Modeling and vibration feedback control of rotating tapered composite thin-walled blade

This paper addresses the problem of the modeling and vibration control of tapered rotating blade modeled as thin-walled beams and incorporating damping capabilities. The blade model incorporates non-classical features such as anisotropy, transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. For the rotating blade system, a thorough validation and assessment of a number of non-classical features including the taper characteristics is accomplished. The damping capabilities are provided by a system of piezoactuators bonded or embedded into the structure and spread over the entire span of the beam. Based on the converse piezoelectric effect, the piezoactuators produce a localized strain field in response to a voltage and consequently, a change of the dynamic response characteristics is induced. A velocity feedback control law relating the piezoelectrically induced transversal bending moment at the beam tip with the appropriately selected kinematical response quantity is used and the beneficial effects upon the closed-loop dynamic characteristics of the blade are highlighted.     

Bending vibrations of adaptive cantilevers with external stores

The vibrational behavior of cantilevers carrying externally mounted stores and featuring adaptive capabilities is investigated. The structure is modeled as a thin-walled beam, and the adaptive capabilities are provided by a system of piezoactuators bonded or embedded into the structure. Based on the converse piezoelectric effect, the piezoactuators produce a localized strain field in response to an applied electric field and, as a result, an adaptive change in the dynamic response characteristics is achieved. Implementation of a control law relating the applied electrical field to one of the mechanical quantities characterizing the motion of the beam, enables one to obtain the free vibration characteristics as a function of the applied voltage (or in other terms, of the feedback gain).The obtained numerical results suggest that the application of this technology can play a major role in the enhancement of the dynamic response and the control of free vibration characteristics of this type of structures.     

Dynamic response analysis of rotating composite-VEM thin-walled beams incorporating viscoelastic materials in the time domain

This paper addresses the analytical modeling and dynamic response of the advanced composite rotating blade modeled as thin-walled beams and incorporating viscoelastic material. The blade model incorporates non-classical features such as anisotropy, transverse shear, rotary inertia and includes the centrifugal and coriolis force fields. The dual technology including structural tailoring and passive damping technology is implemented in order to enhance the vibrational characteristics of the blade. Whereas structural tailoring methodology uses the directionality properties of advanced composite materials, the passive material technology exploits the damping capabilities of viscoelastic material (VEM) embedded into the host structure. The VEM layer damping treatment is modeled by using the Golla-Hughes-McTavish (GHM) method, which is employed to account for the frequency-dependent characteristics of the VEM. The case of VEM spread over the entire span of the structure is considered. The displayed numerical results provide a comprehensive picture of the synergistic implications of both techniques, namely, the tailoring and damping technology on the dynamic response of a rotating thin-walled beam exposed to external time-dependent excitations.     

形状记忆合金驱动梁的变形分析及试验研究

将预拉伸的形状记忆合金 (Shapememoryalloy ,简称SMA)薄片作为驱动器 ,粘贴在构件表面。加热SMA ,当其发生相变时 ,会产生很大的恢复力 ,驱动构件发生变形。建立了粘有SMA薄条应变驱动器的简化机翼—梁的力学模型 ,分析了单边粘贴SMA梁的压弯复合变形 ,给出了其应变分布及弯曲变形的解析表达式。同时通过试验对理论结果进行了验证。     

Adaptive feedforward control of ionic polymer metal composites with disturbance cancellation

Ionic polymer-metal composites (IPMCs) are promising candidates in various sensing and actuation applications due to their light weight, large bending, and low actuation voltage requirements. However, IPMCs are still in the early stage of development, and their bending response can vary widely depending on various factors such as fabrication process, water content, temperature, and contact with electrodes. To control IPMCs in a predictable manner and to minimize the effects of plant uncertainty and external disturbances, a precise and robust control scheme is required. In the present work, a three-part adaptive feedforward control architecture is employed for IPMC deflection control. First, adaptive identification is performed to identify changes in the dynamic behavior over time and in the input voltage using a gradient descent method. Second, an adaptive feedforward controller is implemented to control the dynamic response of the plant, where the IPMC displacement is observed and is used to adjust the parameters of the controller. Third, noise and disturbance cancelling is performed using an additional adaptive canceller, which does not affect the system dynamics. Our results show that the adaptive identification and feedforward controller with disturbance cancellation using the gradient descent method provides accurate tracking performance under plant variation and disturbance. Especially, the fast convergence speed of the proposed technique makes it practical for online control.     

热载荷作用下旋转叶片频率转向特性

基于薄板弯曲理论,采用梁函数组合法对叶片进行动力特性分析,推导了变转速状态下叶片频率和振型的解析解的一般表达式,提出了在离心力场和温度场效应下研究叶片“频率转向”的一种方法,建立了计算叶片各阶频率和振型的理论依据。研究结果对提高叶片疲劳检测效率具有意义。     

Asymptotic decay rate of non-classical strain gradient Timoshenko micro-cantilevers by boundary feedback

In non-classical micro-beams, the strain energy of the system is obtained based on the non-classical continuum mechanics. This paper presents the problem of boundary control of a vibrating non-classical micro-cantilever Timoshenko beam to achieve the asymptotic decay rate of the closed loop system. For this aim, we need to establish the well-posedness of the governing partial differential equations (PDEs) of motion in presence of boundary feedbacks. A linear control law is constructed to suppress the system vibration. The control forces and moments consist of feedbacks of the velocities and spatial derivatives of them at tip of the micro-beam. To verify the effectiveness of the proposed boundary controllers, numerical simulations of the open loop and closed loop PDE models of the system are worked out using finite element method (FEM). New Timoshenko beam element stiffness and mass matrices are derived based on the strain gradient theory and verification of this new beam element is accomplished.     

梁杆碰撞激发瞬态波传播的动态子结构模型

针对梁杆碰撞问题,通过推导物理坐标和模态坐标下的动力学控制方程,采用黏结接触模型和单轴压缩局部接触模型处理碰撞产生的接触约束,提出一种适用于梁杆碰撞激发瞬态波传播研究的动态子结构模型。与理论解的比较表明,该动态子结构模型具有良好的数值收敛性和较高的计算精度。数值计算结果显示,该模型能够有效地分析碰撞激发的杆中轴向波和梁中弯曲波的传播、反射和相互干涉。借助该模型,分别研究轴向波和弯曲波通过碰撞接触约束的传播效应,研究结果表明,柔性构件碰撞的一个显著特征是波传播效应直接影响碰撞力响应,并使碰撞力响应形式变得异常复杂。     

液压弯辊系统的优化神经网络内模控制

针对轧机液压弯辊系统存在非线性、时变性等特点,采用基于前馈神经网络的内模控制方法,将优化网络用于神经网络辨识器和内模控制器的离线训练,采用学习率自适应调整的改进BP算法在线调整网络权值。仿真研究表明,将优化网络用于液压弯辊系统控制,提高了液压弯辊系统的动态响应速度和稳态跟踪精度,具有较强的快速性和鲁棒性,能够取得理想的控制效果。     

Experimental study on dynamic characteristics of linear parametrically excited system

An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam transversely in the laboratory. It showed good potential for the experimental investigation of linear parametric system. Therefore, experiments for the natural frequency, the response (both free and forced) spectra and frequency response characteristics of a cantilever beam under electromagnetic excitation, are, respectively, conducted to study the dynamic characteristics of linear parametrically excited system. The vibrational model of the cantilever beam system is established using the assumed mode method. Theoretical results, related to the natural frequency, response spectra and external resonant condition, are presented to verify the experimental results. It is shown that the dynamic characteristics of linear time-periodic system do have some typical features, which differ distinctly from that of the linear time-invariant system.     

耦合梁中高频抖动的行波分析与主动控制

为研究中高频扰动下耦合梁结构的动力学响应与主动控制,基于Timoshenko梁理论,考虑梁中转动惯量和剪切变形的影响,采用行波方法分别建立梁结构纵向运动、弯曲运动的单元模型与结点散射模型,进而获得耦合梁的行波动力学模型及其精确的中高频抖动响应;引入“功率流”的分析思想,并以此为目标函数,优化得到了最优控制力的大小与相位,然后对结构施加最优控制力,实现耦合梁结构的功率流主动控制。在此基础上,进行数值仿真分析,并与Euler-Bernoulli梁理论计算结果进行对比。结果表明,采用行波方法计算耦合梁结构的动力学响应准确可靠;Timoshenko梁模型较Euler-Bernoulli梁模型在中、高频段更为精确,且更接近工程实际;功率流主动控制可以明显降低耦合梁结构全频域内的抖动,验证了基于行波方法功率流主动控制的正确性与有效性。     

Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle

In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled equations of motion are solved using Runge-Kutta algorithm with adaptive time step and the instability boundary is determined using the Floquet theory. Numerical results present effects of some parameters such as fluid flow fluctuation, bending-to-torsional rigidity ratio, nozzle inclination angle, nozzle mass and viscoelastic material on the stability margin of the system and some conclusions are drawn.     

Nonlinear dynamic behavior of rotating blade with breathing crack

This study aims at investigating the nonlinear dynamic behavior of rotating blade with transverse crack. A novel nonlinear rotating cracked blade model (NRCBM), which contains the spinning softening, centrifugal stiffening, Coriolis force, and crack closing effects, is developed based on continuous beam theory and strain energy release rate method. The rotating blade is considered as a cantilever beam fixed on the rigid hub with high rotating speed, and the crack is deemed to be open and close continuously in a trigonometric function way with the blade vibration. It is verified by the comparison with a finite element-based contact crack model and bilinear model that the proposed NRCBM can well capture the dynamic characteristics of the rotating blade with breathing crack. The dynamic behavior of rotating cracked blade is then investigated with NRCBM, and the nonlinear damage indicator (NDI) is introduced to characterize the nonlinearity caused by blade crack. The results show that NDI is a distinguishable indicator for the severity level estimation of the crack in rotating blade. It is found that severe crack (i.e., a closer crack position to blade root as well as larger crack depth) is expected to heavily reduce the stiffness of rotating blade and apparently result in a lower resonant frequency. Meanwhile, the super-harmonic resonances are verified to be distinguishable indicators for diagnosing the crack existence, and the third-order super-harmonic resonances can serve as an indicator for the presence of severe crack since it only distinctly appears when the crack is severe.     

Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang–bang control

Electrostrictive materials, hard ceramics and soft polymers, have been used as precision actuators in many engineering applications. This study is to examine bang–bang control performance of a hybrid Plexiglas beam laminated with polymeric electrostrictive (RTV 270) actuator and piezoelectric polyvinylidene fluoride (PVDF) sensor layers using both analytical and experimental techniques. Material characteristics are calibrated via static testing first; a hybrid beam model is then fabricated and an experiment set-up, consisting of a bang–bang controller, high-voltage amplifier, data acquisition system and the hybrid beam system, is designed to evaluate vibration control characteristics (i.e., damping ratio estimation) of the hybrid beam subjected to various control conditions. Due to the quadratic behaviour of electrostrictive materials, the controller activates the electrostrictive actuator only in upward motion of the beam, with reference to signals generated from the piezoelectric sensor. Base on constitutive equations and dynamic/control characteristics, a mathematic hybrid beam model is also derived from the electrostrictive thin shell theory and its dynamic responses, based on the finite difference discretization, are simulated to predict damping ratios resulting from control forces induced by the electrostrictive actuators. Dynamic responses (with and without control) of the physical beam model are measured and compared with simulation results. Favourable comparison suggests that the mathematical model describes the experimental model very well and its application to other advanced structures can be proceeded.     

带摩擦阻尼器长叶片振动特性优化研究

为了防止透平机械长叶片因振动而导致的疲劳损坏,目前普遍采用的方法是在叶片上增加摩擦阻尼结构.针对带摩擦阻尼器长叶片的结构特点,采用扭曲梁与空间直梁单元模化叶片,推导叶片阻尼连接单元的力学模型,由此建立叶片总的动力特性分析方程.然后详细分析某阻尼围带长叶片具有不同围带厚度和围带间隙的振动响应,由此获得优化的阻尼围带结构,该分析结果还与自由叶片的响应数值进行对比,发现共振时由于围带的阻尼效果,优化阻尼结构的最大响应值只有自由叶片的42.4%.最后分析添加整圈松拉金结构的叶片振动响应,发现松拉金的加入将进一步降低叶片振动响应值.分析结果表明,该数值模型可以应用于多种摩擦阻尼器长叶片的振动特性分析及优化设计,将为阻尼叶片的设计提供实用工具.     

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations?? amplitudes and increasing stability.     

Theoretical Model for Friction-Induced Vibration of Ball Joint System under Mode-Coupling Instability

A theoretical model for the friction-induced vibration in ball joint systems is proposed. In a ball joint system, a small contact area is formed on the surface of the ball due to clearance between the ball and hemispherical cup. To analyze the dynamic instability induced by friction in the ball joint system, the dynamic beam-on-socket model with nonconformal contact under three-dimensional rotation was theoretically proposed. The results from stability analysis revealed that the mode-coupling type instability occurred for the lower bending modes at a specific combination of rotation components as well as an increase in the friction coefficient. In particular, the spinning component was essential in generating the mode-coupling instability between the doublet bending modes of the beam.     

Effect of blade tip pattern on blade load and vibration characteristics of a twin-stage axial flow fan

Focusing on a twin-stage axial fan, this paper investigates the effect of blade tip pattern on blade load and vibration characteristics. Steady simulations are first conducted to quantify the aerodynamic performance of various blade tip patterns. The finite element modeling analysis is performed to capture blade load and vibration characteristics, and Campbell diagram is introduced to evaluate resonance margin of different blade tip patterns. Results show that for all selected patterns, the first three mode shapes are mainly the bending of blade tip, which results in stress concentration at the blade root, while the last three are the waving in small range. The proposed blade tip patterns not only increase maximum stress and average deformation, but also significantly increase resonance margin near the rated speed. In addition, based on the harmonic response analysis, we find that the stress and amplitude frequency response will be notably altered by blade tip patterns.

     

Analysis of rotating nonuniform pretwisted beams with an elastically restrained root and a tip mass

Using Hamilton's principle derives the governing differential equations for the coupled bending–bending vibration of a rotating pretwisted beam with an elastically restrained root and a tip mass, subjected to the external transverse forces and rotating at a constant angular velocity. Using the mode expansion method derives the closed-form solutions of the dynamic and static systems. The orthogonal condition for the eigenfunctions of the system with elastic boundary conditions is discovered. The self-adjointness of the system is proved. Moreover, the Green functions of the system are obtained. The symmetric properties of the Green functions are revealed. The frequency response on the steady response of the beam is also investigated.     

非惯性系下旋转叶片的动力学分析

利用Ho-Hoon Lee提出的在满足叶片弯曲机制情形下的新的动力学建模方法对盘叶这种常见的机械系统进行动力学建模。并用拉格郎日方法和假设模态法离散推导出了系统的动力学方程。在建立系统动力学方程的过程中考虑了未被Ho-Hoon Lee[2]所考虑的盘的半径,同时给出了盘叶系统的数值仿真结果。并与文献[3]中简化的一阶近似耦合模型在理论上和数值上进行了比较。