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Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 2,   Pages 177-190 doi: 10.1007/s11465-014-0288-8

Abstract:

In the present paper, three complicated nonlinear differential equations in the field of vibrationAGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differentialis not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear

Keywords： Algebraic Method (AGM)     Angular Frequency     Vanderpol     Rayleigh     Duffing    

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Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

Frontiers of Structural and Civil Engineering 2020, Volume 14, Issue 6,   Pages 1520-1530 doi: 10.1007/s11709-020-0672-x

Abstract: this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinearWe use a reduced-order model based on the differential quadrature method (DQM) to discretize the governingnonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system.The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is

Keywords： velocity gradient elasticity theory     nanotube resonators     differential-quadrature method     nonlinear vibration    

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Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 1,   Pages 58-70 doi: 10.1007/s11465-014-0289-7

Abstract: paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlineardifferential equation governing on the presented system in three different cases by Algebraic Methodresults have been indicated that this approach is very efficient and easy so it can be applied for other nonlinearengineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlineardifferential equations.

Keywords： Algebraic Method (AGM)     tower crane     oscillating system     angular frequency    

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Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by

M. R. AKBARI,M. NIMAFAR,D. D. GANJI,M. M. AKBARZADE

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 4,   Pages 402-408 doi: 10.1007/s11465-014-0316-8

Abstract: also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinearIn this study, solving the nonlinear differential equation governing the calculation of the large rotationBy considering the small slope in the linearization of the governing differential equation, the solvingIn this paper nonlinear differential equations governing on this system are solved analytically by Akbari-GanjiMoreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily

Keywords： AGM     critical load of columns     large deformations of beam     nonlinear differential equation    

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High Order Differential Feedback Control for Nonlinear Systems

Qi Guoyuan,Chen Zengqiang,Yuan Zhuzhi

Strategic Study of CAE 2003, Volume 5, Issue 8,   Pages 35-44

Abstract:

This article presents high differential feedback control idea that does not rely on the model of theIts control objective is that the output of the system and its differential and high differentials approximatethe given reference input and its differential and high order differentials.Based on the idea, the high order differentiator (HOD) that is well able to extract differential andnonlinear SISO and MIMO systems with unknown disturbance are presents respectively, the analysis of

Keywords： high order differentiator     high differential feedback controller     stability     robustness     decoupling control    

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Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie

Frontiers of Mechanical Engineering 2008, Volume 3, Issue 2,   Pages 193-199 doi: 10.1007/s11465-008-0023-4

Abstract: equations are formulated by combining equations for rotor motion and decentralized proportional integral differentialNonlinear unbalanced periodic motions and their stability margins are obtained using the shooting method

Keywords： proportional integral     bifurcation     corresponding     integral differential     predictor-corrector mechanism    

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Analytical method of capsizing probability in the time domain for ships in the random beam seas

LIU Liqin, TANG Yougang, LI Hongxia

Frontiers of Structural and Civil Engineering 2007, Volume 1, Issue 3,   Pages 361-366 doi: 10.1007/s11709-007-0048-5

Abstract: The nonlinear differential equation of the rolling motion of ships in random beam seas was establishedconsidering nonlinear damping, nonlinear restoring moment, and random waves.The random rolling differential equation was solved in the time domain by applying the harmonic acceleration

Keywords： different     survival probability     different significant     nonlinear differential     narrowband    

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Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of

Abrar ALLAG,Abdelhamid BENAKCHA,Meriem ALLAG,Ismail ZEIN,Mohamed Yacine AYAD

Frontiers in Energy 2015, Volume 9, Issue 4,   Pages 413-425 doi: 10.1007/s11708-015-0379-1

Abstract: The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systemsA simple systematic and useful synthesis method is proposed based on the use of the differential meanThe proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error

Keywords： Takagi-Sugeno (T-S) fuzzy systems     sector nonlinearity     nonlinear controller     linear matrix inequality (LMI) approach     differential mean value theorem (DMVT)     field oriented control (FOC)     linear parameter varying    

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Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous

Ridha CHEIKH, Arezki MENACER, L. CHRIFI-ALAOUI, Said DRID

Frontiers in Energy 2020, Volume 14, Issue 1,   Pages 180-191 doi: 10.1007/s11708-018-0537-3

Abstract: In this paper, the method for the nonlinear control design of a permanent magnet synchronous generatorThe method is based on the differential geometric feedback linearization technique (DGT) and the Lyapunov

Keywords： permanent magnet synchronous generator     wind energy conversion system     stochastic     differential geometric    

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Nonlinear programming control using differential aerodynamic drag for CubeSat formation flying Article

Sheng-chao DENG, Tao MENG, Zhong-he JIN

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 7,   Pages 867-881 doi: 10.1631/FITEE.1500493

Abstract: We conduct aerodynamics analysis and design a multidimensional nonlinear constraint programming (MNLP

Keywords： QB50     ZJUCubeSat     Atmospheric drag     Formation flying    

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Tuned reactive power dispatch through modified differential evolution technique

S. BISWAS (RAHA), N. CHAKRABORTY

Frontiers in Energy 2012, Volume 6, Issue 2,   Pages 138-147 doi: 10.1007/s11708-012-0188-8

Abstract: This paper explores the capability of modified differential evolution (MDE) technique for solving theThe proposed method is based on the basic differential evolution (DE) technique with a few modifications

Keywords： reactive power dispatch (RPD)     modified differential evolution (MDE)     differential evolution algorithm    

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Review of MEMS differential scanning calorimetry for biomolecular study

Shifeng YU, Shuyu WANG, Ming LU, Lei ZUO

Frontiers of Mechanical Engineering 2017, Volume 12, Issue 4,   Pages 526-538 doi: 10.1007/s11465-017-0451-0

Abstract:

Differential scanning calorimetry (DSC) is one of the few techniques that allow direct determination

Keywords： differential scanning calorimetry     biomolecule     MEMS     thermodynamic    

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Precision analysis of a weakly-coupled parallel mechanism with three translational degrees of freedom

MA Lv-zhong, GUO Zong-he, YANG Qi-zhi, YIN Xiao-qin, HAN Ya-li, SHEN Hui-ping

Frontiers of Mechanical Engineering 2006, Volume 1, Issue 2,   Pages 227-232 doi: 10.1007/s11465-006-0005-3

Abstract: analysis, the inverse and forward solutions are analyzed and the precision is studied using complete differentialIt is found that the position errors of the moving platform have nonlinear relation with the positionThe δθ' error has the biggest influence on the nonlinear errors of the position.

Keywords： manipulator     nonlinear     δθ     influence     differential    

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Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution

Belkacem MAHDAD, K. SRAIRI

Frontiers in Energy 2013, Volume 7, Issue 1,   Pages 75-89 doi: 10.1007/s11708-012-0222-x

Abstract: In this paper, a simple strategy based differential evolution was proposed for solving the problem of

Keywords： differential evolution     multi-objective function     optimal power flow     economic dispatch     valve point effect    

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Cluster voltage control method for “Whole County” distributed photovoltaics based on improved differential

Frontiers in Energy   Pages 782-795 doi: 10.1007/s11708-023-0905-8

Abstract: strategy of “reactive power compensation first, active power curtailment later,” it employs an improved differential

Keywords： distributed photovoltaics (DPVs)     cluster partitioning     improved differential evolution algorithm     voltage    

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Title Author Date Type Operation

Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI

Journal Article

Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

Journal Article

Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

Journal Article

Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by

M. R. AKBARI,M. NIMAFAR,D. D. GANJI,M. M. AKBARZADE

Journal Article

High Order Differential Feedback Control for Nonlinear Systems

Qi Guoyuan,Chen Zengqiang,Yuan Zhuzhi

Journal Article

Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie

Journal Article

Analytical method of capsizing probability in the time domain for ships in the random beam seas

LIU Liqin, TANG Yougang, LI Hongxia

Journal Article

Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of

Abrar ALLAG,Abdelhamid BENAKCHA,Meriem ALLAG,Ismail ZEIN,Mohamed Yacine AYAD

Journal Article

Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous

Ridha CHEIKH, Arezki MENACER, L. CHRIFI-ALAOUI, Said DRID

Journal Article

Nonlinear programming control using differential aerodynamic drag for CubeSat formation flying

Sheng-chao DENG, Tao MENG, Zhong-he JIN

Journal Article

Tuned reactive power dispatch through modified differential evolution technique

S. BISWAS (RAHA), N. CHAKRABORTY

Journal Article

Review of MEMS differential scanning calorimetry for biomolecular study

Shifeng YU, Shuyu WANG, Ming LU, Lei ZUO

Journal Article

Precision analysis of a weakly-coupled parallel mechanism with three translational degrees of freedom

MA Lv-zhong, GUO Zong-he, YANG Qi-zhi, YIN Xiao-qin, HAN Ya-li, SHEN Hui-ping

Journal Article

Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution

Belkacem MAHDAD, K. SRAIRI

Journal Article

Cluster voltage control method for “Whole County” distributed photovoltaics based on improved differential

Journal Article