Modeling and analysis of rotating plates by using self-sensing active constrained layer damping

This paper proposes a new finite element model for active constrained layer damped (CLD) rotating plate with self-sensing technique. Constrained layer damping can effectively reduce the vibration in rotating structures. Unfortunately, most existing research models the rotating structures as beams that are not the case many times. It is meaningful to model the rotating part as plates because of improvements on both the accuracy and the versatility. At the same time, existing research shows that the active constrained layer damping provides a more effective vibration control approach than the passive constrained layer damping. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate. Unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Also, the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator. Then, a proportional control strategy is implemented to effectively control the displacement of the tip end of the rotating plate. Additionally, a parametric study is conducted to explore the impact of some design parameters on structure??s modal characteristics.     

Piezoelectric smart structures for noise reduction in a cabin

The feasibility of piezoelectric smart structures for cabin noise problem is studied numerically and experimentally. A rectangular enclosure, one side of which is a plate while the other sides are assumed to be rigid, is considered as a cabin. A disk-shaped piezoelectric sensor and actuator are mounted on the plate structure and the sensor signal is returned to the actuator with a negative gain. An optimal design of the piezoelectric structure for active noise control of the cabin is performed. The design variables are the locations and sizes of the disk-shaped piezoelectric actuator and sensor and the actuator gain. To model the enclosure structure, a finite element method based on a combination of three dimensional piezoelectric, flat shell and transition elements is used. For the interior acoustic medium, the theoretical solution of a rectangular cavity in the absence of any elastic structures is used and the coupling effect is included in the finite element equation. The design optimigation is performed at resonance and off-resonance frequencies, with the results showing a remarkable noise reduction in the cavity. An experimental verification of the optimally designed configuration confirms the feasibility of piezoelectric smart structures in resolving cabin noise problems.     

Vibration Control of a Composite Beam Using Self-sensing Semi-active Approach

Structural vibration control was an active research area for the past twenty years because of their potential applications in aerospace structures,civil structures,naval structures,etc.Semi-active vibration control methods based on piezoelectric actuators and synchronized switch damping on inductance(SSDI) techniques attract the attention of many researchers recently due to their advantages over passive and active methods.In the SSDI method,a switch shunt circuit is connected to the piezoelectric patch to shift the phase and amplify the magnitude of the voltage on the piezoelectric patch.The most important issue in SSDI method is to control the switching actions synchronously with the maximum vibration displacement or maximum strain.Hence,usually a displacement sensor is used to measure the vibration displacement or a collocated piezoelectric sensor is needed to measure the strain of the structure near the piezoelectric actuator.A self-sensing SSDI approach is proposed and applied to the vibration control of a composite beam,which avoids using a separate sensor.In the self-sensing technique,the same piezoelectric element functions as both a sensor and an actuator so that the total number of required piezoelectric elements can be reduced.One problem in the self-sensing actuator,which is the same as that in the traditional collocated piezoelectric sensors,is the noise generated in the sensor signal by the impact of voltage inversion,which may cause extra switching actions and deteriorate control performance.In order to prevent the shunt circuit from over-frequent on-and-off actions,a simple switch control algorithm is proposed.The results of control experiments show that the self-sensing SSDI approach combined with the improved switch control algorithm can effectively suppress over-frequent switching actions and gives good control performance by reducing the vibration amplitude by 45%,about 50% improvement from the traditional SSDI with a separate piezoelectric element and a classical switch.     

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.     

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。     

Vibration control efficiency of piezoelectric shunt damping system

The piezoelectric shunt damping technique based on the direct piezoelectric effect has been known as a simple, low-lost, lightweight, and easy to implement method for passive damping control of structural vibration. In this technique, a piezoelectric material is used to transform mechanical energy to electrical energy. When applying the piezoelectric shunt damping technique to passively control structural vibration, the piezoelectric materials must be bonded on or embedded in host structure where large strain is induced during vibration, thus to ensure vibrational mechanical energy to be transformed into electrical energy as much as possible. In this paper, the concept of vibration control efficiency of a piezoelectric shunt damping system is proposed and studied theoretically and experimentally. In the study, PZT patches are used as energy converter, and the vibration control efficiency is expressed by the vibration reduction rate per area of the PZT patches. Emphasis is laid on the effect of the generalized electromechanical coupling coefficient K ₃₁ on the vibration control efficiency. Four PZT patches with different sizes are bonded on the geometrical central area of four similar clamped aluminum plates, respectively, and vibration control experiments are conducted for these plates using the R-L shunt circuit. The results indicate that the bigger the coupling coefficient K ₃₁, the larger the rate of vibration reduction, and hence, the higher the vibration control efficiency. It also shows that the vibration responses of the first mode of the plates bonded with different PZT patches can be reduced by about 30.5%, 48.58%, 85.47%, and 89.91%, respectively. It comes to a conclusion that the vibration control efficiency of the piezoelectric shunt damping system decreases with the increase of the area of the PZT patch, whereas the vibration reduction of the plate increases with the area of the PZT patch. Therefore, it is necessary to make topology optimization for the PZT patch in the vibration control utilizing the piezoelectric shunt damping technique.     

Modeling and analysis of curved beams with debonded piezoelectric sensor/actuator patches

In this paper, a mathematical model for thin-walled curved beams with partially debonded piezoelectric actuator/sensor patches is presented for investigating the effect of debonding of the actuator/sensor on their open- and closed-loop behaviors. The actuator equations and the sensor equations of the curved beam in perfectly bonded and debonded regions are derived. In the perfect bonding region, the adhesive layer is modeled to carry constant peel and shear stresses; while in the debonding area, it is assumed that there is no peel and shear stress transfer between the host beam and the piezoelectric layer. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the bonded and debonded regions. Based on the model and the sensing equation of the sensor, a closed-loop vibration control for the curved beams is performed. To obtain the frequency response from the presented model, a solution scheme for solving the complex governing equations is given. Using this model and the solution scheme, the effects of the debonding of actuator and sensor patches on open- and closed-loop control are investigated through an example. The results show that edge debonding of the piezoelectric patch has a significant side effect on the closed-loop control of the curved beams.     

Analysis of nonlinear vibration response of a functionally graded truncated conical shell with piezoelectric layers

The nonlinear vibration response of a functionally graded materials (FGMs) truncated conical shell with piezoelectric layers is analyzed. The vibration amplitude is suppressed by the positive and inverse piezoelectric effects. And the bifurcation phenomenon is described to reveal the motion state of the conical shell. Firstly, a truncated conical shell composed of three layers is described. And the effective material properties of the FG layer are defined by the Voigt model and the power law distribution. Next, the electric potentials of piezoelectric layers are defined as cosine distribution along the thickness direction. Meanwhile, the constant gain negative velocity feedback algorithm is used to suppress the vibration amplitude by the electric potential produced by the sensor layer. Thereafter, considering the first-order shear deformation theory and the von Karman nonlinearity, the relationship between the strain and displacement is defined. And the corresponding energy of the conical shell is calculated. After that, the motion equations of the conical shell are derived based on the Hamilton principle. Again, the nonlinear single degree of freedom equation is derived by the Galerkin method and the static condensation method. In the end, the nonlinear vibration response of FGMs truncated conical shell with piezoelectric layers under the external excitation is analyzed via using the harmonic balance method and the Runge-Kutta method. The effects of various parameters, such as ceramic volume fraction exponent, external excitation’s amplitude, control gain and geometric parameters on the nonlinear vibration response of the system are evaluated by case studies. Results indicate that the control gain plays an important role on the suppression of the vibration amplitude. The ceramic volume fraction exponents are not sensitive to the nonlinear vibration response compared with other parameters. The bifurcation behavior is observed under different parameters. The FGMs truncated conical shell with piezoelectric layers has three types of motion state, such as periodic motion, multi-periodic motion, and chaos motion.

     

VIBRATION CONTROL OF A ROTATING DISK

The transverse vibration of a rotating disk has been receiving increasing attention because of its prevailing role as a basic element in rotating machinery applications. To suppress the vibration without suffering from spillover, a feedback controller which can eliminate an infinite number of vibration modes is absolutely needed. The control approach is developed based on the root locus of an infinite number of poles and zeros using one set of discrete sensor and actuator. The root-locus approach can yield the controller of simple scheme. For the colocated sensor and actuator, a feedback controller which contributes the phase angle between 0 and 180° can stabilise all vibration modes. By properly positioning the non-colocated sensor and actuator, a feedback controller that possesses the phase angle between 0 and 180° and a satisfactory amplitude attenuation can lead to the elimination of all the vibration modes except the much higher frequency modes. The sustained oscillation of the much higher frequency modes are usually insignificant, and will eventually die out due to internal structural damping. The proposed controllers have been successfully implemented for simulation.     

Vibration control efficiency of piezoelectric shunt damping system

The piezoelectric shunt damping technique based on the direct piezoelectric effect has been known as a simple, low-lost, lightweight, and easy to implement method for passive damping control of structural vibration. In this technique, a piezoelectric material is used to transform mechanical energy to electrical energy. When applying the piezoelectric shunt damping technique to passively control structural vibration, the piezoelectric materials must be bonded on or embedded in host structure where large strain is induced during vibration, thus to ensure vibrational mechanical energy to be transformed into electrical energy as much as possible. In this paper, the concept of vibration control efficiency of a piezoelectric shunt damping system is proposed and studied theoretically and experimentally. In the study, PZT patches are used as energy converter, and the vibration control efficiency is expressed by the vibration reduction rate per area of the PZT patches. Emphasis is laid on the effect of the generalized electromechanical coupling coefficient K₃₁ on the vibration control efficiency. Four PZT patches with different sizes are bonded on the geometrical central area of four similar clamped aluminum plates, respectively, and vibration control experiments are conducted for these plates using the R-L shunt circuit. The results indicate that the bigger the coupling coefficient K₃₁, the larger the rate of vibration reduction, and hence, the higher the vibration control efficiency. It also shows that the vibration responses of the first mode of the plates bonded with different PZT patches can be reduced by about 30.5%，48.58%，85.47%, and 89.91%, respectively. It comes to a conclusion that the vibration control efficiency of the piezoelectric shunt damping system decreases with the increase of the area of the PZT patch, whereas the vibration reduction of the plate increases with the area of the PZT patch. Therefore, it is necessary to make topology optimization for the PZT patch in the vibration control utilizing the piezoelectric shunt damping technique.     

PIEZOELECTRIC ACTUATOR AND SENSOR MODELS FOR AN INFLATED TOROIDAL SHELL

Due to their low mass and conformability, actuators and sensors made of active materials can be used in the vibration control of inflatable structures. In this study, we model piezoelectric patches attached to an inflated toroidal shell as actuators and sensors. Using Sanders' shell theory in the presence of initial stresses, the generalised forces due to the piezoelectric actuators are derived for the inflated toroidal shell assuming quasi-static conditions. The derivations are given for both unimorph and bimorph configurations. Effects of the mass and stiffness of the patches are incorporated in the equations of motion. Thereafter, a sensor equation is presented. Within linear shell theory, the methodology is quite general in nature and can be applied easily to other types of shells and membranes. To demonstrate this, we specialise the actuator and sensor equations for a circular cylinder. Using the formulations for the inflated toroidal shell, the modal forces and modal sensing constants are calculated for different sizes and locations of the piezoelectric patches. Along with this, controllability and observability indices are calculated to quantify the performance of the actuators and sensors. A study of the stiffness and mass effects of the piezoelectric patches is performed using frequency response function.     

VIBRATION CONTROL OF FLUID- FILLED PRISMATIC SHELL WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

Active constrained layer damping （ACLD） combines the simplicity and reliability of passive damping with the light weight and high efficiency of active actuators to obtain high damping over a wide frequency band. A fluid-filled prismatic shell is set up to investigate the validity and efficiency of ACLD treatments in the case of fluid-structure interaction. By using state subspace identification method, modal parameters of the ACLD system are identified and a state space model is established subsequently for the design of active control laws. Experiments are conducted to the fluid-filled prismatic shell subjected to random and impulse excitation, respectively, For comparison, the shell model without fluid interaction is experimented as well. Experimental results have shown that the ACLD treatments can suppress vibration of the fluid-free and fluid-filled prismatic shell effectively. Under the same control gain, vibration attenuation is almost the same in both cases.     

Note: Self-sensing based on charge control improves the performance of active damping using piezoelements

A piezoelectric element can be used separately as a sensor or an actuator. A self-sensing strategy based on a charge driver can utilize a piezoelectric element as a sensor while actuating. The strategy was proven via experiments on a cantilever vibrator using a piezoelectric plate with both sensing and actuating functions. The amplitude of the vibration was actively damped by a factor exceeding 90%. The method can be used in numerous fields, including scanning probe microscopy, vibration suppression, and monitoring the health of structures.     

柔性自适应桁架结构的振动控制方法实验研究

为提高结构对外部环境的抗干扰能力,构造了空间柔性自适应桁架结构,并对其主动控制进行了研究。通过加速度传感器测量位移的实验,建立了由dSPACE数据采集与处理系统、压电传感器、压电作动器、桁架结构和微机实时测控组成的实时计算机控制系统。基于自适应桁架结构的有限元理论,采用改进的二次积分力反馈控制方法,研究了空间柔性自适应桁架结构的振动主动控制问题。通过正弦激励进行了实时控制实验,给出了控制前后节点18x方向的位移振幅抑制变化情况及功率谱响应曲线。实验研究结果表明,该控制方案对空间柔性结构的低频大幅振动有很好的控制效果。     

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.     

高速转子系统振动控制技术评述

高速转子系统在正常工作过程中必须通过临界转速,此时由于不平衡质量的作用,转子系统会产生共振,导致强烈的振动。降低系统支承刚度以降低临界转速、增大支承阻尼,以减小振幅,这些措施可以抑制系统通过临界转速时的振动幅值和外传力。在振动被动控制技术中,常用弹性支承和挤压油膜阻尼器、金属橡胶减振器、高聚物复合材料减振结构等,降低系统支承刚度,增大支承阻尼,以减小系统振动;在主动控制技术中,通过主动控制挤压油膜阻尼器的参数,改变支承的刚度和阻尼的大小,以控制系统的振动;以及采用形状记忆合金调节器、电磁阻尼器、压电调器等装置,来主动控制系统的振动。目前控制技术仍存在装置结构复杂、性能不稳定等问题,采用粘弹阻尼复合材料与滚动轴承钢外圈复合结构的一体化滚动轴承,足一种有发展前途的研究方向。     

Vibration control of smart hull structure with optimally placed piezoelectric composite actuators

Active vibration control to suppress structural vibration of the smart hull structure was investigated based on optimized actuator configurations. Advanced anisotropic piezoelectric composite actuator, Macro-Fiber Composite (MFC), was used for the vibration control. Governing equations of motion of the smart hull structure including MFC actuators were obtained using the Donnell-Mushtari shell theory and Lagrange's equation. The Rayleigh-Ritz method was used to obtain the dynamic characteristics of the smart hull structure. Experimental modal tests were conducted to verify the proposed mathematical model. In order to achieve high control performance, optimal locations and directions of the MFC actuators were determined by genetic algorithm. Optimal control algorithm was then synthesized to suppress structural vibration of the proposed smart hull structure and experimentally implemented to the system. Active vibration control performances were evaluated under various modes excitations. Vibration tests revealed that optimal configurations of MFC actuators improved the control performance of the smart hull structure in case of the limited number of actuators available.     

Passive vibration damping enhancement of piezoelectric shunt damping system using optimization approach

Piezoelectric materials can be used for structural damping because of their ability to efficiently transform mechanical energy to electrical energy and vice versa. The electrical energy may be dissipated through a connected load resistance. In this paper, a new optimization technique for the optimal piezoelectric shunt damping system is investigated in order to search for the optimal shunt electrical components of the shunt damping circuit connected to the piezoelectric patch on a vibrating structure for the structural vibration suppression of several modes. The vibration suppression optimization technique is based on the idea of using the piezoelectric shunt damping system, the integrated p-version finite element method (p-version FEM), and the particle swarm optimization algorithm (PSOA). The optimal shunt electrical components for the piezoelectric shunt damping system are then determined by wholly minimizing the objective function, which is defined as the sum of the average vibration velocity over a frequency range of interest. Moreover, the optimization technique is performed by also taking into account the inherent mechanical damping of the controlled structure with the piezoelectric patch. To numerically evaluate the multiple-mode damping capability by the optimal shunting damper, an integrated p-version FEM for the beam with the shunt damping system is modeled and developed by MATLAB. Finally, the structural damping performance of the optimal shunt damping system is demonstrated numerically and experimentally with respect to the beam. The simulated result shows a good agreement with that of the experimental result. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Jin-Young Jeon received his Ph.D. degree in Mechanical and Aerospace Engineering from Tokyo Institute of Technology in 2005. Dr. Jeon is currently a senior engineer at Digital Printing Division, Digital Media & Communications Business at Samsung Electronics Co., Ltd., Korea. His research interests are the areas of structural-acoustic optimization, sound quality, motion quality, and vibration control.     

Active vibration control of clamped beams using positive position feedback controllers with moment pair

This paper investigates the active vibration control of clamp beams using positive position feedback (PPF) controllers with a sensor/moment pair actuator. The sensor/moment pair actuator which is the non-collocated configuration leads to instability of the control system when using the direct velocity feedback (DVFB) control. To alleviate the instability problem, a PPF controller is considered in this paper. A parametric study of the control system with PPF controller is first conducted to characterize the effects of the design parameters (gain and damping ratio in this paper) on the stability and performance. The gain of the controller is found to affect only the relative stability. Increasing the damping ratio of the controller slightly improves the stability condition while the performance gets worse. In addition, the higher mode tuned PPF controller affects the system response at the lower modes significantly. Based on the characteristics of PPF controllers, a multi-mode controllable SISO PPF controller is then considered and tuned to different modes (in this case, three lowest modes) numerically and experimentally. The multi-mode PPF controller can be achieved to have a high gain margin. Moreover, it reduces the vibration of the beam significantly. The vibration levels at the tuned modes are reduced by about 11 dB.     

超声切割用压电换能器理论设计及有限元仿真

基于波动方程和频率方程,建立了电镀金刚石线锯超声切割用压电换能器的解析模型,得到了压电换能器各组成部分的结构尺寸。借助有限元分析软件ANSYS对理论设计的压电换能器进行了动力学分析和优化设计,得到了压电换能器的优化模型。分析结果表明,有限元法对压电换能器的设计和分析具有很好的指导作用。这种换能器具有良好的性能,对下一步的应用研究有重要意义。