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Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

Propulsion and Power Research 2013年第3期2卷 208-213页

作者： Haitao Liaon Ge Gao Chinese Aeronautical Establishment Beijing 100012China

An original method for calculating the limit cycle oscillations of nonlinear aeroelastic system is *** problem of detemining the maximum vibration amplitude of limit cycle is transfomed into a nonlinear optimization *** hamonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality *** resulting constrained maximization problem is then solved by using the MultiStart ***,the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and *** examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

关键词： Limit cycle harmonic balance method Floquet theory The MultiStart algorithm

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A ground-limited nonlinear energy sink

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Acta Mechanica Sinica 2022年第5期38卷 135-146,I0003页

作者： Xiao-Feng Geng Hu Ding Xiao-Ye Mao Li-Qun Chen Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China

The nonlinear energy sink(NES)is outstanding in vibration control for the well-known character of energy targeted transmitting and resonance automatically *** enhance the practicability,this paper proposes a ground-limited *** novel design can be encapsulated in a certain ***,as the vibration region of NES is limited,the control efficiency of it must be considered ***,the ground-limited NES is discussed via the analytical method,the simulation method,and especially the experiment in forced *** parameters involved in this study are obtained through the parameter identification based on the experimental *** piecewise nonlinearity is fitted into the continuous nonlinearity by the hyperbolic tangent *** the harmonic balance method(HBM)is used during the analytical processing to promote the accuracy of the *** direct numerical method produces results to verify the analytical method together with the experimental *** discussion on the control parameters shows that a proper limiting spring can effectively reduce the vibration of the NES while the cost of the control efficiency is *** a word,this work provides a simple and reliable approach for restricting the NES,which is beneficial to the design of the NES and broadens the application of the NES in engineering.

关键词： Nonlinear energy sink Vibration suppression Piecewise nonlinearity harmonic balance method

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Nonlinear free vibration of graphene platelets reinforced composite corrugated plates

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Journal of Central South University 2022年第9期29卷 3054-3064页

作者： LIU Yun-fei QIN Zhao-ye CHU Fu-lei State Key Laboratory of Tribology Department of Mechanical EngineeringTsinghua UniversityBeijing 100084China

The nonlinear vibration of graphene platelets reinforced composite corrugated(GPRCC)rectangular plates with shallow trapezoidal corrugations is *** graphene platelets are prone to agglomeration,a multi-layer distribution is adopted here to match the engineering ***,an equivalent composite plate model is obtained,and then nonlinear equations of motion are derived by the von Kármán nonlinear geometric relationship and Hamilton’s ***,the Galerkin method and harmonic balance method are used to obtain an approximate analytical *** show that the unit cell half period,unit cell inclination angle,unit cell height,graphene platelet dispersion pattern and graphene platelet weight fraction and geometry play important roles in the nonlinear vibration of the GPRCC plates.

关键词： corrugated composite plate graphene platelets nonlinear vibration Galerkin method harmonic balance method

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Forced Resonance of a Slightly-Curved Hydraulic Pipe Fixed at Two Ends

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Transactions of Nanjing University of Aeronautics and Astronautics 2022年第3期39卷 271-279页

作者： MAO Xiaoye XIAO Lu DING Hu CHEN Liqun School of Mechanics and Engineering Science Shanghai UniversityShanghai 200444P.R.China

The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.

关键词： forced resonance hydraulic pipe slightly-curved pipe harmonic balance method

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Nonlinear identification and characterization of structural joints based on vibration transmissibility

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Journal of Southeast University(English Edition) 2018年第1期34卷 36-42页

作者： Liu Xin Sun Beibei Li Lie Chen Jiandong Xue Fei School of Mechanical Engineering Southeast UniversityNanjing 211189China

In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a corresponding nonlinearity identification method is ***,the sine-sweep vibration test with different baseexcitation levels areapplied to the structural joint system to study the dominant modal of mass rigid ***,based on t e harmonic balance method principle,t e measured vibration transmissibilities a e utilized for nonlinearity identification using different excitation *** results show that nonlinear spring and damping force can be represented by a polynomial order *** identified nonlinear stiffness and damping force can predict the system’s response,and they can reveal t e shifts of resonant frequency or damping due to discontinuity of contact mechanisms within a certain range.

关键词： structural joint vibration transmissibility nonlinear identification harmonic balance method

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Tuning of Nonlinearity on Phononic Crystals and Elastic Metamaterials

Tuning of Nonlinearity on Phononic Crystals and Elastic Meta...

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第十四届全国振动理论及应用学术会议(NVTA2021)

作者： Nansun Shen Fang Zhang State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics

The mechanisms and applications of linear phononic crystals and elastic metamaterials, which can prohibit effectively the elastic wave propagation in the bandgap frequency range, have been widely studied. They have broad application prospects in the field of vibration and noise reduction. However, once their structure is determined, the bandgap is also determined. This paper numerically and theoretically studies the tuning of nonlinearity on one-dimensional phononic crystals and elastic metamaterials. harmonic balance method is used to derive the nonlinear dispersion relation combined with Bloch theorem. The theoretical results show that the nonlinearity will change the starting frequency and cut-off frequency of the bandgap. In addition, the amplitude can also influence the bandgap. Finally, the theoretical results are verified by numerical simulation, and the results are in good agreement with each other.

关键词： nonlinearity phononic crystals elastic metamaterial bandgap harmonic balance method Block theorem

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An analytical method for Mathieu oscillator based on method of variation of parameter

An analytical method for Mathieu oscillator based on method ...

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第十届动力学与控制学术会议

作者： LI Xiang-hong HOU Jing-yu CHEN Ju-feng Department of Mathematics and Physics Shijiazhuang Tiedao University

This paper proposed a simple, but very accurate analytical method for forced Mathieu oscillator, the idea of which is based on the method of variation of parameter, and the method have two advantages, i.e., the simplicity in solving procedure and higher precision of the obtained solution in large range of system parameters. Assuming that the time-varying parameter in Mathieu oscillator is constant, one could easily obtain its accurately analytical solution. Then the approximately analytical solution for Mathieu oscillator could be established after substituting periodical time-varying parameter for the constant one in the obtained accurate analytical solution. In order to certify the correctness and precision of the proposed analytical method, the firstorder and ninth-order approximation solutions by harmonic balance method(HBM) are also presented. The comparisons between the results by the proposed method with those by the numerical simulation and HBM verify that the results by the proposed analytical method agreevery well with those by the numerical simulation. The effects of five system parameters on the computation precision of the presented method are studied based on the time histories, phase diagrams, and the variances between the numerical simulation and the approximately analytical solutions. Through a lot of comparisons, it is found that the proposed new analytical method is not only higher than the approximation solution by first-order HBM, but also better than the approximation solution by the ninth-order HBM in large ranges of system parameters.

关键词： Mathieu oscillator Analytical solution The method of variation of parameter harmonic balance method

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