OPTIMAL CONTROL OF NONLINEAR VIBRATION RESONANCES OF SINGLE-WALLED NANOTUBE BEAMS

An optimal time-delay feedback control method is provided to mitigate the primary resonance of a single-walled carbon nanotube （SWCNT） subjected to a Lorentz force excited by a longitudinal magnetic field. The nonlinear governing equations of motion for the SWCNT under longitudinal magnetic field are derived and the modulation equations are obtained by using the method of multiple scales. The regions of the stable feedback gain are worked out by using the stability conditions of eigenvalue equation. Taking the attenuation ratio as the objective function and the stable vibration regions as constrained conditions, the optimal control parameters are worked out by using minimum optimal method. The optimal controllers are designed to control the dynamic behaviors of tile nonlinear vibration systems. It is found that the optimal feedback gain obtained by the optimal method can enhance the control performance of the primary resonance of SWCNT devices.     

Characteristics and efficiency of a new vibrating screen with a swing trace

A new vibration type and motion characteristics were proposed according to the principle of manual sieving.A mechanical model of the new motion was established and the characteristics of the new vibrating screen were analyzed to establish its equation of motion by using the vibration theory,to include as technological parameters,amplitude,movement velocity,and throwing index through theoretical calculation.The efficiency of particle screening was studied at different values of frequency and swing declination angle.The discrete element method(DEM) was used to simulate the screening with the swing trace.The functional relationship between screening efficiency and the parameters was fitted with the least square method.The results show that high frequency and large swing angle are suitable for small particles,while small values are suitable for particles close to the aperture size.Compared to the linear vibration trace,both screening efficiency and processing capacity were effectively improved.     

Vibration problems of flexible circular plates with initial deflection

In this paper,the differential equations of flexible circular plates with initialdeflection are derived.The stability of motion is investigated in phase plane.Theperiodical solutions of nonlinear vibration for circular plates with initial deflection areobtained by use of Galerkin method and Lindstedt-Poincare perturbation method.Theeffect of initial deflection on the dynamic behavior of the flexible plates are alsodiscussed.     

Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells

The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations are investigated by an analytical method.The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear deformation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh–Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.     

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

This paper studies self-synchronization and stability of a dual-motor driven vibration system with a two-stage vibration isolation frame. Oscillation amplitude of the material box large enough can be ensured on the vibration system in order to screen materials. Reduction of the dynamic load transmitted to the foundation can also be achieved for the vibration system. A Lagrange equation is used to set up the motion differential equations of the system, and a dimensionless coupled equation of the eccentric rotors is obtained using a method of modified average small parameter. According to the existence condition of zero solution in the dimensionless coupled equation of the eccentric rotors, the precondition for commencing self-synchronization motion is achieved.The stability condition of self-synchronization is obtained based on the Routh-Hurwitz criterion. The theoretical analysis is validated by simulations and experiments.     

Transverse vibration characteristics of axially moving viscoelastic plate

The dynamic characteristics and stability of axially moving viscoelastic rect- angular thin plate are investigated.Based on the two dimensional viscoelastic differential constitutive relation,the differential equations of motion of the axially moving viscoelastic plate are established.Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method.The effects of the aspect ratio,moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed.     

Pseudospectral analysis of the interfacial stability of free jets with different velocity profiles

A double fluid model for a liquid jet surrounded by a coaxial gas stream was constructed. The interfacial stability of the model was studied by Chebyshev pseudospectral method for different basic velocity profiles. The physical variables were mapped into computational space using a nonlinear coordinates transformation. The general eigenvalues of the dispersion relation obtained are solved by QZ method, and the basic characteristics and their dependence on the flow parameters are analyzed.     

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.     

Nonlinear dynamical behavior of shallow cylindrical reticulated shells

By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral tri- angle cell are founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support.The tensile force is solved out from the compati- ble equations,a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin.The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.The existence of the chaotic motion of the single-layer shallow cylin- drical reticulated shell is approved by using the digital simulation method and Poincarémapping.     

Time domain parameters identification of foundation-structure interaction system

The time domain parameter laenuncauon memoa oi me iounuauon-structure interaction system is presented. On the basis of building the computation mode and the motion equation of the foundation-structure interaction system, the system parameter identification method was established by using the extended Kalman filter （EKF） technique and taking the unknown parameters in the system as the augment state variables. And the time parameter identification process of the foundation-structure interaction system was implemented by using the data of the layer foundation-storehouse interaction system model test on the large vibration platform. The computation result shows that the established parameter identification method can induce good parameter estimation.     

轴同期涡动和轴承座激振对轴承油膜稳定性的影响

在自行设计的轴承试验台上研究了轴颈同期涡动和轴承座激振对油膜层流失稳的影响 .结果表明 :随着轴颈偏心的增大 ,涡动倾向增强 ,流体出现层流失稳 ;当涡动倾向较弱时 ,影响油膜层流失稳的主要因素是轴承激振的强度以及低频激振 ,而高频激振对其影响较小 ;但当涡动倾向较强时 ,轴承激振的强度以及激振频率对油膜层流的失稳几乎没有影响     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

An anisothermal,compressible, piezoviscous model for journal‐bearing lubrication

Compressibility plays a significant role in the load‐bearing capacity of a journal bearing. This paper offers more realistic modelling of the lubricant than presented in an earlier paper (Int. J. Numer. Meth. Fluids 2007; 55 (11):1091–1120) by including variable sound speed, piezoviscosity and both temperature and shear thinning. The load‐bearing capacity of the journal bearing is sensitive to all of these attributes of the model, but piezoviscosity is found to be the most significant. The equations of motion are adapted to a moving frame to explore the stability of the journal in a more dynamic setting and it is found that a free journal using this model will spiral outward exhibiting half speed whirl. The model is discretized in 2D, semi‐implicitly in time and using the spectral element method in space. Numerical results are presented that highlight the contributions of the different elements in the model to journal stability. Copyright © 2008 John Wiley & Sons, Ltd.     

Bifurcation of a shaft with hysteretic-type internal friction force of material

IntroductionItwasfoundlongtimeagothattheinternalfrictionofmaterialcancauseinstabilityofrotatingshaft.Soitisalwaysoneoftheimportantsubjectsinrotordynamics[1].Earlyinvestigationswerefocusedonthedynamicalstabilityproblemofrotorinfluencedbythelinearinternalfrictionofmaterial,aimingtoobtainthecriterionofstability[2～4 ].Asthedevelopmentofnonlineardynamics,moreandmoreattentionswerepaidtothestudyoftheself_excitedmotionofrotatingshaft,thatisthebifurcation .Thestabilityregionsandbifurcationsofbothanau…     

Radial and torsional vibration characteristics of a rub rotor

The nonlinear dynamics characteristics of a vertical Jeffcott rotor with radial rub-impact are investigated in this paper. Considering the influence of speed whirling, the radial-torsional coupling model of the rub rotor in polar coordinate system is established. With the improved model, the dynamics characteristics of radial vibration, whirl and torsional vibration are analyzed under no rub, full annual rub and partial rub conditions. The radial harmonic frequency is obtained by the harmonic balance method. The torsional vibration has the harmonic frequency component similar to the radial vibration. The new harmonic frequency is useful to help diagnose the occurrence of rub fault. A reasonable explanation of backward whirl instability is presented in this paper. With development of partial rub, the backward whirl will occur. When the backward whirling frequency is near the natural frequency, the instability is observed. The numerical method gives the quantitative results and reveals the backward whirl instability process of rub.     

多自由度转子-轴承系统周期运动分岔及稳定性研究

建立考虑诸多因素的转子-轴承系统多自由度模型,将与Newmark结合的打靶法应用到多自由度转子-轴承系统的周期稳定性分析中。着重研究了转子-轴承系统失稳转速随系统偏心量、轴承间隙、润滑油动力粘度以及轴承长径比的变化规律,研究结果表明:提高系统偏心量、减小轴承间隙、增大润滑油动力粘度以及选择适当的轴承长径比均能提高转子-轴承系统的失稳转速;对于不同的参数值,系统表现出不同的分岔规律,系统发生半速涡动时表现为倍周期分岔或拟周期分岔,发生油膜振荡时则表现为拟周期分岔。     

Numerical and experimental analysis of the first-and second-mode instability in a rotor-bearing system

Aiming at the oil film instability of the sliding bearing at high speeds, a rotor test rig is built to study the non-linear dynamic behaviours caused by the first- and second-mode instability. A lumped mass model (LMM) of the rotor system considering the gyroscopic effect is established, in which the graphite self-lubricating bearing and the sliding bearing are simulated by a spring–damping model and a nonlinear oil film force model based on the assumption of short bearings, respectively. Moreover, a finite element model is also established to verify the validity of the LMM. The researches focus on the effects of two loading conditions (the first- and second-mode imbalance excitation) on the onset of instability and nonlinear responses of the rotor-bearing system by using the amplitude–frequency response, spectrum cascade, vibration waveform, orbit, and Poincaré map. Finally, experiments are carried out on the test rig. Simulation and experiment all show that oil film instability can excite complicated combination frequency components about the rotating frequency and the first-/second-mode whirl/whip frequency.     

Flexible shaft whirl induced by dry friction and its stability

This paper is devoted to the study of the whirling phenomena of flexible rotors due to dry friction. The mechanical model used here is a two-degree-of-freedom system in which the rubbing plane is not coincident with the rotating plane of the lumped mass. The characteristic equation of whirl speeds is derived and the whirling modes are obtained. The dynamic stability of each admissible whirling motion is also discussed. The results show that the whirl speeds are always higher than the critical speed of the shaft.     

高速涡轮增压器轴承-转子系统不平衡响应及稳定性分析

汽车涡轮增压器广泛采用浮环轴承支承的小型轻质转子系统,以实现100 000~300 000 r/min的工作转速,提高发动机功率和动力性能,并降低燃油消耗和排放. 在此超高速工况下,动压油膜的强非线性作用和转子固有的不平衡效应使该系统呈现出复杂的动力学现象,其中油膜涡动、振荡、跳跃、倍周期分岔和混沌等非线性动力学行为对增压器的健康运转意义重大,因而备受关注. 本文作者从摩擦学动力学耦合的角度出发,基于流体动压轴承润滑理论和有限差分法计算非稳态油膜压力,结合达朗贝尔原理和传递矩阵法建立了转子离散化动力学方程,提出了一种由双油膜浮环支承的涡轮增压器转子系统动力学模型,并从转子轨迹、轴承偏心率、频谱响应、庞加莱映射和分岔特性等方面比较分析,描述了该非线性轴承-转子系统的不平衡效应及油膜失稳特征. 结果表明:转子一般在相对低速下作稳定的单周期不平衡振动,在高转速下其被油膜失稳引起的次同步涡动所抑制,但不平衡量的增加可阻碍转子以拟周期运动通向混沌运动的路径;适当不平衡补偿下,由于内、外油膜间交互的非线性刚度和阻尼作用,在油膜失稳区间之间的中高速区会出现适合增压器健康运转的稳定区间.      

非线性转子-轴承系统涡动的机械化数学分析

为研究转子一轴承系统中非线性油膜力引起的半速涡动，本文给出了将吴文俊消去法和符号计算相结合的分析方法。基于短轴承假设，得到了单盘转子系统涡动时盘心、轴心及涡动角速度相对于无量纲转速的关系式。分析研究了转子涡动角速度变化规律及出现的双稳态现象。