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.     

压电分流阻尼控制悬臂梁振动的实验研究

采用压电分流阻尼原理,对根部粘贴压电陶瓷片的柔性悬臂梁振动控制进行了实验研究。实验中设计了一个由电容、电阻和运算放大器组成的等效电感电路,解决了压电分流电路设计中的超大电感器问题。根据测试得到的带压电分流电路悬臂梁的闭路和开路自然频率,确定出了压电分流电路的最优参数,对悬臂梁的瞬态振动和单频简谐激励下的稳态振动控制实验表明了压电分流阻尼被动控制结构振动的有效性。     

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.     

压电分流阻尼控制悬臂梁振动的参数优化分析

采用阻抗分析技术,根据压电材料的机电耦合特性和RLC电路的电学阻抗特性,详细推导了RLC串联压电分流阻尼系统的机械阻抗特性,研究了作单模态振动的悬臂梁在粘贴压电片后形成的压电悬臂梁系统的位移传递函数特性。借助于调谐质量阻尼减振理论,进行了压电分流阻尼系统的参数优化分析,并通过算例验证了参数优化前后压电分流阻尼系统对悬臂梁振动的被动控制效果。     

采用压电开关分流电路技术的半主动振动控制

利用压电材料的正压电效应,设计出一种新型的状态开关型压电分流电路.由压电换能器将结构振动变形的应变能转化为电介能,当压电换能器极化表面的电荷积聚达到最大值时,闭合分流电路中的状态开关,分流电路短路,压电换能器上下表面的正负电荷中和抵消,以焦耳热的形式耗散掉电介能,达到抑制结构振动的目的.将这种振动控制技术应用于柔性悬臂梁的振动抑制,研究状态开关闭合持续时间对抑振效果的影响.实验结果表明,开关的闭合持续时间约为结构振动周期的1/10时,抑振效果最佳,悬臂梁第一阶稳态响应幅值降低量约为55%.     

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.     

Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator

Shell type components and structures are very common in many mechanical and structural systems. Modeling and analysis of adaptive piezothermoelastic shell laminates represent a high level of sophistication and complexity. In this paper a finite element model is developed for the active control of thermally induced vibration of laminated composite shells with piezoelectric sensors and actuators. The present model takes into account the mass, stiffness and thermal expansion of the piezoelectric patches. A C_o continuous nine-node degenerated shell element is implemented to model the structure. The piezoelectric sensing layer senses the structural vibration and a suitable voltage applied in the piezoelectric actuator layer suppresses the oscillation. Actuator and sensor are coupled together with a control algorithm so as to actively control the dynamic response of the structure in a close loop. Numerical results are generated for a cylindrical shell and it is observed that thermally induced vibration of a laminated cylindrical shell can be suppressed through the application of piezoelectric sensor and actuator. Effects of variation in control gain and piezoelectric layer area coverage (PAC) have been studied. Higher control gain is more effective in damping out the vibration. Although the damping is enhanced by increase in PAC, increase beyond a certain level may not be useful in view of smaller efficacy and increased weight.     

Passive suppression of nonlinear panel flutter using piezoelectric materials with resonant circuit

In this study, a passive suppression scheme for nonlinear flutter problem of composite panel, which is believed to be more reliable than the active control methods in practical operations, is proposed. This scheme utilizes a piezoelectric inductor-resistor series shunt circuit. The finite element equations of motion for an electromechanically coupled system is derived by applying the Hamilton’s principle. The aerodynamic theory adopted for the present study is based on the quasi-steady piston theory, and von-Karrnan nonlinear strain-displacement relation is also applied. The passive suppression results for nonlinear panel flutter are obtained in the time domain using the Newmark-β method. To achieve the best damping effect, optimal share and location of the piezoceramic (PZT) patches are determined by using genetic algorithms. The effects of passive suppression are investigated by employing in turn one shunt circuit and two independent shunt circuits. Feasibility studies show that two independent inductor-resistor shunt circuits suppresses flutter more effectively than a single shunt circuit. The results clearly demonstrate that the passive damping scheme that uses piezoelectric shunt circuit can effectively attenuate the flutter.     

Optimal design of smart panel using admittance analysis

Optimal configuration of piezoelectric shunt structures is obtained by analyzing admittance of the system. The dissipated energy in the shunt circuit is a function of admittance. Therefore, admittance was selected as the cost function in the process of optimization. Taguchi method was used to determine the optimal configuration of piezoceramic patch bonded on the host structure. Full three dimensional finite element models were analyzed to simulate vibration modes of smart panel and to obtain the admittances of the system. Numerical admittance was validated by experiment. After optimizing process using admittance, the optimal configuration of piezoceramic patch was obtained. It is observed that the performance of smart panel can be predicted by analyzing admittance of piezoelectric structure and admittance can be used as a design index of smart panel.     

基于滚压的悬架振动俘能装置设计与特性分析

振动能量俘获装置能够回收路面不平引起的汽车悬架振动能量,为主动悬架提供动力,可有效降低主动悬架的能耗和使用成本。基于滚压原理,提出一种用于电动汽车自供能智能悬架的滚动压迫振动能量俘获装置概念设计。该装置通过滚珠滚压凸起金属片的方式将上下的随机振动转换为幅值相对稳定的单向压力,使其中的压电材料受压变形,从而输出电压。笔者建立了滚动压迫俘获振动能量的理论模型,并对其在随机路况下的振动俘能效果进行了仿真分析。结果显示,该俘能装置占用空间小,在悬架的各种运动状态下,都能俘获振动能量,具有较高的俘能效率,能满足悬架实际应用。     

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.     

Effect of boundary (support) conditions on piezoelectric damping in the case of SSDI vibration control technique

Piezoelectric transducers in conjunction with appropriate electric networks can be used as a mechanical energy dissipation device. If a piezoelectric element is attached to a structure, it is strained as the structure deforms and converts a portion of the vibration energy into electrical energy that can be dissipated through a shunt network in the form of heating. These vibration control devices experienced a great development in recent years, due to their performances and advantages compared with active techniques. One of them is the synchronized switch damping (SSD) and derived techniques, which were developed in the field of piezoelectric damping, and which lead to a very good trade-off between the simplicity, the required power supply and their performances. This technique consists in a non-linear processing of the piezoelectric voltage, which induces an increase in electromechanical energy conversion. The control law consists in triggering the inverting switch on each extremum of voltage (or displacement). In this study, the proposed method for the switching sequence is based on the statistical evaluation of structural deflection. The purpose of this paper is to present an experimental study of the synchronized switch damping on inductance (SSDI) control technique sensitivity to the system boundary conditions. It is observed that the fundamental natural frequency greatly depends on these conditions. The effect of these constraints is distributed all over the system and significantly affects the results.     

基于压电元件的悬臂梁半主动振动控制研究

为了探讨非线性同步开关阻尼技术(synchronized switch damping,简称SSD)的半主动振动控制系统中开关切换效率对控制效果的影响,详细推导了基于开关切换效率的SSDI(synchronized switch damping on inductor)及SSDV(synchronized switch damping on voltage)的振动阻尼表达式,并搭建了悬臂复合梁振动半主动试验平台,对理论分析结果进行了试验验证.试验结果表明,开关切换的延时越小,控制效果越佳.     

Performance analysis of piezoelectric bimorph generator

In this paper, the theoretical model and simulation of the performance of a piezoelectric (PZT) bimorph generator is introduced. The generator consists of two piezoelectric plates bonded on a substrate metal plate. For an effective electromechanical coupling coefficient (EECC) and the generated energy, the analytical formulae are established with the thickness ratio and the Young’s modulus ratio as variables. After giving correlative material parameters, the EECC and generated energy can be computed. The results show that there is a optimal thickness ratio for a piezoelectric bimorph generator to achieve the maximum EECC and electrical energy. The EECC and generated energy decrease with an increase of the Young’s modulus ratio. In addition, the influence of mechanical source on electrical energy generation and power output is also considered.     

Performance analysis of piezoelectric bimorph generator

In this paper, the theoretical model and simulation of the performance of a piezoelectric (PZT) bimorph generator is introduced. The generator consists of two piezoelectric plates bonded on a substrate metal plate. For an effective electromechanical coupling coefficient (EECC) and the generated energy, the analytical formulae are established with the thickness ratio and the Young’s modulus ratio as variables. After giving correlative material parameters, the EECC and generated energy can be computed. The results show that there is a optimal thickness ratio for a piezoelectric bimorph generator to achieve the maximum EECC and electrical energy. The EECC and generated energy decrease with an increase of the Young’s modulus ratio. In addition, the influence of mechanical source on electrical energy generation and power output is also considered.     

Development and application of an ultra-precision lathe

This paper deals with the detailed development of an ultraprecision lathe for the purpose of machining magnetic disks. The rotational and feed accuracy and stiffness of the air bearing and the air slide were tested, respectively. A microcutting device using a piezoelectric material was also developed in order to maintain a uniform and precise depth of cut. Experiments machining a magnetic disk were carried out.Nomenclature A [m²] Area of piezoelectric actuator - C _o [mF] Capacitance of PZT - d ₃₃ [m V^–1] Piezoelectric constant - K _f [N V^–1] Equivalent force constant - K _m [N m^–1] Coefficient of force feedback - k _h [N m^–1] Stiffness of hinge - l [m] Length of PZT - M [kg] Mass of PZT system - r [mm] Radius of notch - U [m] Displacement of piezoelectric - ₃ [F m^–1] Dielectric constant of PZT - b [mm] Width of hinge - D _e [N s^–1] Equivalent damping coefficient - F _l [N] External load - K _e [N m^–1] Equivalent stiffness of PZT - k [m² N^–1] Elastic compliance of PZT - L [mm] Distance between hinge holes - M _e [kg] Equivalent mass of PZT - R _o [W] Output impedance of amp. - t [mm] Thickness between hinge holes - V _i [V] Input voltage - [g cm^–3] Density of PZT     

压电振动电阻尼与能量转换特性研究

根据压电构造方程和振动原理,建立压电振动能量收集的耦合场动力学模型。详细推导电阻尼与外接电阻和机电耦合系数之间的数学关系,并揭示外接电阻对系统固有弹性的作用效果。通过数值模拟研究电阻尼特性对谐振频率、振动幅值和功率的影响关系,并从能量转换效率的角度分析优化电阻与最大输出功率的关系。分别对多种外接电阻条件下压电梁的输出电压及功率进行实验测试,实验结果表明,电阻尼导致压电梁的谐振频率发生偏移,其大小与外接电阻值成正比,而且在外接优化电阻时输出功率最大。     

Design and Characterization of a Low-Cost Piezoelectric Vibration Energy Harvester with Bulk PZT Film

To improve the efficiency of MEMS piezoelectric vibration energy harvesters(PVEHs), the bulk lead zirconate titanate(PZT) has been used to substitute the thin f...     

通过压电分流阻尼技术抑制结构振动的实验研究

以一四边固定矩形板为例,通过实验方法对三种不同的压电分流阻尼技术（RL串联压电分流电路、RL并联压电分流电路以及RL-C并联压电分流电路）的振动控制效果进行分析和比较。实验结果表明,当压电分流电路的参数调节到最优值时,能够有效降低结构振动;RL串联压电分流电路和RL并联压电分流电路的控制效果基本相等;RL—C并联压电分流电路能够降低分流电路中的最优电感值,但是控制效果也随之变差。实验结果还表明压电分流电路对电感值相当敏感,如果电感值偏离最优值,有可能会使得控制效果大幅下降。     

Semi-passive piezoelectric structural damping based on a pulse-width modulation switching circuit

Studies in the past focused on the implementation of semi-passive damping techniques that could significantly reduce structural vibration. Recently, the performances of these damping techniques have been enhanced by artificially increasing the voltage amplitude delivered by the piezoelectric patches with an external voltage source. To maintain the stability of this damping method, an adaptive voltage source must be used. To satisfy this requirement, this study proposes an enhanced semi-passive damping technique based on pulse-width modulation. The proposed method allows the waveform of the piezoelectric voltage to adapt to the vibration velocity. Thus, this method can maintain its stability with a constant voltage source and simultaneously exhibit superior performance. This study consists of a theoretical part and an experimental proof-of-concept demonstration of the proposed damping technique.