Transient piezothermoelasticity for a cylindrical composite panel composed of cross-ply and piezoelectric laminae

This paper is concerned with the theoretical treatment of transient piezothermoelastic problem is developed for a cylindrical composite panel composed of cross-ply laminae and piezoelectric material of crystal class mm2, subject to nonuniform heat supply in the circumferential direction. We obtain the exact solution for the two-dimensional temperature change in a transient state, and transient piezothermoelastic response of a simply supported cylindrical composite panel under the state of plane strain. Some numerical results for temperature change, displacement, stress and electric potential distributions in a transient state are shown in figures. Furthermore, the influence of thickness of the cross-ply laminate on thermal stress or electric field are investigated.     

功能梯度压电材料壳体热残余应力

功能梯度压电材料结构成型冷却后会出现热残余现象,影响结构强度.借鉴复合材料层合结构的研究方法,将功能梯度压电材料球壳和圆柱壳沿厚度分为若干层,各层视为均匀材料,根据层间连续条件导出递推关系,得到显式的力—电—热多场耦合热残余解.统一了多层功能梯度压电材料壳体和连续功能梯度压电材料壳体热残余解.对于前者,其解为精确解;对于后者,其解为渐近解,随层数增加而收敛于精确解.其解也适用于功能梯度压电材料涂层.该方法对材料性能的变化方式(函数)没有要求,适应性强.并讨论影响热残余应力和界面强度的因素,球壳因双曲率的影响,热残余应力显著大于柱壳.     

Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting

Electromechanical responses of compositionally graded piezoelectric layers are analysed. The layers consist of polycrystalline piezoelectric ceramics poled along the thickness direction, and thus exhibit material symmetry of a hexagonal crystal in class 6mm. Two cases for layers (i) covered by surface electrodes and (ii) without surface electrodes are considered. Analytical solutions are exact in Saint Venant's sense for both cases. However, solutions are obtained for layers subjected to uniform mechanical loads, including stretch, bending and twisting. Numerical results to show the effects of different compositional gradients are presented.     

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.     

Axisymmetric response of circular plates with piezoelectric layers: an exact solution

Electromechanical responses of symmetric circular laminates consisting of piezoelectric layers are studied, and the influence of surface and interlayer electrodes are involved. The laminates are traction-free on the top and bottom surfaces, but may be subjected to external forces at the lateral edge and to voltages applied across certain layers. Under axisymmetric deformation conditions, an approximate model which employs Kirchhoff hypothesis and incorporates the charge equation of electrostatic is established. Then, a closed-form three-dimensional solution of the laminates is generated in a very straightforward manner by the solution of the approximate model. The three-dimensional solution fulfills all field equations and interface or surface conditions as well as the specified electric edge boundary conditions; the only restriction is that the mechanical edge boundary conditions are satisfied in an average manner, rather than point by point. Thus, according to Saint-Venant's principle the proposed solution is exact in the interior region of the laminates.     

Development of a PZT fiber/piezo-polymer composite actuator with interdigitated electrodes

Piezoelectric Fiber Composites with Interdigitated Electrodes (PFCIDE) were previously introduced as an alternative to monolithic wafers with conventional electrodes for applications of structural actuation. This paper is an investigation into the performance improvement of piezoelectric fiber composite actuators by changing the matrix material. This paper presents a modified micro-electromechanical model and numerical analyses of piezoelectric fiber/ piezopolymer matrix composite actuator with interdigitated electrodes (PFPMIDE). Various concepts from different backgrounds including three-dimensional linear elastic and dielectric theories have been incorporated into the present linear piezoelectric model. The rule of mixture and the modified method to calculate effective properties of fiber composites were extended to apply to the PFPMIDE model. The new model was validated when compared with available experimental data and other analytical results. To see the structural responses of a composite plate integrated with the PFPMIDE, three-dimensional finite element formulations were derived. Numerical analyses show that the shape of the graphite/epoxy composite plate with the PFPMIDE may be controlled by judicious choice of voltages, piezoelectric fiber angles, and elastic tailoring of the composite plate.     

Analysis of Natural Vibrations of Round Bimorph Piezoelectric Ceramic Plates of Arbitrary Dimensions. I. Simply Supported Piezoelectric Plate

The problem of natural vibrations of a round bimorph simply supported piezoelectric ceramic plate (piezoplate) of an arbitrary thickness with arbitrary axisymmetric electrodes is solved in the exact formulation using the method of finite elements. The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distribution over the piezoplate surfaces (vibration modes) is also analyzed and the dynamic electromechanical coupling coefficient (DCC) is investigated as a function of the relative plate thickness for various piezoelectric ceramic compositions. Round bimorph piezoplates with partial electrodes have been also considered. The results obtained make it possible to estimate the limits of applicability of an approximate one-dimensional theory and choose the optimum geometric dimensions of the plate and electrodes that ensure the maximum DCC.     

Analysis of Natural Vibrations of Round Flexing Membrane-Type Piezoelectric Transducers with an Arbitrary Dimension Ratio

The problem of natural vibrations of a round exing membrane-type piezoelectric transducer (piezoelectric plate) with an arbitrary dimension ratio is solved in the exact formulation using the finite element method for two variants of fastening the membrane (simply supported and rigidly fixed plate). The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the plate surfaces are also analyzed and the dependences of the dynamic electromechanical coupling coefficient are investigated as functions of the geometric dimensions of the piezoelectric transducer, the plate material, and the piezoelectric ceramic composition. The optimum geometric dimensions of the transducer which ensure the maximum dynamic electromechanical coupling coefficient are determined and the value of the coefficient is estimated.     

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters.     

The unified equations to obtain the exact solutions of piezoelectric plane beam subjected to arbitrary loads

The unified equations to obtain the exact solutions for piezoelectric plane beam subjected to arbitrary mechanical and electrical loads with various ends supported conditions is founded by solving functional equations. Comparing this general method with traditional trial-and-error method, the most advantage is it can obtain the exact solutions directly and does not need to guess and modify the form of stress function or electric displacement function repeatedly. Firstly, the governing equation for piezoelectric plane beam is derived. The general solution for the governing equation is expressed by six unknown functions. Secondly, in terms of boundary conditions of the two longitudinal sides of the beam, six functional equations are yielded. These equations are simplified to derive the unified equations to solve the boundary value problems of piezoelectric plane beam. Finally, several examples show the correctness and generalization of this method.     

宏微直线压电电机微驱动机构设计与分析

为了解决宏微驱动直线压电电机微驱动位移较小、对宏动定位误差的补偿能力不足的问题,提出一种宏微驱动钹型直线压电电机。采用钹型复合压电叠堆为驱动单元替换压电陶瓷片组成的压电叠堆,实现轴向位移的一次放大,通过弹性拨齿的柔性铰链结构将钹型压电叠堆输出的微位移二次放大。该电机可在特定的驱动频率、工作电压和相位差下实现振子振动模态下的超声驱动,也可以通过微位移放大机构实现静态变形的微驱动(蠕动)。建立了该直线压电电机的三维有限元模型,利用有限元软件分别对弹性拨齿、钹型压电叠堆和复合振子进行静力学分析和静态优化设计。有限元仿真表明:基于柔性铰链结构的弹性拨齿经过优化后,最小刚度小于钹型压电叠堆的最小刚度;在相同条件下,优化后钹型压电叠堆沿轴向方向的静态变形量比由压电陶瓷片组成的压电叠堆的静态变形量提高了8.45倍;采用基于柔性铰链结构的弹性拨齿和钹型压电叠堆组成的复合振子的拨齿质点沿水平方向的静态位移量比优化前提高了12.1%,大幅提高了微驱动对宏动定位误差的补偿能力,为压电电机微驱动的结构设计及优化提供依据。     

Active structural-acoustic control of laminated cylindrical panels using smart damping treatment

In this paper, the performance of active constrained layer damping (ACLD) treatment for active structural-acoustic control of a vibrating thin laminated cylindrical panel has been investigated. The constraining layer of the ACLD treatment has been considered to be made of piezoelectric fiber-reinforced composite (PFRC) material. A finite element model has been developed for the laminated panels integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the panels enclosing an acoustic cavity. Both velocity and pressure rate feedback controls have been implemented to activate the patches. Symmetric and antisymmetric cross-ply and antisymmetric angle-ply panels have been considered for evaluating the numerical results. Emphasis has also been placed on investigating the effect of the piezoelectric fiber orientation in the PFRC layer and the shallowness angle of the cylindrical panels on the performance of the patches.     

基于谱元法的板结构中导波传播机理与损伤识别

建立板结构的三维谱元法模型和结构-压电晶片耦合模型,对铝合金板中Lamb波的传播机理和与损伤作用规律进行研究。以单点激励力模型研究了板中Lamb波的频散关系,从理论上对所建立的模型进行了验证;基于压电晶片模型研究了在施加电压激励条件下导波的传播规律;研究单一压电晶片、板中上下表面施加同相位或反相位激励电压的两个压电晶片三种情况下结构的响应;对板中传播Lamb波的幅值与传播距离的关系进行分析;采用减小结构单元刚度的方法模拟结构中的裂纹损伤,研究Lamb波与损伤的作用;结合试验分析,验证所仿真结果结论的正确性。相对二维谱元法模型,所建立的板结构三维谱元法模型能更真实地模拟结构中导波的激励与接收以及波的传播。     

Nanoscale surface deformation inspection using FFT and phase-shifting combined interferometry

In this paper, a flexible optical interferometer incorporated with both fast Fourier transform (FFT) and phase-shifting method is developed for three-dimensional (3D) testing of micro-components. Using light interference, microscopic optics, piezoelectric transducer (PZT) nanoscanning and a CCD camera, the proposed system can detect deformation and surface contour in the order of nanometers. An application of the proposed technique is demonstrated using two micro-components: a micro-beam in an accelerometer and a micromirror. The resulting interference fringes that are related to the deformation and surface contour are analyzed using FFT method or three-step phase-shifting method depending on the test surface features. Experimental results show the feasibility of the proposed method for 3D deformation and surface contour measurement of micro-components.     

非对称智能减振板优化设计

通过分析非对称智能板的导纳值,实现了智能板压电片的优化设计。由于压电分流阻尼电路中能量的消耗是导纳值的函数,因此用导纳值来评价智能板的减振效果。用模态分析得到智能板的振型和固有频率,再通过谐响应分析求得智能板的导纳值。针对3个非对称模态,采用子问题的优化方法,优化设计压电片的位置,使其减振效果达到最佳。     

压电式超声振动系统开发设计

针对压电式超声振动系统中换能器和变幅杆的设计公式及步骤复杂的问题,提出利用软件的二次开发,在UG软件平台上研究振动系统的三维造型的方法.开发结果表明该方法可以很好的解决压电超声换能器和变幅杆在设计过程中存在的问题,简化了设计过程,缩短了新产品的开发周期.     

Comparative analysis of two impact-sensitive sensors for improved estimation of time difference of arrivals

In this study, an intensive comparative analysis of two impact-sensitive cantilever sensors for improved estimation of time difference of arrivals on plates is presented. Precise locating of the impact point requires exact bending wave propagation velocity due to the impact and time differences between each sensor. However since the bending wave velocity is dispersive on a plate, it is very difficult to decide the velocity when a vibration sensor such as an accelerometer is used. The new sensor philosophy is to provide a more exact bending wave velocity by designing the sensor as a cantilever type with a piezo transducer. Thus in this paper, two different cantilever sensors are considered: a rectangular type with a piezoelectric magnesium niobate ?? lead titanate single crystal patch and a circular type with a piezoelectric zirconate titanate disc. Their responses against impacts are compared with the response of a commercial accelerometer. The two sensors were manufactured and tested on a glass plate and an MDF plate separately. The impact test results showed that the two sensors give narrow band responses against impacts on the both plates and can provide a constant bending wave propagation velocity.     

An exact solution for functionally graded piezoelectric laminates in cylindrical bending

In the present paper, the exact solutions of a simply supported functionally graded piezoelectric plate/laminate under cylindrical bending are derived. With similar derivation procedure as that used for Stroh formalism, the eigenrelation and general solutions for the problems can be expressed in very concise forms, which are convenient for further treatments of both analytic and numerical studies. The exact solutions can be served as benchmarks to verify and improve various approximate theories and numerical methods. To show the influence of material gradients, numerical examples based on the exact solutions are given, and some properties of the mechanical and electric responses of the plates under mechanical and electrical forces are discussed.     

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.     

Stability and free vibration analysis of thick piezoelectric composite plates using spline finite strip method

In the present study, a spline finite strip with higher-order shear deformation is formulated for stability and free vibration analysis of piezoelectric composite plates. At each knot, the electric potentials on the surfaces and middle plane of each piezoelectric layer are taken as nodal degrees of freedom. However, if a continuous electrode is installed on the surface of the layer, the electric potential on the electrode is changed to structural degree of freedom, so that the equipotential condition on the electrode is automatically satisfied. The analysis can be conducted based on Reddy's third-order shear deformation theory, Touratier's “Sine” model, Afaq's exponential model or Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick plates over the first-order shear deformation theory is achieved at only little extra computational cost.The numerical results obtained based on different shear deformation theories are presented in comparison with the three-dimensional solutions. The effects of length-to-thickness ratio, fiber orientation, boundary conditions and electrical conditions on the natural frequency and critical buckling load of piezoelectric composite plates are investigated through numerical examples.