 2002

본 논문에서는 $E^{2}\;_{N}$상에서 비국소 초기 조건을 갖는 비선형 퍼지 미분방정식에 대한 제어가능성에 관한 연구이다.

• Journal of Information Processing Systems
• /
• 제14권2호
• /
• pp.455-468
• /
• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.