Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.

TORSIONAL OSCILLATION CHARACTERISTICS OF ROTARY SHAFTS BASED ON TORSION AND BENDING COUPLED VIBRATION

The torsional oscillation characteristics on the bending and torsioh coupled vibration of rotary shaft system were investigated using the elasto-dynamic theory and other mathematic methods, such as difference approach, Fourier transform, and wavelet transform. It is concluded that mass eccentricity and other exciting modalities affect the bending and torsion coupled vibration of rotary shafts. Torsional vibration caused by bending vibration features linearity along with the change of amplitude of bending vibration. Meanwhile, energy spectrum concentrates on high frequency area with the wavelet analysis.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

Dynamic Characteristics of the Crankshaft System with Coupling Effect

The nonlinear dynamic model of the marine diesel crankshaft system with a propeller and 6 cranks is established, in which the variable moment of inertia of the linkage and the piston, coupling effect between torsional and axial vibration, the actuating force applied on the piston, the actuating torque and force applied on the propeller is included. The governing equations of the model denote a strong nonlinear and non autonomous system. By numeric simulation, the dynamic response of the system to initial displacement and initial speed, variable moment of inertia, the pressure applied on the piston by combustion gas, the torque and the axial force applied on the propeller by fluid is researched respectively. According to the research results, the variable moment of inertia and coupling effect between torsional and axial vibration are the fundamental reason for nonlinear vibration. Different actuating factors can not only result in different frequency components of the response, but make the same frequency component have different vibration amplitude. The dynamic behavior of the system is not influenced obviously by the actuating torque and force applied on the propeller. There is obvious difference in sensitivity of the dynamic response in the different direction to the same actuating factor.

Coupled flexural-torsional vibration band gap in periodic beam including warping effect

The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Torsional vibration active control of hybrid construction machinery complex shafting

Due to the coaxial connection of engine, motor and pump, the dynamic characteristics of hybrid construction machinery are changed, which generates a new torsional vibration problem of multi-power sources. To reduce the torsional vibration of the hybrid construction machinery complex shafting, torsional vibration active control was proposed. The three-mass model of coaxial shafting of hybrid construction machinery was established. The PID control and the fuzzy sliding mode control were chosen to weaken torsional vibration by controlling the motor speed and torque. The simulation results show that the fuzzy sliding mode control has 12% overshoot of the PID control when the engine torque changes. The active control is effective and can realize smooth power switch.

WELL－POSEDNESS AND CONTROLLABILITY AND OBSERVABILITY OF A COUPLED VIBRATING SYSTEM

In this paper, we derive a new description form of coupled bending and torsionalvibrating system with boundary control and observation through Green's formula and provethat it is equivalent to the original form. On the basis of this. we prove the control system iswell-posed in time and frequency domain and completely controllable and observable.

Combined deformation of filament-wound cylinder and application to torsion vibration control

The combined deformation and mechanical properties of filament-wound cylinder of filament reinforced composite materials are investigated. A method of using filament-winding composites to reduce the amplitude of torsion vibration in the case of special stimulated vibration is established. A design formula of anisotropic filament-wound cylinder to reduce the torsion vibration of axle components is obtained. The results indicate that by putting the filament-wound cylinder on an axis, the torsion vibration of the axis can be reduced effectively.

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Simulation of Reciprocating Compressor Start-up and Shut-down under Loaded and Unloaded Conditions

During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank shaft as well other components of the system will be described. The modelling of the electrical induction motor, coupling, crank shaft, damper as well as the compressor resistance torque are extremely important in simulating start-up and shut-down of reciprocating compressor. Furthermore the switching torque of the electrical motor and the instantaneous moment of inertia of the reciprocating compressor crank gear are important as well. The transient start-up and shut-down process under loaded and unloaded conditions is described using a non-linear differential equation for driven train system： E-motor--coupling--flywheel--reciprocating compressor--damper. Shaft torsional moments on the drive train and especially on the coupling, whether elastic or stiff, can then only be calculated using numerical simulation. This paper will describe some of the key elements in modelling, simulating and measurements of drive train start-up and shut-down carried out on already operational piston compressor units.

Characteristics of Pore Water Pressure of Saturated Silt Under Wave Loading

The characteristics of dynamic stress in the seabed under wave loading are constant principal stress and continuous rotation of the principal stress direction. Cyclic triaxial-torsional coupling shear tests were pefformed on saturated silt by the hollow cylinder apparatus under different relative densities, deviator stress ratios and vibration frequencies to study the development of pore water pressure of the saturated silt under wave loading. It was found that the development of pore water pressure follows the trend of ＂fast - steady - drastic＂. The turning point from fast to steady stage is not affected by relative density and deviator stress ratio. However, the turning point from steady to drastic stage relies on relative density and deviator stress ratio. The vibration cycle for the liquefaction of saturated silt decreases with increasing deviator stress ratio and increases with relative density. The vibration cycle for the liquefaction of the saturated silt increases with vibration frequency and reaches a peak value, after which it decreases with increasing vibration frequency for the relative density of 70%. But the vibration cycle for the liquefaction of saturated silt increases with vibration frequency for the relative density of 30%. The development of pore water pressure of the saturated silt is influenced by relative density and vibration frequency.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

钻杆纵-扭耦合振动的试验研究

提出了一种新型的钻杆纵-扭耦合振动模拟测试系统。基于该系统设计了单因素试验,研究了驱动转速、进给速度、钻头直径、岩样强度和钻杆刚度对钻杆振动的影响规律,并通过正交试验探究了以上各因素对钻杆振动的影响程度。单因素试验结果表明,随着转速的增加,纵向振动幅值先减小后增大,但扭转振动幅值逐渐减小;随着进给速度的增大,纵向振动幅值逐渐减小,但扭转振动的幅值逐渐增大;转速增加导致扭矩和钻压下降,而进给速度增加导致扭矩和钻压上升;采用小直径钻头,低强度岩样,低刚度钻杆均有助于减小钻杆纵向振动幅值,但均导致扭转振动幅值增加。正交试验结果表明,转速对纵向振动的影响程度最大,进给速度对扭转振动的影响程度最大。试验结果与已有钻杆纵-扭耦合振动两自由度模型的数值仿真结果基本吻合。

某大型水电站机组特定负荷区间厂房振动噪声成因分析与探讨

某大型水电站机组在低水头特定负荷区间运行时厂房出现低沉的轰鸣噪声,并伴随厂房楼板、楼梯明显振动的现象,参建各方对引起该异常现象的原因进行了逐一排查但至今尚未解决。对此进行了机组变水位稳定性和能量试验,根据试验成果对机组及厂房结构耦合振动成因进行了分析与推测,初步判断原因为固定导叶卡门涡激发了活动导叶的弯扭耦合共振,通过轴承和顶盖传导至混凝土,并导致母线层楼板及下方立柱发生共振。

基于同频弯扭耦合强迫振动的桥梁断面颤振导数识别方法改进

为拓展强迫振动法在桥梁断面颤振导数识别领域中的应用能力,采取让断面做2次同频异相的弯扭耦合简谐运动模式,理论推导出任意非零相位差条件下的桥梁断面颤振导数识别公式。以理想平板的Theodorsen解为气动力数据源,对该方法的识别能力进行数值验证,并在此基础上研究弯扭耦合运动相位差、高斯白噪声、整数倍频有色噪声对平板颤振导数识别结果的影响规律。基于Fluent软件,将该方法与计算流体动力学(Computational Fluid Dynamics,CFD)技术结合,识别得到丹麦大带东桥主梁断面的颤振导数。研究结果表明:当平板气动力不包含噪声时,在任意非零相位差取值条件下,按照该方法识别所得颤振导数结果与理论值完全吻合;当平板气动力含有高斯白噪声时,在考察的3个低水平噪声条件下(5%、10%、15%),颤振导数识别误差与高斯白噪声比例水平、折算风速均成正相关,但不同颤振导数对高斯白噪声敏感程度各异;当平板气动力包含整数倍频有色噪声时,3倍频、4倍频噪声对颤振导数的识别精度影响显著,其他低倍频噪声和超高倍频噪声的影响较小,在8个颤振导数的识别结果中,H_(2)^(*)、H_(4)^(*)、A_(2)^(*)、A_(4)^(*)对倍频有色噪声更敏感。应用该方法结合CFD数值模拟识别得到的大带东桥主梁颤振导数与既有文献结果吻合良好,经计算得到的颤振临界风速也较为接近。研究结果可满足同类桥梁颤振设计的工程计算需求。

基于空耦超声激励的微结构模态频率温度特性研究

为了研究微悬臂结构弯曲振动模态频率的温度特性,首先针对各向异性材料的等截面矩形微悬臂结构建立了其各阶模态频率温度系数的理论模型;然后搭建了包括激光测振单元、空耦超声激励单元和温度控制单元的非接触式微结构动态特性测试系统;最后利用所搭建的测试系统分别对等截面矩形单晶硅微悬臂梁在室温~300℃时的动态特性进行了测试,获得了微悬臂梁前三阶弯曲振动模态频率随温度的变化规律和频率温度系数。研究结果表明,单晶硅微悬臂梁前三阶弯曲振动模态频率随着温度的升高而呈近似线性的减小,并且微悬臂梁前三阶弯曲振动模态具有几乎相同的频率温度系数,其中一阶模态频率的温度系数为-2.18×10-5/℃,二阶模态频率的温度系数为-1.91×10^(-5)/℃,三阶模态频率的温度系数为-2.01×10^(-5)/℃,前三阶模态频率温度系数的测试结果与理论模型预测值的偏差分别3×10^(-7)/℃,3×10^(-6)/℃和2×10^(-6)/℃。

基于流固耦合的单轴跟踪式光伏结构风致扭转研究

以某跟踪式光伏发电系统为研究对象,通过编写自定义程序代码UDF对Fluent进行二次开发,建立单轴跟踪式光伏结构的二维模型,研究其在风荷载作用下的扭转振动问题。研究结果表明:风速达到某一特值后,结构出现等幅周期性振动,发生软颤振现象,而其阻尼比对抑制扭转振动有一定的作用,这同实际情况较吻合;光伏组件倾角在0°~20°范围内时,倾角越大,扭转振动的临界风速越低。

大功率内燃发电机组联轴器对轴系扭振性能影响分析及应用研究

联轴器的刚度特性对内燃发电机组轴系低阶扭振模态及响应特性有决定性的影响。采用理论分析和仿真研究的方法,全面分析了联轴器刚度参数对大功率内燃发电机组轴系扭振模态特性和响应特性的影响规律,并结合工程应用实例进行了内燃机各缸功率均衡的正常运行工况、各缸做功不均衡工况以及机组启动、停机过程的仿真研究和实验验证。