Free vibration analysis of beams with non-ideal clamped boundary conditions

A non-ideal boundary condition is modeled as a linear combination of the ideal simply supported and the ideal clamped boundary conditions with the weighting factors k and 1-k, respectively. The proposed non-ideal boundary model is applied to the free vibration analyses of Euler-Bernoulli beam and Timoshenko beam. The free vibration analysis of the Euler-Bernoulli beam is carried out analytically, and the pseudospectral method is employed to accommodate the non-ideal boundary conditions in the analysis of the free vibration of Timoshenko beam. For the free vibration with the non-ideal boundary condition at one end and the free boundary condition at the other end, the natural frequencies of the beam decrease as k increases. The free vibration where both the ends of a beam are restrained by the non-ideal boundary conditions is also considered. It is found that when the non-ideal boundary conditions are close to the ideal clamped boundary conditions the natural frequencies are reduced noticeably as k increases. When the non-ideal boundary conditions are close to the ideal simply supported boundary conditions, however, the natural frequencies hardly change as k varies, which indicate that the proposed boundary condition model is more suitable to the non-ideal boundary condition close to the ideal clamped boundary condition.     

Active robust vibration control of flexible composite beams with parameter perturbations

In this paper, a time domain approach is presented to treat the problem of active controlling simultaneously the bending and torsional vibration of flexible composite beams under both mode truncations and parameter perturbations. In the proposed approach, the residual model, which is known as unstructured uncertainty, is viewed as an additive perturbation to the controlled model. Based on a state space model, which incorporates both bending and torsional deformation effects, of the flexible composite beam with piezoelectric sensors and actuators, a robust stability condition is derived to guarantee that both bending and torsional vibration of the flexible composite beam, which is subject to both mode truncation and linear time-varying parameter perturbations, can be actively controlled by an observer-based controller. The proposed robust stability condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effects and additive time-varying parameter perturbations. Finally, an active robust vibration control problem of a cantilevered flexible composite beam with piezoelectric sensors and actuators is provided for illustration.     

Active vibration control of a structure with output feedback based on simultaneous optimization design method

Recent advances in the field of control theory have enabled us to design active vibration control systems for various structures. In many studies, the controller used to suppress vibration has been synthesized for the given mathematical model of structure. In these cases, the designer has not been able to utilize the degree of freedom to adjust the structural parameters of the control object. To overcome this problem, so called “Structure/ Control Simultaneous Optimization Method” is used. In this context of view, this paper is concerned with the active vibration control of bridge towers, platforms and ocean vehicles etc. Simultaneous design method is used to achieve optimal system performance. Here, a general framework for the simultaneous design problem of output feedback case is introduced based on LMI (Linear Matrix Inequality). The simulation results show that the proposed design method achieves desirable control performance.     

Diamond turning using position and AE dual feedback control system

A control scheme to improve machining accuracy by means of an acoustic emission root mean square (AErms) signal measured on-line during diamond turning is proposed. Preliminary experiments have verified a correlation between a machining error and measured AErms. Based on the correlation, a control algorithm to apply a compensation signal to a position feedback control loop, named the position and AE dual feedback control scheme is proposed. Machining tests using a diamond turning machine controlled with a PC-based open architecture controller showed that the proposed control scheme accomplishes 20% reduction of machining error compared to conventional position feedback control. Machining tests using new and worn diamond tools showed that an on-line tool-wear recognition is possible using the AE feedback control system.     

Active vibration suppression of a flexible structure using sliding mode control

In this paper, sliding mode control (SMC) is designed and applied to an elastic structure to suppress some of its vibration modes. The system is an elastic beam clamped on one end and the designed controller uses only the deflection measurement of the free end. The infinite dimensional mathematical model of the beam is reduced to an ordinary differential equation set to represent the behavior of required modes. Since the states of the finite dimensional model are not physically measurable quantities, an observer is designed to estimate these states by measuring the tip deflection of the beam. The performance of the observer is important because the observed states are used in the SMC design. In this study, by using the output information, an observer is designed and tested to estimate the states of the finite dimensional model of the beam. Then the designed SMC is applied to the experimental beam system which gives satisfactory suppressed vibrations.     

Modal space vibration control of a beam by using the feedforward and feedback control loops

This paper introduces a vibration control method for a flexible beam subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted. Here, we choose the modal filters as the state estimator to obtain the modal coordinates and modal velocities for the modal space control. Because of the existence of the disturbance forces, applying only the state feedback to suppress the vibration usually cannot achieve the desired control performance. The modal space feedforward control is then introduced to cancel out the disturbance forces. In this paper, the feedforward and feedback control method is implemented to reduce the beam vibration. The disturbance force observer is established to observe the disturbance modal forces for the feedforward control. The control gains are derived from the extended optimal control algorithm, where the disturbance modal forces are treated as exogenous state variables. By combining the feedback, feedforward control laws and the disturbance force observer together, the vibration control performances are discussed.     

Spindle vibration suppression for advanced milling process by using self-tuning feedback control

The goal of this work is to concurrently counterbalance the dynamic cutting force and regulate the spindle position deviation under various milling conditions by integrating active magnetic bearing (AMB) technique, fuzzy logic algorithm, and an adaptive self-tuning feedback loop. The experimental data, either for idle or cutting, are utilized to establish the database of milling dynamics so that the system parameters can be on-line estimated by employing the proposed fuzzy logic algorithm as the cutting mission is engaged. Based on the estimated milling system model and preset operation conditions, i.e., spindle speed, cut depth, and feed rate, the current cutting force can be numerically estimated. Once the current cutting force can be real time estimated, the corresponding compensation force can be exerted by the equipped AMB to counterbalance the cutting force, in addition to the spindle position regulation by feedback of spindle position. At the end, the experimental simulations on realistic milling are presented to verify the efficacy of the fuzzy controller for spindle position regulation and the capability of the dynamic cutting force counterbalance.     

压电智能悬臂梁结构振动主动控制仿真

为了提高LQR最优控制方法对压电类智能结构的振动控制效果,推导了表面离散分布压电元件的柔性悬臂梁结构的驱动和传感方程以及梁的弯曲振动方程,用模态分析方法对方程进行解耦和模型降阶,建立控制系统的状态空间方程。利用有限元分析方法来衡量压电元件对梁固有特性的影响,对状态空间方程的自振频率和振型函数进行修正,得到更为精确的数学模型。通过一悬臂梁的LQR最优控制仿真实例表明,经过模型修正后的最优振动控制效果更好。     

静压气浮溜板的振动主动控制系统研究

静压气浮溜板主要用在超精密加工机床中,它的振动将通过刀架直接反映到被加工工件表面,影响工件的表面质量。采用自行研制的空气作动器作为执行器,以实现无摩擦接触;采用神经网络-PID控制策略,通过BP神经网络在线学习调整PID控制参数,实现最佳参数组合。实验结果表明气浮溜板的振动主动控制系统是可行性的和有效性的。     

Active vibration control of flexible cantilever beam using piezo actuator and Filtered-X LMS algorithm

This paper presents the active vibration control of a flexible cantilever beam. The cantilever beam was excited by steady-state sinusoidal and white noise point forces. The vibrational control system was implemented using one piezo ceramic actuator bonded on the beam and the adaptive controller based on the Filtered-X LMS algorithm. Control results indicated that a considerable vibrational reduction could be achieved in a few seconds. Experimental results, demonstrate the feasibility of active vibration control of the flexible cantilever beam based on piezo ceramic actuator and the Filtered-X LMS algorithm.     

A compressional-shear model for vibration control of beams with active constrained layer damping

In the modeling of the active constrained layer damping (ACLD) structures, the transverse displacements of the constraining layer and the host structures are usually assumed to be compatible. However, when performing active control, even a small difference between the transverse displacement of the constraining layer attached with actuator and that of the host structures bonded with sensor may destabilize the closed-loop control system. In order to understand the effect of incompatible transverse displacements, a model for the beam with ACLD in which both compressional vibration and shear damping are considered, is developed. In this model, the viscoelastic layer is modeled to carry not only the shear strain but also the peel strain. In addition, a thorough solution scheme to obtain the eigenvalues and frequency response of the closed-loop controlled beam is also given based on multiple shooting method. The effects of the compressional vibration on passive and active control are investigated through simulation examples. It is found that the compressional vibration can significantly affect the frequencies and damping ratios of higher-order modes of an actively controlled beam and may even destabilize the active control.     

Active vibration control of trim panel using a hybrid controller to regulate sound transmission

This paper presents a method for actively controlling the sound transmission through an aircraft trim panel using a hybrid feedforward/feedback control technique. The method involves measuring the frequency transfer function of the trim panel system and then creating an autoregressive moving average model using frequency domain curve fitting. The control technique is designed to minimize the vibration of a panel that has a limited piston-like motion. The hybrid controller consists of an adaptive feedforward controller that operates in conjunction with a linear quadratic Gaussian feedback controller. The feedback controller increases the damping capacity of the secondary plant to augment the convergence rate of the adaptive feedforward controller. Experimental results indicate that the hybrid controller effectively reduces the vibration of active trim panels and therefore also reduces the sound transmission of the panel.     

Design of feedforward and feedback position control for passive bilateral teleoperation with delays

Bilateral teleoperation systems connected to computer networks such as the internet must be able to operate with varying time delays since such systems can easily become unstable. A passivity concept has been used as the framework to solve the stability problem in the bilateral control of teleoperation systems. Passivity and tracking performance are recovered using a control architecture that incorporates time varying gains into the transmission path, feedforward, and feedback position control. The proposed architecture has an inner component that can accommodate any configuration but still remain stable and passive even with varying time delay. The simulation results for a single degree of freedom master/slave system demonstrate the performance of the proposed control architecture.     

Impulsive loading of fully clamped beams with finite plastic deflections and strain-rate sensitivity

A review is given of earlier work on the plastic response to impulsive loading of a beam clamped against end rotations and axial displacements, taking account of small finite transverse displacements and of strain-rate dependence of the yield stress. New solutions are derived from rigid-plastic analysis which include both effects in simple approximate ways. Deflections are compared as obtained from these formulas, from experiments described here on mild steel beams and from finite-difference numerical solutions using the M.I.T. rod model with elastic-plastic strain-rate sensitive behavior. The significance of agreements observed is discussed.     

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.     

Flexural-torsional coupled vibration of slewing beams using various types of orthogonal polynomials

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. Performance of various orthogonal polynomials is compared to each other in terms of their efficiency and accuracy in determining the required natural frequencies. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the special trigonometric functions used in conjunction with Hermite cubics, and beam characteristic orthogonal polynomials. A total of 5 cases of beam boundary conditions and rotation are studied for their natural frequencies. The obtained natural frequencies and mode shapes are compared to those available in various references and the results for coupled flexural-torsional vibrations are especially compared to both previously available references and with those obtained using NASTRAN finite element package. Among all the examined orthogonal functions, Legendre orthogonal polynomials are the most efficient in overall CPU time, mainly because of ease in performing the integration required for determining the stiffness and mass matrices.     

重复控制与积分正反馈组合的磁轴承低功耗控制

本文提出一种重复控制与积分正反馈相结合的控制方法,以抑制磁轴承系统功耗。首先建立了磁轴承系统的数学模型,分析了由重力、转子不平衡和位移传感器噪声引起的电流噪声的频率特性,分析发现其可分为直流和多谐波两大类;其次推导了用于消除直流电流的控制器需满足的条件,在此基础上,设计了一种电流积分正反馈算法。通过调节转子的悬浮位置,利用混合磁轴承中永磁体产生的磁力抵消重力,抑制电流的直流分量,采用根轨迹方法确定保证闭环系统稳定的参数取值范围;然后提出一种嵌入式重复控制方法抑制转子不平衡和位移传感器引起的多谐波电流噪声,采用重构谱理论判定系统的稳定性。最后以磁悬浮控制力矩陀螺为测试平台,对所提出的控制算法进行仿真和实验研究。结果表明:采用该算法后,电流的直流分量基本被抑制,谐波分量的峰峰值减小了88.3%,功耗减小了7W,验证了该算法的有效性。     

轴向运动弦线横向振动状态反馈的 H∞控制

首先运用鲁棒控制理论中状态反馈的H∞控制,对轮带系统作动器的角位移和角速度进行调控,实现了对轴向运动皮带横向振动的位移和角速度的控制。然后运用MATLAB进行仿真,对该控制方法的有效性进行了验证。结果表明,该方法解决了轴向运动弦线横向振动系统的不确定系统鲁棒镇定控制器的设计难题,保证了控制器的有效性、可靠性和实用性。     

Modeling and bending vibration control of nonuniform thin-walled rotating beams incorporating adaptive capabilities

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

温度对两端固支管道振动特性影响分析

采用三种有限元模型和实验的方法分析了两端固支管道各阶固有频率,选择其中一个较好有限元模型.利用该模型计算了管道在高温下的振动特性.提出了管道设计过程中不仅要在常温下进行振动特性分析,而且更应该注意对管道在工作温度下的振动特性分析,最终为管道系统的安全性和设计提供了理论依据.