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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

《机械工程前沿（英文）》 2014年 第9卷 第1期   页码 58-70 doi: 10.1007/s11465-014-0289-7

摘要：

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

关键词： 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

《机械工程前沿（英文）》 2014年 第9卷 第4期   页码 402-408 doi: 10.1007/s11465-014-0316-8

摘要：

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji’s method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.

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

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

null

《机械工程前沿（英文）》 2014年 第9卷 第2期   页码 177-190 doi: 10.1007/s11465-014-0288-8

摘要：

In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.

关键词： 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

《结构与土木工程前沿（英文）》 2020年 第14卷 第6期   页码 1520-1530 doi: 10.1007/s11709-020-0672-x

摘要： In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear 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 investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.

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

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非线性系统高阶微分反馈控制

齐国元,陈增强,袁著祉

《中国工程科学》 2003年 第5卷 第8期   页码 35-44

摘要：

提出了不依赖系统模型的高阶微分反馈控制思想，控制目标是系统输出及其微分和高阶微分逼近设定输入及其微分和高阶微分，极大地提高了对控制品质要求。基于这种思想设计了能高品质地提取量测信号的微分和高阶微分的高阶微分器（HOD, high order differentiator），该HOD参数少，容易调节，并给出其稳定性、收敛性和滤波特性的证明；另外，对带有未知扰动、模型未知的非线性SISO和MIMO系统分别设计了基于HOD的高阶微分反馈自适应控制器（HODFC, high order differentials feedback adaptive controller），给出了闭环系统稳定性和鲁棒性分析，并且实现了线性化解耦控制。

关键词： 高阶微分器     高阶微分反馈控制器     稳定性     鲁棒性     解耦控制    

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Nonlinear sealing force of a seawater balance valve used in an 11000-meter manned submersible

《机械工程前沿（英文）》 2023年 第18卷 第1期 doi: 10.1007/s11465-022-0726-y

摘要： Balance valve is a core component of the 11000-meter manned submersible “struggle,” and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa. The increasing sealing force improves the sealing performance and increases the system’s energy consumption at the same time. A hybrid analytical–numerical–experimental (ANE) model is proposed to obtain the minimum sealing force, ensuring no leakage at the valve port and reducing energy consumption as much as possible. The effects of roundness error, environmental pressure, and materials on the minimum sealing force are considered in the ANE model. The basic form of minimum sealing force equations is established, and the remaining unknown coefficients of the equations are obtained by the finite element method (FEM). The accuracy of the equation is evaluated by comparing the independent FEM data to the equation data. Results of the comparison show good agreement, and the difference between the independent FEM data and equation data is within 3% when the environmental pressure is 0–118 MPa. Finally, the minimum sealing force equation is applied in a balance valve to be experimented using a deep-sea simulation device. The balance valve designed through the minimum sealing force equation is leak-free in the experiment. Thus, the minimum sealing force equation is suitable for the ultrahigh pressure balance valve and has guiding significance for evaluating the sealing performance of ultrahigh pressure balance valves.

关键词： seawater balance valve     sealing performance     hybrid ANE model     FEM     minimum sealing force equation    

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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

《机械工程前沿（英文）》 2008年 第3卷 第2期   页码 193-199 doi: 10.1007/s11465-008-0023-4

摘要： The stability and coupling dynamic behavior of a journal active electromagnetic bearing rotor system are analyzed. The gyroscopic effect is considered in the rotor model. The system equations are formulated by combining equations for rotor motion and decentralized proportional integral differential (PID) controllers. A method combining the predictor-corrector mechanism and the Netwon-Raphson method is presented to calculate the critical speed at the corresponding Hopf bifurcation point of the system. For periodic motions, a continuation method combining the predictor-corrector mechanism and shooting method is presented. Nonlinear unbalanced periodic motions and their stability margins are obtained using the shooting method and established continuation method for periodic motions. With the change of control parameters, the system local stability and bifurcation behaviors are obtained using the Floquet theory. The numerical examples show that the schemes not only significantly save computing cost, but also have high precision.

关键词： 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

《结构与土木工程前沿（英文）》 2007年 第1卷 第3期   页码 361-366 doi: 10.1007/s11709-007-0048-5

摘要： The methods for constructing safe basins of ships and predicting their survival probability in random waves were studied. The nonlinear differential equation of the rolling motion of ships in random beam seas was established considering nonlinear damping, nonlinear restoring moment, and random waves. The random rolling differential equation was solved in the time domain by applying the harmonic acceleration method and by synthetically considering the instantaneous state of ships and the narrowband wave energy spectrum. The numerical simulation of random capsizing course was brought forward, the safe basins were constructed for safe navigation, and the survival probabilities of ships were calculated. As an example, the safe basins on the rolling initial value plane were constructed for a 30.27-meter-long fishing vessel according to different initial conditions and random wave parameters. The survival probabilities of the fishing vessel under different significant wave heights were predicted. Thus, the survival probabilities of ships in random seas can be predicted quantitatively by the proposed method.

关键词： different     survival probability     different significant     nonlinear differential     narrowband    

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非常泄洪设施对大坝防洪安全的研究

吴时强,姜树海

《中国工程科学》 2000年 第2卷 第12期   页码 66-72

摘要：

文章引人随机微分方程，采用泄洪风险分析方法评估水电站采用非常泄洪设施对大坝安全所带来的影响，并结合某一工程设置两条非常泄洪洞的可行性进行论证。在充分分析计算条件对风险率灵敏性的前提下，讨论了调洪方案下两条非常泄洪洞启用的条件及相关的泄洪风险，为导流洞改建方案的确定提供依据。分析结果表明该方案基本维持原设计方案的泄洪风险水平，说明设置非常泄洪设施是可行的。

关键词： 大坝安全     泄洪     风险分析     随机微分方程    

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连续非线性最优控制问题的勒让德—伽辽金逼近方法 Article

Xue-song CHEN

《信息与电子工程前沿（英文）》 2017年 第18卷 第10期   页码 1479-1487 doi: 10.1631/FITEE.1601101

摘要： 使用逼近方法获得一类连续非线性最优控制问题的近似最优解。该方法基于伽辽金逼近理论（Galerkin approximation）求解广义哈密尔顿—雅可比—贝尔曼（Hamilton-Jacobi-Bellman, GHJB）方程。勒让德—伽辽金逼近方法（GALP）尚未被用于求解连续非线性最优控制问题。由于勒让德多项式（Legendre polynomials）具有正交性，在计算函数内积时，该方法可以明显减少积分计算量。详细证明了此方法的稳定性和收敛性。数值算例表明，按此方法获得的控制律，能够收敛到连续非线性控制系统的最优控制。

关键词： 广义哈密尔顿—雅可比—贝尔曼方程；非线性最优控制；伽辽金逼近（Galerkin approximation）；勒让德多项式（Legendre polynomials）    

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Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method

H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI

《机械工程前沿（英文）》 2011年 第6卷 第4期   页码 435-441 doi: 10.1007/s11465-011-0243-x

摘要：

Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step.

关键词： min-max method     nonlinear oscillation     duffing equation     mathematical pendulum     He’s energy balance method    

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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

《能源前沿（英文）》 2015年 第9卷 第4期   页码 413-425 doi: 10.1007/s11708-015-0379-1

摘要： The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed based on the use of the differential mean value theorem (DMVT) and convex theory. The proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as linear parameter varying (LPV) systems. Using the Lyapunov theory, stability conditions are obtained and expressed in terms of linear matrix inequalities (LMIs). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for closed loop-field oriented control (CL-FOC) of permanent magnet synchronous machine (PMSM) drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed.

关键词： 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 (LPV)    

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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

《能源前沿（英文）》 2020年 第14卷 第1期   页码 180-191 doi: 10.1007/s11708-018-0537-3

摘要： In this paper, the method for the nonlinear control design of a permanent magnet synchronous generator based-wind energy conversion system (WECS) is proposed in order to obtain robustness against disturbances and harvest a maximum power from a typical stochastic wind environment. The technique overcomes both the problem of nonlinearity and the uncertainty of the parameter compared to such classical control designs based on traditional control techniques. The method is based on the differential geometric feedback linearization technique (DGT) and the Lyapunov theory. The results obtained show the effectiveness and performance of the proposed approach.

关键词： permanent magnet synchronous generator     wind energy conversion system     stochastic     differential geometric     feedback linearization     maximum power point tracking     Lyapunov     robust control    

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基于大气阻力的立方星编队飞行非线性规划控制算法 Article

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

《信息与电子工程前沿（英文）》 2017年 第18卷 第7期   页码 867-881 doi: 10.1631/FITEE.1500493

摘要： 立方星由于体积和功率限制，难以配置传统的推进系统以实现编队飞行。而大气阻力是低轨卫星可以用于轨道调整的空间环境动力之一。本文提出一种通过大气阻力实现轨道面内沿迹跟飞编队的综合策略，并将用于浙江大学下一颗皮纳卫星（该卫星是国际QB50项目成员之一）。QB50项目主要任务是90–300 km高度近地大气层探测。在这一轨道高度，大气阻力对卫星姿态和轨道的影响均不能忽略。本文通过空气动力学分析，同时考虑大气阻力对轨道半长轴和偏心率的影响，设计了一种多维非线性约束规划策略，以计算实现编队所需的卫星之间不同的目标面质比和相应的轨道调整保持时间。此外，通过俯仰姿态机动调整目标面质比。该算法策略无需卫星配置任何展开机构。基于ZJUCubeSat的数值仿真验证了这一设计的可行性和优势。

关键词： QB50；ZJUCubeSat；大气阻力；编队飞行    

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用二极管统一构建两个n阶电路网络 Research Article

林小燕,谭志中

《信息与电子工程前沿（英文）》 2023年 第24卷 第2期   页码 289-298 doi: 10.1631/FITEE.2200360

摘要： 本文通过二极管将两个不同的n阶拓扑电路网络连接起来，建立起一个统一的网络模型，这是一个以前没有研究解决的新问题。该网络模型不仅包含五个电阻元件，还包含二极管器件，因此该网络包含多种不同的网络类型。该问题可以通过三个主要步骤来解决：首先，将网络简化为两个不同的等效电路模型；其次，应用基尔霍夫定律建立非线性差分方程模型；最后，对结构相似的两个方程进行统一处理，并利用等效变换技术得到非线性差分方程的通解。作为应用，文章推导出几个有趣的特殊结果。网络模型的研究非常重要，可以应用于跨学科研究。

关键词： 复杂网络；等效变换；非线性差分方程；等效电阻    

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标题 作者 时间 类型 操作

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

期刊论文

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

期刊论文

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

null

期刊论文

Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

期刊论文

非线性系统高阶微分反馈控制

齐国元,陈增强,袁著祉

期刊论文

Nonlinear sealing force of a seawater balance valve used in an 11000-meter manned submersible

期刊论文

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

期刊论文

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

LIU Liqin, TANG Yougang, LI Hongxia

期刊论文

非常泄洪设施对大坝防洪安全的研究

吴时强,姜树海

期刊论文

连续非线性最优控制问题的勒让德—伽辽金逼近方法

Xue-song CHEN

期刊论文

Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method

H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI

期刊论文

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

期刊论文

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

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

期刊论文

基于大气阻力的立方星编队飞行非线性规划控制算法

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

期刊论文

用二极管统一构建两个n阶电路网络

林小燕,谭志中

期刊论文