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Stability analysis of the active control system with time delay using ihb method

Theoretical & Applied Mechanics Letters 2013年第6期3卷 55-58页

作者： Qing Sun Mingwei Zhang Zhengwei Liu Xiaohong Wu Department of Civil Engineering Xi’an Jiaotong University School of Aerospace Xi’an Jiaotong University

In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact to the relative magnitude of the two feedback gains. the condition of the well-matched feedback gains. control strategy of time-delayed feedback.

关键词： active control system double time delays ihb method stability

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NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION

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Acta Mechanica Solida Sinica 2009年第3期22卷 206-212页

作者： Yiming Fu Rengui Bi Pu Zhang State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body Hunan University Changsha 410082 China College of Mechanics and Aerospace Hunan University Changsha 410082 China

A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube （DWNT） can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.

关键词： carbon nanotube Euler-Bernoulli-beam van der Waals force nonlinear dynamic instability ihb method

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In-line response of vertical cylinders in regular and random waves

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Acta Oceanologica Sinica 2007年第6期26卷 124-138页

作者： LI Yok-sheung SU Wei ZHAN Jiemin ZHAN Sheng Department of Civil ＆ Structural Engineering The Hong Kong Polytechnic UniversityHong Kong China Department of Applied Mechanics and Engineering Zhongshan University Guangzhou 510275 China

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported. Both theoretical analyses and experimental measurements have been performed. The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method. Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves. The interaction between waves and vibrating cylinders are investigated.

关键词： in-line response cylinder waves ihb method

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Incremental Harmonic Balance method with Multiple Time Scales for Quasi-periodic Motions of Axially Moving Beams with Internal Resonances Subjected to a Single-tone Excitation

Incremental Harmonic Balance Method with Multiple Time Scale...

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第十届动力学与控制学术会议

作者： HUANG Jian-liang ZHU Wei-dong CHEN Shu-hui Department of Applied Mechanics and Engineering Sun Yat-sen University Department of Mechanical Engineering University of Maryland

Quasi-periodic motion is an oscillation of dynamic systems characterized by m basic frequencies w, w,,w with m≥2, which are incommensurable with one another. In this work, an incremental harmonic balance method with multiple time scales is developed for analyzing quasi-periodic motion of an axially moving beam with 1:3 internal resonance subjected to a single tone excitation. For periodic response of the axially moving beam, a single basic frequency w is introducing into the ihb method to obtain dynamic solutions. For quasi-periodic motion of the axially moving beam, one basic frequency w and the others basic frequencies are introduced in the ihb method as multiple time scales to obtain dynamic solutions, which is computed through amplitude increment approach including a greater number of harmonics to determine the basic frequencies, together with theirs combination frequencies. Numericalexample shows that the solution form of quasi-periodic motions based on a multiple Fourier series contains incommensurable basic frequencies and their combination frequencies consist of the basic frequencies. All incommensurable basic frequencies and their combination frequencies, together with their corresponding amplitudes involved obtained from the ihb method with multiple time scales agree very well with those obtained from the numerical integration.

关键词： quasi-periodic motion ihb method multiple time scales axially moving beam internal resonance

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Limit cycles and acoustic radiation analysis of a self-excited vibration system

Limit cycles and acoustic radiation analysis of a self-excit...

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第十届动力学与控制学术会议

作者：周奇郑王德石 Naval University of Engineering

The approximate analytical solution of the limit cycle and the acoustic radiation characteristics of a nonlinear vibro-acoustic coupling system consisting of a self-excited vibration system are investigated. The nonlinear coupling equations of the vibro-acoustic coupling system under external excitation are derived using variational theory. The modal expression method and the incoherent superposition assumption are employed to discretize the displacements and the surface acoustic pressure of the plate, and then the incremental harmonic balance(ihb) method is used to drive the approximate analytical expressions for the limit cycles of the coupling system. The acoustic radiation power level and the surface average velocity under multi-frequency excitation are defined to describe the response of the plate. The results are that there are limit cycle motions in the vibration of the vibro-acoustic coupling system due to the system’s selfexcited vibration, and there are more harmonic components in the system when the parameters are increased. The vibro-acoustic characteristics of the plate present nonlinear variation because of the oscillator’s nonlinear damping force. The method combining the ihb method and the modal expression method can be used to investigate the nonlinear vibro-acoustic coupling characteristics of a structure under external and self-excited excitation.

关键词： self-excited vibration acoustic radiation vibro-acoustic coupling limit cycle ihb method

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Bifurcations of the nonlinear vibro-acoustic coupling of a Duffing Oscillator-plate structure system

Bifurcations of the nonlinear vibro-acoustic coupling of a D...

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中国交叉科学学会第15届学术年会

作者： Qizheng Zhou Deshi Wang Department of Weaponry Engineering Naval University of Engineering

The bifurcations of the nonlinear vibro-acoustic coupling system consisted by a Duffing oscillator and a plate structure are investigated by the incremental harmonic balance（ihb）method and the modal superposition *** Hamilton principle,the nonlinear vibro-acoustic coupling equations of the Duffing oscillator-plate structure system are developed The displacement and the surface pressure of plate are expressed in terms of normal modes based on boundary conditions by the modal superposition *** ihb method and the Floquet theory are employed to derive the solution and the stability of the vibro-acoustic coupling *** on the type of bifurcation,the solution of the coupling equations is constructed,and the ihb method and the Floquet theory are applied to obtain the solution of the coupling equations and the *** repeating the procedure,a series bifurcation points and the solutions are ***,the surface average velocity level and the acoustic radiation power level of the plate are defined based in different period *** results show that there are imaginary parts in the coupling system due to the acoustic pressure,the bifurcations of the Duffing oscillator are delayed,and the stability is *** the first bifurcation,the vibro-acoustic characteristics of the plate are changed.

关键词： vibro-acoustic coupling system plate structure Duffing oscillator bifurcation ihb method

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