Active damping of a micro-cantilever piezo-composite beam

Thick PZT films are of major interest in the actuation of mechanical structures. One of the promising fields deals with active damping. Since it is a dynamic application, hard-PZT type of screen-printed films are suited to this kind of use. Nevertheless, the drop in dielectric, ferroelectric and piezoelectric properties induced by the fabrication process is a serious constraint and it needs to be evaluated. The first section of this paper will present the mechanical system used for the experimental investigations. These investigations look to quantify the electromechanical properties of the films once the deposition process is achieved. The experimental observations highlighting the efficiency of hard-PZT thick films in active damping despite the drop in the electromechanical properties will then be considered. The control strategy used in the experiments can be called pseudo-direct-velocity feedback. Then the constitutive relations of the composites will be needed to derive the roots locus analysis by means of finite element modelling on one hand and through the roots of the partial derivative equations on the other hand. The unconditional stability of the uncollocated system will be demonstrated and its typical asymptotic behavior when the gain tends towards infinity will be explained.     

Three different guises for the dynamics of a rotating beam

The dynamics of a flexible beam forced by a prescribed rotation around an axis perpendicular to its plane is addressed. Three approaches are considered, two of them related with simplified theories, within Strength of Materials, and the third one using Finite Elasticity. In the Strength of Materials approaches, the governing equations of motion are derived by superposing the deformations and the rigid motion in the first model, and in the second by stating the stationarity of the Lagrangian (including first- and second-order effects in order to capture the stiffening due to the centrifugal forces) through Hamilton's principle. Two actions are considered: gravity forces (pendulum) and prescribed rotation. Comparison of the two Strength of Materials models with the model derived from Finite Elasticity is carried out. Predictions for the same problems, interpreted in the context of the specific model, are compared and it was found that sometimes they give rather different results, both in the results and in the computational cost. Energy analyses are performed in order to obtain information about the quality of the numerical solutions. The paper ends with an example of a pendulum with a finite pivot including friction and flexibility. When the structural elements are sufficiently slender and the rotational speeds are low, so that the resulting deformations are small, the Strength of Material model that includes the load stiffening and the Finite Elasticity approach, lead to similar results. It can be concluded that the stiffening phenomenon is appropriately considered in the first model. On the contrary, when the Strength of Material hypothesis are not fulfilled, the problem should be addressed via the Finite Elasticity model. Additionally, cases with complexities such as friction at a finite pivot can only be addressed by Finite Elasticity.     

Active vibration control of beam structures using acceleration feedback control with piezoceramic actuators

In this study, the active vibration control of clamped–clamped beams using the acceleration feedback (AF) controller with a sensor/moment pair actuator configuration is investigated. The sensor/moment pair actuator is a non-collocated configuration, and it is the main source of instability in the direct velocity feedback control system. First, the AF controller with non-collocated sensor/moment pair actuator is numerically implemented for a clamped–clamped beam. Then, to characterize and solve the instability problem of the AF controller, a parametric study is conducted. The design parameters (gain and damping ratio) are found to have significant effects on the stability and performance of the AF controller. Next, based on the characteristics of AF controllers, a multimode controllable single-input single-output (SISO) AF controller is considered. Three AF controllers are connected in parallel with the SISO architecture. Each controller is tuned to a different mode (in this case, the second, third and fourth modes). The design parameters are determined on the basis of the parametric study. The multimode AF controller with the selected design parameters has good stability and a high gain margin. Moreover, it reduces the vibration significantly. The vibration levels at the tuned modes are reduced by about 12 dB. Finally, the performance of the AF controller is verified by conducting an experiment. The vibration level of each controlled mode can be reduced by about 12 dB and this value is almost same as the theoretical result.     

The dynamics of co- and counter rotating coupled spherical pendula

The dynamics of co- and counter-rotating coupled spherical pendula (two lower pendula are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. The linear modes allow us to understand the nonlinear normal modes, which are visualized in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendula having different energies. The results for co-rotating (all pendula rotate in the same direction) and counter-rotating motion (one of lower pendula rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendula are found to be higher than in the co-rotating case.     

通过压电式传感器进行简支梁声辐射有源控制

以简支梁为例,通过声辐射模态研究简支梁声辐射的有源控制。由于在中、低频时,声辐射模态对应的辐射效率随着模态阶数的增加而迅速降低。本文提出了一种新的控制策略,即通过设计特定形状的PVDF作为传感器来测量前L阶声辐射模态的伴随系数,使前L阶声辐射模态的声功率最小化。最后通过数值计算研究了控制力和传感器数目对控制效果的影响。     

Thermal effect on frequencies of coupled vibrations of a rotating beam of linearly varying semi-circular cross-section

An analysis is presented of the effect of a constant thermal gradient on coupled vibrations of a beam of linearly varying semi-circular cross-section attached to a rotating disc. A method based on Rayleigh's quotient is used to obtain upper bounds of the frequencies corresponding to the first three modes of vibrations. The frequencies for various values of cross-section variation, hub-radius and temperature gradient are obtained.     

旋转柔性悬臂梁动力学的Bezier插值离散方法研究

在旋转柔性梁变形场描述中,引入Bezier插值离散方法.首先构建旋转运动悬臂梁物理模型,接着采用第二类Lagrange动力学方程和Bezier插值离散方法,在计入柔性梁横向弯曲变形引起的纵向缩短的情况下,推导了旋转柔性梁的刚柔耦合动力学方程,并编制旋转柔性梁的动力学仿真软件,然后通过仿真算例对系统的动力学问题进行研究.最后将仿真结果与有限元法、假设模态法进行分析比较,验证了提出的Bezier插值离散方法的正确性,并得出Bezier插值离散法的计算效率较高;计算精度符合工程实际需要,高速时计算精度大于假设模态法;Bezier插值离散方法在处理大柔性问题时比假设模态法合理.因此在多体系统动力学领域具有优良性能和应用价值的Bezier插值离散方法将具有推广价值.     

有源噪声控制的一种变换域算法

有源噪声控制广泛应用于中低频噪声控制中。传统的有源控制都是在时域内使用LMS算法进行控制，由于LMS算法的收敛速度跟输入信号的自相关矩阵特征值分布有关，当特征值分布较大时，LMS算法的收敛速度会变的很慢。本文使用离散余弦变换(DCT)技术，在变换域内进行有源噪声控制的研究，同时考虑了变换域约束。仿真表明算法的有效性。     

Multi-objective optimal design and experimental validation of tracking control of a rotating flexible beam

This paper investigates the tracking control problem for a rotating flexible beam. A proportional-integral-derivative control is designed to meet multiple objectives including overshoot, peak time, tracking error of the rigid movement of the rotating base, and the defectional angle of the flexible beam. A multi-objective optimization problem is then formulated for the control design and is solved with the cell mapping method. Numerical simulations and experiments are carried out to demonstrate the effect of the different control gains in the Pareto set, and to study the difference between a linear and a nonlinear model of the flexible beam.     

Control of a rotating cantilever beam using a torque actuator and a distributed piezoelectric polymer actuator

A torque actuator and a distributed piezoelectric polymer (PVDF) actuator are utilized for control of a rotating cantilever flexible beam. The torque control contains proportional and derivative (PD) feedback for rigid motion control and a PVDF actuator control for vibration damping. Unlike previous approaches in the literature in which the angular velocity feedback was utilized, in this study we propose to use the linear velocity feedback (L-type) in our controller design for feasible implementation and avoiding modal truncation. The stability of the system with the L-type control has been analyzed, using the concept of a virtual joint model. The advantage of the proposed scheme lies in easy implementation, avoidance of modal truncation, efficient suppression of the dominant mode of vibration, and allowing high-speed motions. Numerical examples demonstrate the effectiveness of the proposed approach.     

Vibration of a rotating beam with tip mass

The vibration frequency of a rotating beam with tip mass is investigated. The finite element method is used, a third order polynomial being assumed for the variation of the lateral displacement. The effects of the root radius, the setting angle and the tip mass are incorporated into the finite element model. The results are compared with results from previous authors utilizing Myklestad and extended Galerkin methods. The results show that the setting angle has a significant effect on the first mode frequencies but not on the high frequencies. The tip mass tends to depress the frequencies at low speeds of rotation but it tends to increase the frequencies at high speeds of rotation. The results of this work have applications in wind turbine rotors, helicopter rotors, etc., and the method used here can be extended to investigate the vibration frequency of flexible blade auto cooling fans.     

Active and passive structural acoustic control of the smart beam

Structural noise and vibrations control can be achieved using two strategies: active - with feed-forward controller, a sensor and an actuator [1-3] or passive, by piezoelectric shunt damping [4-8], when a piezoelectric transducer will act as a sensor and an actuator. Potential applications of these structures are investigated. Two numerical (FEM) models based on the active and passive damping strategies are compared. The numerical solutions were confirmed experimentally.     

Filamentation of a rotating electron beam in a magnetized plasma

Filamentation of a nonrelativistic rotating electron beam in a magnetized plasma is investigated by solving the kinetic equation and finding its dielectric permitivity. The period and the establishment time of the filamentation structure and threshold for instability development are obtained. It will be shown that only when the external magnetic field strength becomes smaller than a characteristic value, filamentation appears.     

Active health monitoring in a rotating cracked shaft using active magnetic bearings as force actuators

We consider the active health monitoring of rotordynamic systems in the presence of breathing shaft cracks. The shaft is assumed to be supported by conventional bearings and an active magnetic bearing (AMB) is used in a mid-shaft or outboard location as an actuator to apply specified, time-dependent forcing on the system. These forces, if properly chosen, induce a combination resonance that can be used to identify the magnitude of the time-dependent stiffness arising from the breathing mode of the shaft crack.     

Mathematically trivial control of sound using a parametric beam focusing source

By exploiting a case regarded as trivial, this paper presents global active noise control using a parametric beam focusing source (PBFS). As with a dipole model, one is used for a primary sound source and the other for a control sound source, the control effect for minimizing a total acoustic power depends on the distance between the two. When the distance becomes zero, the total acoustic power becomes null, hence nothing less than a trivial case. Because of the constraints in practice, there exist difficulties in placing a control source close enough to a primary source. However, by projecting a sound beam of a parametric array loudspeaker onto the target sound source (primary source), a virtual sound source may be created on the target sound source, thereby enabling the collocation of the sources. In order to further ensure feasibility of the trivial case, a PBFS is then introduced in an effort to meet the size of the two sources. Reflected sound wave of the PBFS, which is tantamount to the virtual sound source output, aims to suppress the primary sound. Finally, a numerical analysis as well as an experiment is conducted, verifying the validity of the proposed methodology.     

Dynamic stability of a rotating beam with a constrained damping layer

The dynamic behavior and dynamic instability of the rotating sandwich beam with a constrained damping layer subjected to axial periodic loads are studied by the finite element method. The influences of rotating speed, thickness ratio, setting angle and hub radius ratio on the resonant frequencies and modal system loss factors are presented. The regions of instability for simple and combination resonant frequencies are determined from the Mathieu equation that is obtained from the parametric excitation of the rotating sandwich beam. The regions of dynamic instability for various parameters are presented.     

Global noise characteristics of a laser Doppler vibrometer-II. Experiments using beam dynamics

The use of a laser Doppler vibrometer to obtain velocity information from vibrating structures has gained wide acceptance in recent years. Although use of such an instrument can yield a spatially dense matrix of velocity information, several users have noted ‘noise’ at certain points in the spatial field. The technique by which the SLDV system operates results in occasional velocity ‘drop-outs’ which are unidirectional, always estimating the velocity response closer to zero than reality. These ‘drop-out’ areas occur more predominately at points of maximum velocity response with small rotational components. Alternatively, points exhibiting minimum velocity response with large rotational components are less susceptible to the ‘noise’. In this paper, an experiment to visualize the speckle pattern motions received by the photo-detectors during these vibration conditions is presented. Theories regarding the source(s) of the ‘noise’ are developed.