Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh–Ritz modes using genetic algorithm

In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh–Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel–Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called “Saturated Negative Velocity Feedback Rule (SNVF)”. The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.     

Design of piezoelectric actuators using a multiphase level set method of piecewise constants

This paper presents a multiphase level set method of piecewise constants for shape and topology optimization of multi-material piezoelectric actuators with in-plane motion. First, an indicator function which takes level sets of piecewise constants is used to implicitly represent structural boundaries of the multiple phases in the design domain. Compared with standard level set methods using n scalar functions to represent 2ⁿ phases, each constant value in the present method denotes one material phase and 2ⁿ phases can be represented by 2ⁿ pre-defined constants. Thus, only one indicator function including different constant values is required to identify all structural boundaries between different material phases by making use of its discontinuities. In the context of designing smart actuators with in-plane motions, the optimization problem is defined mathematically as the minimization of a smooth energy functional under some specified constraints. Thus, the design optimization of the smart actuator is transferred into a numerical process by which the constant values of the indicator function are updated via a semi-implicit scheme with additive operator splitting (AOS) algorithm. In such a way, the different material phases are distributed simultaneously in the design domain until both the passive compliant host structure and embedded piezoelectric actuators are optimized. The compliant structure serves as a mechanical amplifier to enlarge the small strain stroke generated by piezoelectric actuators. The major advantage of the present method is to remove numerical difficulties associated with the solution of the Hamilton–Jacobi equations in most conventional level set methods, such as the CFL condition, the regularization procedure to retain a signed distance level set function and the non-differentiability related to the Heaviside and the Delta functions. Two widely studied examples are chosen to demonstrate the effectiveness of the present method.     

Piezoelectric transducer design via multiobjective optimization

The design of piezoelectric transducers is usually based on single-objective optimization only. In most practical applications of piezoelectric transducers, however, there exist multiple design objectives that often are contradictory to each other by their very nature. It is impossible to find a solution at which each objective function gets its optimal value simultaneously. Our design approach is to first find a set of Pareto-optimal solutions, which can be considered to be best compromises among multiple design objectives. Among these Pareto-optimal solutions, the designer can then select the one solution which he considers to be the best one. In this paper we investigate the optimal design of a Langevin transducer. The design problem is formulated mathematically as a constrained multiobjective optimization problem. The maximum vibration amplitude and the minimum electrical input power are considered as optimization objectives. Design variables involve continuous variables (dimensions of the transducer) and discrete variables (the number of piezoelectric rings and material types). In order to formulate the optimization problem, the behavior of piezoelectric transducers is modeled using the transfer matrix method based on analytical models. Multiobjective evolutionary algorithms are applied in the optimization process and a set of Pareto-optimal designs is calculated. The optimized results are analyzed and the preferred design is determined.     

Simulation of elastic wave propagation in cylindrical structures including excitation by piezoelectric transducers

The development and optimization of non-destructive testing procedures usually needs experimental data. As experiments are time-consuming and expensive to conduct, we would like to use numerical data instead. This is admissible, if the simulation describes the physical experiments accurately. A three-dimensional displacement-stress finite-difference model is presented for a piezoelectric transducer coupled to an anisotropic tube. The allocation of the displacement and stress components on a staggered grid leads to a stable scheme. A full piezoelectric model of the transducer is used, including transverse isotropy in the elastic, dielectric, and piezoelectric constants. Similar to an experiment, elastic waves are excited in the corresponding simulation by applying a voltage signal to the electrodes of the piezoelectric transducer. Predictions of the simulation model for a piezoelectric ring transducer coupled to a carbon-fibre-reinforced shell are compared to experimental results to test the validity of the numerical data.     

Placement and dimension optimization of shunted piezoelectric patches for vibration reduction

Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this paper. We present a strategy to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. This procedure is based on the maximization of the modal electro-mechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunt is tuned. To illustrate the method, a general analytical model of a laminated beam is proposed. Two particular configurations are investigated: (i) a beam with two collocated piezoelectric patches connected in series or in parallel to the shunt and (ii) a cantilever beam with one patch. After a modal expansion, original closed-form solutions of the MEMCF are exhibited, which enables to compute optimal values for the placement, length and thickness of the piezoelectric patches that maximize the MEMCF. A dimensionless model is used so that this study can be used to design any smart beam, whatever be its dimensions. More general results about the coupling mechanisms between the piezoelectric patches and the host structure are also raised. In particular, it is found that the patches thickness is an essential parameter and that several configurations are possible, depending on the considered vibration mode. Experiments are also proposed to validate the model.     

Nonlinear generation of airborne sound by waves of ultrasonic frequencies

The results of research into the design and optimization of laboratory sources of intense airborne ultrasound are reported. Two types of sources are studied: multielement arrays of small-size piezoelectric radiators and single membrane transducers of a capacitor type. The measured characteristics of the ultrasound fields and the audible sound fields generated in air due to the nonlinear interaction of high-frequency waves are presented. Applications of nonlinear acoustic problems in air are discussed.     

压电驱动器布置对光栅拼接误差的影响

分析了两种光栅拼接调整机构（三角形和L形）,利用有限元分析软件对这两种光栅调整机构进行了模态分析和优化分析设计。相同光栅尺寸下（以口径为450 mm420 mm60 mm光栅为例）,驱动器三角形分布的固有频率与L形分布的固有频率相差无几,一阶频率分别为58.816 Hz和58.864 Hz。对两种驱动器布置方式引入的误差进行了分析比较,计算结果表明:三角形调整机构的最大误差比L形的大,同时三角形分布控制算法较L形的复杂。在主动控制中三角形模型误差迭代次数多,不利于控制。因此L形的压电驱动器布置方式优于三角形。     

Design optimization of a Class VII Flextensional Transducer

Class VII Flextensional Transducers (FTs) have been proposed as a means of overcoming the limitation of very high prestress in Class IV FTs. These transducers are made from shells shaped like dog bone and hence are also known as dog-bone shell transducers. In this work, we report design optimization of a low frequency aluminum shell Class VII FT, resonating at 2.5 kHz, using piezoelectric drive. Two and three dimensional Finite Element Modeling (FEM), with the help of a commercially available package ATILA have been used for the design optimization. Dimensional details of the base model have been adapted from previous literature. Parametric analyses have been done with respect to various aspects like type of rubber, shell height, shell material, etc. in order to optimize the design. Experimental results obtained from an initial prototype are also presented. The results match fairly well with the predicted values.     

自适应压电式移相器的研究

移相器是移相干涉仪中的重要部件,压电式移相器由于分辨力高、响应快、控制容易而被大量采用。但压电陶瓷的非线性误差与位移量小,一直影响其应用范围的扩大。针对该问题,从压电式移相器机构与扩展方法入手,设计了具有放大特性的柔性铰链式移相器。采用单神经元(Proportional sum derivative,PSD)控制算法,实现微驱动定位的自适应实时控制,改善了非线性,降低了环境干扰的影响,提高了压电式移相器的性能。所设计的压电式移相器用3组压电陶瓷堆驱动,可用于100 mm孔径镜片,位移行程达30μm以上。实验验证该方法有效,控制精度达0.01μm。     

Parameter optimization of surface acoustic waves via multilayer structures

A method and algorithm for numerical analysis and optimization of the basic parameters of electroacoustic surface waves propagating in multilayer piezoelectric structures are described. Combinations of layer materials and piezoelectric substrates for which an electroacoustic surface wave has optimal parameters of propagation (low dispersion, high electromechanical coupling coefficient, high thermal stability, low diffraction losses, etc.) are found.     

内窥式二维光纤扫描探头及其驱动方法

基于压电换能器技术设计了一种应用于光学相干层析成像的新型内窥式二维光纤扫描探头,即利用两片压电陶瓷片和一片薄导电基片驱动光纤探头.该探头利用光纤悬臂的共振特性,通过对压电陶瓷施加等于光纤共振频率的混频信号,能同时激发光纤悬臂两正交方向上的振动,可以实现光纤悬臂的二维扫描.建立了理论模型并进行了有限元仿真分析,最后搭建了...     

Distributed piezoelectric modal sensors for circular plates

In this note, we deal with finding the shape of distributed piezoelectric modal sensors for circular plates with polar symmetric boundary conditions. The problem is treated by an optimization approach, where a binary function is used to model the design variable: the polarization profile of the piezoelectric layer. The numerical procedure proposed here allows us to find polarization profiles which take on two values only, i.e. either positive or negative polarization, that isolate particular vibration modes in the frequency domain.     

Optimal design of resonant piezoelectric buzzer from a perspective of vibration-absorber theory

In this paper, an optimization technique is presented for the design of piezoelectric buzzers. This design technique aims at finding the optimal configuration of the coupled cavity and diaphragm structure to maximize the sound pressure output. Instead of measuring the material constants of the piezoelectric ceramic and the metal diaphragm, an "added-mass method" is developed to estimate the equivalent electromechanical parameters of the system on which an analogous circuit can be established. The electrical impedance and on-axis sound pressure level of the piezoelectric buzzer can be simulated by solving the loop equations of the electromechanoacoustical analogous circuit. An interesting finding of this research is that the nature of the piezoelectric buzzer bears remarkable resemblance to that in the dynamic vibration absorber theory. Much physical insight can be gained by exploiting this resemblance in search of the optimal configuration. According to the system characteristic equation, a design chart was devised to "lock" the critical frequency at which the system delivers the maximal output. On the basis of the analogous circuit and the vibration absorber theory, an optimal design was found with constrained optimization formalism. Experiments were conducted to justify the optimal design. The results showed that the performance was significantly improved using the optimal design over the original design. Design guidelines for the piezoelectric buzzers are summarized.     

Fabrication and characteristics of thin disc piezoelectric transformers based on piezoelectric buzzers with gap circles

This paper investigates design, fabrication and test of thin disc piezoelectric transformers (PTs) based on piezoelectric buzzers with gap circles at different diameters of the gap circles. The performance test is focused on characteristics of voltage gains, including maximum voltage gains and maximum-gain frequencies, for each piezoelectric transformer under different load conditions. Both a piezoelectric buzzer and a gap circle on a silver electrode of the buzzer are needed to build any type of the PTs. Here, the gap circle is used to form a ring-shaped input electrode and a circle-shaped output electrode for each piezoelectric transformer. To do so, both structure and connection of a PT are first expressed. Then, operating principle of a PT and its related vibration mode observed by a carbon-power imaging technique are described. Moreover, an experimental setup for characterizing each piezoelectric transformer is constructed. Finally, effects of diameters of the gap circles on characteristics of voltage gains at different load resistances are discussed.     

Metal nanowires fabricated by means of magnetostrictive actuator

A new method of fabricating nanowires for electric conductance quantization studies is proposed as an alternative to the method based on converse piezoelectric effect. Commonly used for nanowire fabrication, piezoelectric actuators are expensive and require high-level voltage control signal. The method presented in this paper is based on the use of magnetostrictive actuator. Both the actuator structure and the method of the conversion factor measurement are discussed. The results of the tests of the magnetostrictive actuator are also reported. The parameters of the proposed actuator are compared with those of its piezoelectric counterpart used to date. The results of measurement confirm that the proposed actuator can be used for studying electric conductance quantization in nanowires. Presented at the X-th Symposium on Surface Physics, Prague, Czech Republic, July 11–15, 2005     

A SYNTHETIC ANALYSIS ON DESIGN OF OPTIMUM CONTROL FOR AN OPTIMIZED INTELLIGENT STRUCTURE

A hybrid optimization algorithm is developed to minimize the control energy and the structural weight under the constraints of the structural dynamic property requirements. A 72-bar space truss with two piezoelectric actuators is used to illustrate the complete process of this algorithm. It is shown that the control energy and the structural weight are clearly reduced using the proposed method.     

Evolution of structural and electrical properties of (K,Na,Li)(Nb,Ta,Sb)O3 lead-free piezoceramics through CoO doping

Doping with transition metals is widely used for piezoceramic improvement. In this work, we study the effects of cobalt doping on the properties of the well known (K,Na,Li)(Nb,Ta,Sb)O₃ piezoelectric ceramics. Two different situations were observed: for low concentrations, Co²⁺ cations occupy the A-site of the perovskite structure, whereas for high concentrations they occupy the B-site. The piezoelectric properties of the material are slightly affected with the cobalt concentration, whereas the mechanical quality factor increases by a factor of nearly three.     

ANALYSIS OF A PIEZOELECTRIC MULTIMORPH IN EXTENSIONAL AND FLEXURAL MOTIONS

Impedance and admittance matrices are presented for the analysis of the beam-type piezoelectric multimorph (PM). Each piezoelectric layer is polarized in the thickness direction. The stacking sequence can be arbitrary, and both the extensional and flexural motions are considered. The variational principle is used for deriving the lumped conjugate parameters: two mechanical ports for the extensional motion, four mechanical ports for the flexural motion, and m electrical ports for the m piezoelectric layers. The resonance and antiresonance frequencies are then easily calculated from the admittance matrices. For the case of all the piezoelectric layers either in series or parallel connection, them +6 ports reduce to the seven ports, and its impedance and admittance matrices are presented. The present methods are applied to the cantilevered PM and their electromechanical behavior is studied. The tip trajectory of the cantilevered piezomotor is also investigated using the presented matrices. It is found that the present methods are very effective in analyzing the multilayer piezoelectric transducers.     

The finite-element simulation of low-frequency bimorph transducers for the diagnostics and activation of oil wells

Through the developed technique, the finite-element optimization and the experimental validation of the construction and parameters of low-frequency bimorph piezoelectric transducers designed for the diagnostics and activation of oil wells are carried out.     

Slotted piezoelectric ring deep ocean hydrophone

Based on the energy method,the underwater resonance frequency equation and electrical admittance curve of the slotted piezoelectric ring are derived.By establishing the equivalent circuit of slotted piezoelectric ring in low-frequency receiving condition,the lowfrequency open circuit voltage sensitivity of slotted piezoelectric ring is deduced.Compared the low-frequency receiving sensitivity of the slotted piezoelectric ring and the complete ring,the thought to design the deep ocean hydrophone is presented,which combines the slotted piezoelectric ring and the free flooded structure.By establishing finite element simulation model of free flooded slotted piezoelectric ring,the relationship between ring structure parameters and low-frequency open circuit voltage sensitivity are discussed.Through the simulation and optimization,the deep-sea slotted piezoelectric ring hydrophone with the resonance frequency of 600 Hz is fabricated.The acoustic and pressure tests results indicated that the low-frequency open circuit voltage sensitivity of free flooded slotted piezoelectric ring hydrophone in work bandwidth 100-300 Hz is-193.2 dB and the least value is-197.9 dB with the-4.7 dB fluctuation.Hydrostatic pressure resistance of 30 Mpa is obtained.Compared with the same structure size free flooded piezoelectric ring hydrophone,the low-frequency open circuit voltage sensitivity of slotted piezoelectric ring hydrophone raised 20 dB.The results verify the practicability of deep ocean hydrophone presented here with free flooded slotted piezoelectric ring structure.