• 제목/요약/키워드: Non-linear integral

검색결과 126건 처리시간 0.025초

Free vibration analysis of non-prismatic beams under variable axial forces

  • Saffari, H.;Mohammadnejad, M.;Bagheripour, M.H.
    • Structural Engineering and Mechanics
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    • 제43권5호
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    • pp.561-582
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    • 2012
  • Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

A Comprehensive Harmonic Rejection for DFIG Feeding Non-Linear Loads in Stand-Alone Applications

  • Nguyen, Ngoc-Tung;Lee, Hong-Hee
    • 전력전자학회:학술대회논문집
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    • 전력전자학회 2012년도 전력전자학술대회 논문집
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    • pp.258-259
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    • 2012
  • This paper proposes a new control strategy to eliminate the harmonic components of stator current for stand-alone DFIG system feeding non-linear loads. In this method, the LSC operates as an active filter which is controlled by employing a proportional-integral and a resonant controller. And also, the stator current is used as the feedback signal for the compensator instead of the load current, so that the additional current sensor at the load side can be removed. The experiment is verified to validate the effectiveness of the proposed compensating method.

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전방향 모바일 로봇에서 유전알고리즘을 이용한 적분 슬라이딩 기반 동적 제어 기법 (Integral Sliding-based Dynamic Control Method using Genetic Algorithm on an Omnidirectional Mobile Robot)

  • 박진현;최영규
    • 한국정보통신학회논문지
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    • 제25권12호
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    • pp.1817-1825
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    • 2021
  • 전방향 모바일 로봇은 로봇의 방향을 바꿀 필요 없이 어떤 방향으로든 움직일 수 있어 여러 응용 분야에서 적용이 쉽고 뛰어난 기동성을 제공한다. 전방향 모바일 로봇은 마찰과 같은 비선형 동적 성분을 가지고 있어 정확히 모델링하기에 어렵다. 본 연구에서는 이러한 비선형 성분을 제거하기 위하여 모바일 로봇의 역 다이내믹과 적분 슬라이딩 모드 제어기법을 사용하여 모바일 로봇 시스템을 선형화하고, 제안된 제어기법의 최적 성능을 구현하기 위하여 유전알고리즘을 사용하여 위치 및 속도 이득을 최적화한다. 성능 평가 결과 유전알고리즘을 적용한 제어기법이 임의의 이득을 갖는 제어기법보다 뛰어난 성능을 나타내었다. 그리고 제안된 역 다이내믹과 적분 슬라이딩 모드 제어기법은 다른 제어기법에서도 적용될 수 있으며, 특히 선형제어시스템 설계에 유용하게 사용될 수 있다.

A non-linear tracking control scheme for an under-actuated autonomous underwater robotic vehicle

  • Mohan, Santhakumar;Thondiyath, Asokan
    • International Journal of Ocean System Engineering
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    • 제1권3호
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    • pp.120-135
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    • 2011
  • This paper proposes a model based trajectory tracking control scheme for under-actuated underwater robotic vehicles. The difficulty in stabilizing a non-linear system using smooth static state feedback law means that the design of a feedback controller for an under-actuated system is somewhat challenging. A necessary condition for the asymptotic stability of an under-actuated vehicle about a single equilibrium is that its gravitational field has nonzero elements corresponding to non-actuated dynamics. To overcome this condition, we propose a continuous time-varying control law based on the direct estimation of vehicle dynamic variables such as inertia, damping and Coriolis & centripetal terms. This can work satisfactorily under commonly encountered uncertainties such as an ocean current and parameter variations. The proposed control law cancels the non-linearities in the vehicle dynamics by introducing non-linear elements in the input side. Knowledge of the bounds on uncertain terms is not required and it is conceptually simple and easy to implement. The controller parameter values are designed using the Taguchi robust design approach and the control law is verified analytically to be robust under uncertainties, including external disturbances and current. A comparison of the controller performance with that of a linear proportional-integral-derivative (PID) controller and sliding mode controller are also provided.

Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT

  • Djilali, Nassira;Bousahla, Abdelmoumen Anis;Kaci, Abdelhakim;Selim, Mahmoud M.;Bourada, Fouad;Tounsi, Abdeldjebbar;Tounsi, Abdelouahed;Benrahou, Kouider Halim;Mahmoud, S.R.
    • Steel and Composite Structures
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    • 제42권6호
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    • pp.779-789
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    • 2022
  • This work presents a non-linear cylindrical bending analysis of functionally graded plate reinforced by single-walled carbon nanotubes (SWCNTs) in thermal environment using a simple integral higher-order shear deformation theory (HSDT). This theory does not require shear correction factors and the transverse shear stresses vary parabolically through the thickness. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are considered to be graded in the thickness direction, and are estimated through a micromechanical model. The non-linear strain-displacement relations in the Von Karman sense are used to study the effect of geometric non-linearity and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as benchmarks.

입력 차수 보상기를 이용한 비정방 선형 시스템의 출력 궤환 수동화 (Output Feedback Passivation of Non-square Linear Systems Using an Input-Dimensional Compensator)

  • 손영익
    • 대한전기학회논문지:시스템및제어부문D
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    • 제53권1호
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    • pp.10-15
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    • 2004
  • We present a state-space approach to make non-square linear systems strictly passive by using an input-dimensional parallel feedforward compensator. A necessary and sufficient condition for the existence of the parallel feedforward compensator is given by the static output feedback formulation, which enables to utilize linear matrix inequality. By modifying the structure of the compensator the additional technical assumption in the previous result [1] is removed. The effectiveness of the proposed method is illustrated by some numerical examples which can be stabilized by the proportional-derivative (PD) and proportional-derivative-integral (PID) control laws. The proposed control scheme can successfully replace the measurements of derivative terms in the control laws.

Integral Analysis of the Effects of Non-absorbable gases on the Heat Mass Transfer of Laminar Falling Film

  • Kim, Byong-Joo
    • International Journal of Air-Conditioning and Refrigeration
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    • 제6권
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    • pp.56-66
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    • 1998
  • The absorption process of water vapor in a liquid film is an important process in LiBr-Water absorption system. The composition of the gas phase, in which a non-absorbable gas is combined with the absorbate, influences the transport characteristics. In the present work, the absorption processes of water vapor into aqueous solutions of lithium bromide in the presence of non-absorbable gas are investigated. The continuity, momentum, energy and diffusion equations for the solution film and gas are formulated in integral forms and solved numerically. It is found that the mass transfer resistance in gas phase increases with the concentration of non-absorbable gas. However the primary resistance to mass transfer is in the liquid phase. As the concentration of non-absorbable gas in the absorbate increases, the interfacial temperature and concentration of absorbate in solution decrease, which results in the reduction of absorption rate. The reduction of mass transfer rate is found to be significant for the addition of a small amount of non-absorbable gas to the pure vapor, especially at the outlet of tube where the non-absorbable gas accumulates. At higher non-absorbable gas concentration, the decrease of absorption rate seems to be linear to the concentration of non-absorbable gas.

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Existence and Non-Existence of Positive Solutions of BVPs for Singular ODEs on Whole Lines

  • LIU, YUJI;YANG, PINGHUA
    • Kyungpook Mathematical Journal
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    • 제55권4호
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    • pp.997-1030
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    • 2015
  • This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

ON SOME SPECIAL CONDITIONS OF n-TH ORDER NON-OSCILLATORY NONLINEAR SYSTEMS

  • Alam, M.-Shamsul;Hossain, M.B.
    • 대한수학회논문집
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    • 제18권4호
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    • pp.755-765
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    • 2003
  • Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of n-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.

비선형제어계에 있어서 평가보조함수적용에 관한 연구 (Study on Adaptation of Parameteric Funition in Performance Index for Non-linear Control System Design)

  • 심흥석;김경기
    • 대한전자공학회논문지
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    • 제10권1호
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    • pp.1-8
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    • 1973
  • 비선형제어계의 최적제어는 일반적으로 해석적인 방법에 의하여 그해를 구하기 곤란하다. 그뿐만 아니라 문제대상에 관한 완전한 수학적모형구성이 곤란한 경우도 많다. 본논문에서는 비선형제어계의 설계에 있어서 최적방책을 구하는 과정에서 보조적인 수단으로 평가함수내에 보조함수를 도입하여 최적문제의 해를 구하는 방법을 제시하였다. 평가함수는 적분이차형의 문제를 취급하여 그 보조함수를 적절히 선정하여 소기의 응답특성을 얻을 수 있음을 밝히고 몇가지 예를 취급하여 이러한 보조함수의 유용성을 구체적으로 고찰하였다.

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