Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system’s vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.     

Vibration suppression of rotating beams using time-varying internal tensile force

A new strategy for vibration suppression of a rotating beam using a time-increasing internal tensile force is proposed in this paper. Nonlinear coupled longitudinal and bending equations of motion are derived in non-dimensional form using the Hamilton principle. The first-order analytical solution of the equations of motion is obtained using the Galerkin technique combined with the multiple scales method (MSM). Numerical simulations are then performed for various increasing rates of the internal tensile force and performance of the vibration suppression strategy is studied. A very close agreement between the simulation results obtained by the numerical integration and the first-order analytical solution is achieved. Forced vibrations of the system for input excitations of either a sinusoidal or a random function with white noise time history are considered. The simulation results and dynamic performance of the suppressed system for an externally excited rotating beam show an interesting phenomenon of the form of remarkable effectiveness of the proposed vibration reduction strategy.     

Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm

In the present article, an improved genetic algorithm (GA) based optimal vibration control of smart fiber reinforced polymer (FRP) composite shell structures has been presented. Layered shell finite elements have been formulated and the formulation has been validated for coupled electromechanical analysis of curved smart FRP composite structures having piezoelectric sensors and actuators patches. An integer-coded GA-based open-loop procedure has been used for optimal placement of actuators for maximizing controllability index and a real-coded GA-based linear quadratic regulator (LQR) control scheme has been implemented for optimal control of the smart shell structures in order to maximize the closed-loop damping ratio while keeping actuators voltages within the limit of breakdown voltage. Results obtained from the present work show that this combined GA-based optimal actuators placement and GA-based LQR control scheme is far superior to conventional active vibration control using LQR schemes and simple placement of actuators reported in literatures. Results also show that the present improved GA-based combined optimal placement and LQR control scheme not only leads to increased closed-loop damping ratio but also shows a drastic reduction in input/actuation voltage compared to the already published results.     

Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm

This paper deals with the optimization of piezoelectric actuators and sensors locations for active vibration control. Two modified optimization criteria are used, ensuring good observability or controllability of the structure, and considering residual modes to limit the spillover effect. Two optimization variables are considered for each piezoelectric device: the location of its center and its orientation. Genetic algorithms are used to find the optimal configurations. Several simulations are presented for a simply supported plate.     

Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm

In this paper, the superior mid-frequency vibration isolation of a geometrically optimized lightweight structure is demonstrated. The initial structure under test here was a 4.5 m long satellite boom consisting of 10 identical bays with equilateral triangular cross-sections. An unusual geometric variant of this, with inherent isolation characteristics, has been designed by the use of genetic algorithm (GA) methods. In order to obtain the best design, the joints in the boom were allowed to move around by 20% of the length of each bay (i.e., ±9 cm in all three translational directions). This work is based on results from a Fortran code (which was derived from receptance analysis) that are fully validated against detailed finite element (FE) models of the structure. The experimental forced response of the regular boom structure has been measured and compared with predicted curves. Finally, having obtained the geometrically optimized boom structure, its experimental response is compared with the theoretical results predicted by the receptance method. It is shown that the average of 30 dB isolation in the vibration energy transfer between the ends of the network of beams, over a 100 Hz bandwidth predicted in the design process, is achieved experimentally in an essentially undamped structure.     

Frequency selective surface structure optimized by genetic algorithm

Frequency selective surface (FSS) is a two-dimensional periodic structure which has prominent characteristics of bandpass or bandblock when interacting with electromagnetic waves. In this paper, the thickness, the dielectric constant, the element graph and the arrangement periodicity of an FSS medium are investigated by Genetic Algorithm (GA) when an electromagnetic wave is incident on the FSS at a wide angle, and an optimized FSS structure and transmission characteristics are obtained. The results show that the optimized structure has better stability in relation to incident angle of electromagnetic wave and preserves the stability of centre frequency even at an incident angle as large as 80°, thereby laying the foundation for the application of FSS to curved surfaces at wide angles.     

用多目标遗传算法获取压电材料参数

多目标遗传算法是在遗传算法的基础上,利用在多个给定区域内的遗传优化性能,反演出这些特定区域内的优化特性。本文基于瑞利波的有效介电常数理论,将压电材料的弹性常数CE、压电常数e、介电常数εs看作特定区域的待优化参数,利用压电材料(本文用石英、铌酸锂晶体为例)的同一切割面不同传播方向的表面波速度,运用多目标遗传算法,通过概率分区优化,逐次逼近真值,成功地同时反演出了它们的弹性常数、压电常数与介电常数。证明了该方法同样适用于获取新材料的参数。     

Optimization and implementation of piezoelectric radiators using the genetic algorithm

Very thin and small (45 mm x 35 mm x 0.35 mm) piezoelectric radiators have been developed in this research. The system is modeled by using the energy method in conjunction with the assumed-modes method. Electrical system, mechanical system, and acoustic loading have all been accounted for during the modeling stage. On the basis of the simulation model, the genetic algorithm (GA) is employed to optimize the overall configurations for a low resonance frequency and a large gain. The resulting designs are then implemented and evaluated experimentally. Performance indices for the experimental evaluation include the frequency response, the directional response, the sensitivity, and the efficiency. It is found in the experimental results that the piezoelectric radiators are able to produce comparable acoustical output with significantly less electrical input than the voice-coil panel speakers.     

Disturbance rejection control for vibration suppression of piezoelectric laminated thin-walled structures

Thin-walled piezoelectric integrated smart structures are easily excited to vibrate by unknown disturbances. In order to design and simulate a control strategy, firstly, an electro-mechanically coupled dynamic finite element (FE) model of smart structures is developed based on first-order shear deformation (FOSD) hypothesis. Linear piezoelectric constitutive equations and the assumption of constant electric field through the thickness are considered. Based on the dynamic FE model, a disturbance rejection (DR) control with proportional-integral (PI) observer using step functions as the fictitious model of disturbances is developed for vibration suppression of smart structures. In order to achieve a better dynamic behavior of the fictitious model of disturbances, the PI observer is extended to generalized proportional-integral (GPI) observer, in which sine or polynomial functions can be used to represent disturbances resulting in better dynamics. Therefore the disturbances can be estimated either by PI or GPI observer, and then the estimated signals are fed back to the controller. The DR control is validated by various kinds of unknown disturbances, and compared with linear-quadratic regulator (LQR) control. The results illustrate that the vibrations are better suppressed by the proposed DR control.     

Vibration of piezoelectric elements surrounded by fluid media

In this paper we analyse vibrational characteristics of piezoceramic shells surrounded by acoustic media. Main results are presented for radially polarized piezoceramic PZT5 elements of hollow cylindrical shapes. The coupling in the radial direction between the solid and the acoustic media is accounted for indirectly, via impedance boundary conditions. The model based on such impedance boundary condition approximations offers a robust simplified alternative to a full scale fluid-solid interaction modelling. By using this model, we analyse numerically the influence of the boundary conditions imposed in the axial direction for long, medium, and short (disk-like) piezoceramic elements.     

抑制光束抖动的压电倾斜镜高带宽控制

提出了一种抑制光束平台抖动和压电倾斜镜机械谐振的方法从而提高系统校正带宽和跟瞄精度.通过分析双二阶滤波器参数对频率特性的影响,提出了一种双二阶滤波器的设计方法,并把这种设计方法结合比例积分(PI)控制算法用于抑制光束平台抖动和压电倾斜镜机械谐振.最后,对经典PI控制算法和增加了双二阶滤波器的PI控制算法进行了实验比较,在相同的条件下,增加了双二阶滤波器的PI控制带宽比经典PI控制带宽提高了近1倍,对平台抖动控制精度提高了5倍以上.实验结果表明:增加了双二阶滤波器的PI控制算法对抑制光束平台抖动和压电倾斜镜机械谐振简单有效,可以提高系统校正带宽和跟瞄精度.     

双屏频率选择表面结构的遗传算法优化

双屏频率选择表面能够更好地实现平顶效应和快速下降的边缘,是一种实现雷达舱对探测带外雷达波隐身的有效手段.本文针对双屏频率选择表面(FSS)在电磁波不同角度入射下的宽带通应用,采用遗传算法对FSS介质厚度、介电常数、单元图形、排列周期进行了整体优化,给出优化后的FSS结构和传输特性曲线;同时采用镀膜和光刻技术制备出相应的实验件,在微波暗室进行了测试.结果表明,优化后的结构在保证2 GHz的工作带宽下,对电磁波的入射角度有良好的传输稳定性,这为实现双屏FSS在曲面大角度下的应用奠定了基础. 关键词： 频率选择表面 遗传算法 优化     

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.     

Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm

We demonstrate the enhancement of high-harmonic soft-X-ray generation by adaptive wave-front control of a 745-nm Ti:sapphire laser by use of a 59-channel membrane deformable mirror, combined with a genetic algorithm, for the first time to our knowledge. The harmonics ranging from 17 nm to 28 nm were enhanced by factors up to 13. The numerical calculations illustrate that the enhancements of the plateau harmonics are due to macroscopic phase-matching effect, whereas those of the cutoff harmonics are due to the increase in focal intensity. PACS 42.65.Ky     

Dynamic modeling and experimental verification of a piezoelectric part feeder in a structure with parallel bimorph beams

The study is aimed to perform dynamic modeling of a part feeder powered by piezoelectric actuation. This part feeder consists mainly of a horizontal platform vibrated by a pair of parallel piezoelectric bimorph beams. Owing to intermittent impacts with the platform, the transported part on the platform is able to march forward from one end to another. Dynamic modeling of the feeder is accomplished by essentially using the Rayleigh-Ritz decomposition method. The process of modeling first incorporates material properties and constitutive equations of the piezoelectric materials, and then captures the complex dynamics of the parallel-beam piezo-feeder by three low-order assumed-modes in the transverse direction of the vibrating beams. Applying Lagrange’s equations on the kinetic and strain energies formulated in terms of generalized coordinates associated with the first three modes, the system dynamics is then represented by three coupled discrete equations of motion. Based on these equations, motions of the platform can be obtained. With platform motion in hand, the intermittent impacts between the parts and the platform are modeled, rendering the marching speed of the part. Numerical simulations are conducted along with the experiments. The closeness found between the theoretical predicted transporting speed of the part and the experimental counterparts verify the effectiveness of the models established.     

Vibration based damage detection of a beam-type structure using noise suppression method

In this paper, a method is presented for the localisation of structural damage. The validation of the method is based on simulated data and experimental measurements. Due to measurement errors near resonances, the mode shapes extracted from the frequency response functions (FRFs) and hence the damage indices (DI) can contain many false peaks. The method presented in this paper uses this set of damage indices from each mode generated by the Gapped-Smoothing Method (GSM), and suppresses the noise by allowing only those peaks which show the location of the damage. This paper details the theory of the noise suppression method and the experimental results for a steel beam, damaged with two narrow slots at different locations. A noise addition process was applied to the simulated data in order to more realistically represent experimental measurements. The steel beam was modelled in ANSYS and harmonic analysis was used to obtain FRFs at different locations of the beam. The results were checked for different slot depths by adding 5–10% noise in the simulated results.     

LCR分流电路下压电声子晶体智能材料的带隙

将带有LCR分流电路的压电陶瓷片对贴在铝和环氧树脂组成的声子晶体结构中.使智能材料的机械振动与压电陶瓷的压电效应耦合起来,推导出机械振动在压电陶瓷片上的等效附加应力;使LCR分流电路中的电磁振荡效应和声子晶体的能带特性有机结合,计算了在分流电路作用下智能材料扭转和弯曲振动的带隙特性,研究了电阻、电感、电容元件的改变对压电声子晶体智能材料带隙的影响.研究结果表明:在合理尺寸下,随着分流电路中电阻值的增大,带隙的频率范围变宽,但衰减幅值有所降低;电感和电容值的增大都可以使带隙向低频移动,带隙的衰减幅值随着电感值的增大而升高,但随着电容值的增大而降低.从而给压电声子晶体智能材料减震降噪的控制提供了一种新思路.     

Vibration of a rotating shaft with randomly varying internal damping

A simple Jeffcott rotor is considered with both external and internal damping. Coefficient of internal damping is subject to temporal random variations which may occasionally bring the rotor into the domain of dynamic instability. The corresponding sporadic outbreaks in the rotor's vibrational response (whirl) are studied by applying the Krylov-Bogoliubov averaging method to the complex equation of motion and using parabolic approximation for the random coefficient of the internal damping. This results in an explicit analytical solution for the radius of whirl which may be used for predicting reliability of the rotor. Furthermore, a convenient procedure is described for interpreting measured on-line test data for the rotor. Namely, the mean value of the coefficient of internal damping as well as its standard deviation and mean frequency of temporal variations may be estimated directly from the trace of whirl radius which exhibits spontaneous random outbreaks in response.     

Vibration characteristics of a rotating flexible arm with ACLD treatment

In this paper, the vibration behavior and control of a clamped–free rotating flexible cantilever arm with fully covered active constrained layer damping (ACLD) treatment are investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress–strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton's principle in conjunction with finite element method (FEM) is used to derive the non-linear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezosensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms.     

基于遗传算法的光学膜系初始结构优化设计

膜系初始结构优化设计是膜系优化设计的关键。针对多膜料设计 ,提出了一种新的膜系初始结构优化设计算法 ,将膜系的初始设计视为组合优化问题 ,采用遗传算法 ,求得组合的最优解。给出了算法的原理 ,并给出了相应的设计实例。结果表明 ,本算法是一种简单、有效、通用性强的膜系初始化设计方法