EXPERIMENTAL AND NUMERICAL STUDIES ON PERFORMANCE OF MACRO FIBER COMPOSITES FOR BEAM TWISTING APPLICATIONS

This paper presents the use of macro-fiber composites (MFC) as actuators for twisting control of pre-twisted beams, which is one efficient method of vibration suppression techniques of helicopter rotors. An MFC is a piezoelectric fiber composite which has an interdigitated electrode, rectangular cross-section and unidirectional piezoceramic (PZT) fibers embedded in the polymer matrix. An MFC actuator has much higher actuation performance, flexibility and durability than a traditional piezoceramic (PZT) actuator. This study showed that an MFC could be used as an actuator to change the displacement and twist tip-angle of a pre-twisted beam. In the test, an MFC patch was pasted on the beam’s upper surface to twist the pre-twisted beam actively. Different twist tip-angle changes of the pre-twisted beam were measured under a series of actuation voltages, and a good agreement was observed when experimental results were compared with numerical results. In addition, the actuation performance of MFC was compared with those of PZT4 and PVDF and the influence of anisotropic property of the MFC on its actuation performance was also studied. The experimental and numerical results presented in this paper show the potential of MFC for use in the vibration control of helicopter rotors.     

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.     

基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而，目前应用的压电致动器均是基于线性压电效应，最大应变一般只有0.1-0.15%，实现大的致动应变一直是该领域学者追求的目标。本文中，我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器，一种是径向极化、部分电极（RPPE）的4层圆环，另一种是周期性正交极化（POP）的4层圆环，以期能够实现大的致动应变，而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明，在相同的驱动电场（2kV/mm，0.1Hz）下，4层RPPE最大致动应变为0.27%，约为普通PZT圆环的2倍，但表面变形很不均匀。相比之下，4层的POP圆环致动器的最大输出应变为0.36%，是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小， RPPE致动器在超过1Hz后稳定在0.19%， POP致动器在超过5Hz后稳定在0.2%。而且， POP圆环致动器重复性能很好，经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点，在致动领域具有很好的应用前景。     

基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而,目前应用的压电致动器均是基于线性压电效应,最大应变一般只有0.1-0.15%,实现大的致动应变一直是该领域学者追求的目标。本文中,我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器,一种是径向极化、部分电极（RPPE）的4层圆环,另一种是周期性正交极化（POP）的4层圆环,以期能够实现大的致动应变,而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明,在相同的驱动电场（2kV/mm,0.1Hz）下,4层RPPE最大致动应变为0.27%,约为普通PZT圆环的2倍,但表面变形很不均匀。相比之下,4层的POP圆环致动器的最大输出应变为0.36%,是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小, RPPE致动器在超过1Hz后稳定在0.19%, POP致动器在超过5Hz后稳定在0.2%。而且, POP圆环致动器重复性能很好,经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点,在致动领域具有很好的应用前景。     

A Motion Amplifier Using an Axially Driven Buckling Beam: I. Design and Experiments

For active materials such as piezoelectric stacks, which produce large force and small displacement, motion amplification mechanisms are often necessary – not simply to trade force for displacement, but to increase the output work transferred through a compliant structure. Here, a new concept for obtaining large rotations from small linear displacements produced by a piezoelectric stack is proposed and analyzed. The concept uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. The optimal design of the buckling beam end conditions was determined from a static analysis of the system using Euler's elastica theory. This analysis was verified experimentally. A stack-driven, buckling beam prototype actuator consisting of a pre-compressed PZT stack (140 mm long, 10 mm diameter) and a thin steel beam (60 mm× 12 mm× 0.508 mm) was constructed. The buckling beam served as the motion amplifier, while the PZT stack provided the actuation. The experimental setup, measuring instrumentation and method, the beam pre-loading condition, and the excitation are fully described in the paper. Frequency responses of the system for three pre-loading levels and three stack driving amplitudes were obtained. A maximum 16^∘ peak-to-peak rotation was measured when the stack was driven at an amplitude of 325 V and frequency of 39 Hz. The effects of beam pre-load were also studied.     

Investigation on the Design of Piezoelectric Actuator/Sensor for Damage Detection in Beam with Lamb Waves

Piezoelectric wafer type actuator/sensor is widely used to generate and sense Lamb waves for Structural Health Monitoring (SHM). However, multiple Lamb waves modes are generally excited with this type of transducer. As a result, there is some difficulty in using Lamb waves for damage detection. To selectively generate a single A₀/S₀ Lamb mode, the tuned excitation of Lamb waves has been studied by some researchers. This paper investigates the design of the PZT actuator/sensor bonded to beam-like structure for generating single A₀/S₀ Lamb mode. In the study it is found that some factors, including the bonding layer, the unknown material properties and dynamical characteristics of the beam, will influence the design of PZT actuator/sensor. Piezoelectric impedance technique is introduced to facilitate the design of PZT actuator/sensor. Crack detection in beam using the tuned A₀/S₀ Lamb waves is performed.     

Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

The linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba₂NaNb₅O₁₅/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.     

旋转运动柔性梁的时滞主动控制实验研究

对旋转运动柔性梁的时滞主动控制进行实验研究,验证时滞反馈控制的有效性. 实验中采用交流伺服电机带动柔性梁旋转运动,柔性梁上粘贴有压电作动器,用于控制梁的弹性振动. 实验研究考虑如下3种情况:(1)仅使用电机扭矩进行控制,电机扭矩存在时滞;(2)使用电机扭矩和压电作动器同时控制,仅压电作动器存在时滞;(3)使用电机扭矩和压电作动器同时控制,电机和压电作动器存在不同的时滞量. 重点通过实验验证时滞反馈控制的可行性和有效性.      

智能结构梁传递驱动模型

基于结性应变假设,提出了考虑粘贴层影响的智能结构梁分布模型。通过对双面粘压电驱动器的智能结构梁的数值模拟,得到了应变分布假设对压电驱动顺驱动性能影响的规律。结果表明：忽略粘贴层的影响,将过高地估计压电片产生的驱动力;考虑粘贴层影响的智能结构梁分布力模型更符合实际情况,具有广泛的普遍性。     

非线性压电效应下压电弯曲执行器的弯曲

研究压电弯曲执行器在强电场作用下的非线性弯曲行为。考虑电致伸缩和电致弹性的非线性压电效应,导出了压电悬臂执行器自由端挠度或激励力和作用电场之间的非线性关系。结果表明,考虑非线性压电效应在很大的电场范围内都与实验结果吻合得很好,而线性压电效应只适合于低电场的情况。     

A continuum based modelling approach for adhesively bonded piezo-transducers for EMI technique

In the electro-mechanical impedance (EMI) technique, which is based on induced strain actuation through piezoelectric ceramic (PZT) patch, the knowledge of shear stress distribution in the adhesive bond layer between the patch and the host structure is very pertinent for reliable health monitoring of structures. The analytical derivation of continuum based shear lag model covered in this paper aims to provide an improved and more accurate model for shear force interaction between the host structure and the PZT patch (assumed square for simplicity) through the adhesive bond layer, taking care of all the piezo, structural and adhesive effects rigorously and simultaneously. Further, it eliminates the hassle of determining the equivalent impedance of the structure and the actuator separately, as required in the previous models, which was approximate in nature. The results are compared with the previous models to highlight the higher accuracy of the new approach. Based on the new model, a continuum based interaction term has been derived for quantification of the shear lag and inertia effects.     

Numerical analysis of large elasto-plastic deflection of constant curvature beam under follower load

This paper describes a method to analyze the elasto-plastic large deflection of a curved beam subjected to a tip concentrated follower load. The load is made to act at an arbitrary inclination with the tip tangent. A moment-curvature based constitutive law is obtained from linearly hardening model. The deflection governing equation obtained is highly non-linear owing to both kinematics and material non-linearity. It is linearized to obtain the incremental differential equation. This in turn is solved using the classical Runge–Kutta 4^th order explicit solver, thereby avoiding iterations. Elastic results are validated with published literature and the new results pertaining to elasto-plastic cases are presented in suitable non-dimensional form. The load to end angle response of the structure is studied by varying normalized material and kinematic parameters. It is found that the response curves overlap at small deflection corresponding to elastic deformation and diverge for difference in plastic property. The divergent response curves intersect with each other at higher deflection. The results presented also show that the approach may be used to obtain desired non-uniformly curved beam by suitably loading a uniform curvature beam.     

相似电路耦合模型及其在压电—梁结构分析中的应用

根据线性系统微分方程的相拟性确定机械系统的相似电路,由压电材料的本构和动力方法确定压电材料作为电耦合的变压器,从而用一具耦合的电路系统模拟智能结构的电学和力学行为,通过一个压电－梁智能结构的分析,证明了模型的可用性。     

梯度功能压电悬臂梁的一组基本解及其应用

采用应力函数解法,研究了弹性参数和体积力同时呈梯度变化时压电材料悬臂粱的力-电响应,得到了应力函数和电位移函数的解析表达式及梯度功能压电悬臂梁的一组基本解．作为一种应用形式,给出了梯度功能压电执行器的尖端位移和制动力的确定方法、此外,利用该基本解,可以方便地确定悬臂梁在多种不同典型荷载单独或联合作用下的解答。     

Exact deflection solutions of beams with shear piezoelectric actuators

Exact deflection models of beams with n actuators of shear piezoelectric are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The exact solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors’ previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two shear piezoelectric actuators is attained. It is shown that the first-order beam cannot predict the beam behavior when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of actuators lengths and locations on the deflected shapes of beams with two piezoelectric actuators. Some interesting deflection curves are presented. For example, the deflection curve of a H–H beam resembles saw teeth that rotate clockwise about the central location with the increase of actuators lengths. The presented exact solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n actuators of shear piezoelectric.     

Exact dynamic solutions to piezoelectric smart beams including peel stresses I: Theory and application

This work presents exact dynamic solutions to piezoelectric (PZT) smart beams including peel stresses. The governing equations of partial differential forms are firstly derived for a PZT smart beam made of the identical adherends, and then general solutions of the governing equations are studied. The analytical solutions are applied to a cantilever beam with a partially bonded PZT patch to the fixed end. For the given boundary conditions, exact solutions of the steady state motions are obtained. Based on the exact solutions, frequency spectra, natural frequencies, normal mode shapes, harmonic responses of the shear and peel stresses are discussed for the PZT actuator. The details of the numerical results and sensing electric charges will be presented in Part II of this work. The exact dynamic solutions can be directly applied to a PZT bimorph bender. To compare with the classic shear lag model whose numerical demonstrations will be given in Part II, the related equations are also derived for the shear lag rod model and shear lag beam model.     

Numerical Investigation and Feasibility Study of a PZT-driven Micro-valve Pulsed-jet Actuator

A micro-valve pulsed-jet vortex-generator driven by piezoelectric actuation was successfully modelled numerically to determine the feasibility of such a design. This includes: modelling the dynamic motion of a unimorph cantilever and the fluid-structure interaction occurring between the unimorph and the fluid flowing over such a structure; the unsteady developing channel flow that would occur through the outlet orifice was also modelled. The initial design was found to have several fundamental flaws that were shown to be easily remedied. The fluid-structure interaction was found to have a strong effect on the motion of the piezoelectric beam and therefore the performance of the pulsed-jet actuator. The response time of the actuator was found to be governed by the micro-valve opening rather than the time taken to establish the jet. However, the resistance of the pulsed-jet actuator was shown to be governed by the outlet orifice; it was an order of magnitude larger than the resistance of the micro-valve.     

机敏柔性梁的振动主动控制

提出了用于机敏结构中振动主动控制的仿人控制算法,对压电阻尼技术进行了理论和实验研究,给出了传感器,执行器和受控结构之间的关系,用ＰＺＴ作执行元件实现了柔性梁振动主动控制系统,给出了实验结果。     

Development of a new ultrasonic actuator based on Langevin bending transducer

A new ultrasonic actuator based on a bending-type Langevin piezoelectric transducer has been developed. An actuator consists of a half-wavelength Langevin transducer and an aluminum plate that is mounted in the middle of the transducer. The driving tip is located at the bottom of the aluminum plate. Piezoceramic rings with opposite polarity within each half of the ring are divided into two groups. Two harmonic signals with shifted phases by π/2 are used to excite the first bending mode of the Langevin transducer and aluminum plate. Elliptical trajectory of the contact point motion is obtained by combining these two bending modes. Numerical modelling was carried out to analyze harmonic response of the actuator and to investigate the trajectories of the contact point motion. Optimization of the aluminum plate design was performed to maximize the parameters of elliptical motion of the driving tip. A prototype actuator was fabricated, and output characteristics were measured. The results of numerical and experimental study are discussed.     

Infinite-Dimensional Control of Nonlinear Beam Vibrations by Piezoelectric Actuator and Sensor Layers

An infinite-dimensional approach for the active vibration control of a multilayered straight composite piezoelectric beam is presented. In order to control the excited beam vibrations, distributed piezoelectric actuator and sensor layers are spatially shaped to achieve a sensor/actuator collocation which fits the control problem. In the sense of von Kármán a nonlinear formulation for the axial strain is used and a nonlinear initial boundary-value problem for the deflection is derived by means of the Hamilton formalism. Three different control strategies are proposed. The first one is an extension of the nonlinear H-design to the infinite-dimensional case. It will be shown that an exact solution of the corresponding Hamilton–Jacobi–Isaacs equation can be found for the beam under investigation and this leads to a control law with optimal damping properties. The second approach is a PD-controller for infinite-dimensional systems and the third strategy makes use of the disturbance compensation idea. Under certain observability assumptions of the free system, the closed loop is asymptotically stable in the sense of Lyapunov. In this way, flexural vibrations which are excited by an axial support motion or by different time varying lateral loadings, can be suppressed in an optimal manner. A numerical example serves both to illustrate the design process and to demonstrate the feasibility of the proposed methods.