Free vibration analysis of piezoelectric coupled circular plate with open circuit

A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer.     

Thickness vibrations of a piezoelectric plate under biasing fields

Thickness vibrations of a piezoelectric plate under uniform initial thermoelectromechanical fields are investigated in this article. An exact solution is obtained for materials with general anisotropy. A plate of langasite, a relatively new piezoelectric material with strong piezoelectric coupling, is analyzed with imposed uniform acceleration as the biasing field as an example. The results show that the biasing fields have remarkable effect on the free vibrations of piezoelectric plate.     

Thermally stable optical cavities for Zeeman laser gyroscopes

The problem of increasing the working time of a Zeeman laser gyroscope (LG) without any discontinuities in the output data is considered. It is proposed to solve it using materials with very small linear temperature expansion coefficients in the LG design and apply piezoelectric correctors with passive temperature compensation. Numerous experimental studies of the perimeter drift have been performed for different Zeeman LG samples. The linear temperature expansion coefficients of the material of LG single blocks have been carried out, and the piezoelectric corrector design has been improved.     

压电网络复合板的波动特性与隔声性能分析

在压电网络复合板机电耦合波动方程基础上,首先对在其中传播的弯曲波的波动特性进行了分析,发现压电网络复合板中同时存在两种不同频散特性的弯曲波,电感电阻并联型压电网络复合板中存在的两种弯曲波的频散曲线具有频率转向现象;在频率转向区,弯曲波的衰减常数或达到最大或迅速增大这一结论为压电网络复合板的减振降噪设计提供了参考。对压电网络复合板中的能量分析给出了这一结论的机理:即在频率转向区板中的机械能与电能能够进行最大的能量交换;在波动分析的基础上对压电网络复合板的隔声特性进行了分析,发现压电网络复合板隔声曲线上的低谷随外界电感值的变化能够发生移动或者消失,最后结合压电网络复合板的波动频散特性对复合板的隔声机理进行了分析,为设计压电网络复合板的隔声性能提供了理论参考。      

Sound absorption characteristics of a thin plate with PZT and shunt circuitⅠ.Theoretical analysis

The feasibility of sound absorbing by a vibrating plate with piezoelectric material and shunt circuits is theoretically investigated.Based on an equivalent compliance of a piezoelectric wafer shunted with RL circuits,the governing equations for the flexural vibration of the plate with the piezoelectric wafer are derived using Lagrange's approach.The equations take into account not only the mass,stiffness and structural damping of the plate and the wafer,but also the electrical resistance and electrical i...     

Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate

The nonlinear dynamic response and active vibration control of the piezoelectric functionally graded plate are analyzed in this paper. Based on higher-order shear plate theory and elastic piezoelectric theory, the nonlinear geometric and constitutive relations of the piezoelectric functionally graded plate are established, and then the nonlinear motion equations of the piezoelectric functionally graded plate are obtained through Hamilton's variational principle. The nonlinear active vibration control of the structure is carried out with adoption of the negative velocity feedback control algorithm. By applying finite difference method, the whole problem is solved by using iterative method synthetically. In numerical examples, the effects of mechanical load, electric load, the volume fraction and the geometric parameters on the dynamic response and vibration control of the piezoelectric FGM plate are investigated.     

Closed-form solution for free vibration of piezoelectric coupled annular plates using Levinson plate theory

Free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Levinson plate theory (LPT). The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study the closed-form solution for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. To demonstrate the accuracy of the present solution, comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric and boundary conditions. Present analytical model provides design reference for piezoelectric material application, such as sensors, actuators and ultrasonic motors.     

Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimensional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly, the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then, the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bifurcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally, numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.     

压电基片与金属点阵厚度对行波模式声表面波陀螺仪检测灵敏度的影响

过低的灵敏度性能一直是声表面波(SAW)陀螺仪的瓶颈问题,对此,提出了一种结合金属点阵用以改善陀螺效应的新型行波模式SAW陀螺仪,并对其性能进行了评价。该结构由双延迟线型振荡器构成,两延迟线平行且反向制作于同一压电基片上,在延迟线的声传播路径上分布铜点阵。结合层状介质中声波传输特性的研究方法分析了两种压电晶体材料、不同金属点阵膜厚对传感器响应的影响,从而为确定陀螺仪的设计奠定理论基础。基于理论计算结果,研制了以128°YX LiNbO3及X-112°Y LiTaO₃为压电基片,铜点阵厚度分别为33000 Å,6000 Å,9000 Å的95 MHz声表面波陀螺仪。为改善振荡器的频率稳定性,延迟线采用了具有梳状结构的单相单向换能器结构。振荡器的测试频率稳定度达到了±5 Hz/h。利用精确速率转台对所研制的SAW陀螺仪性能进行了测试。测试结果表明:采用机电耦合系数较高的128°YX LiNbO₃基片并增加金属点阵厚度均能有效提高陀螺仪的检测灵敏度,所获得的最大检测灵敏度为2.7 Hz/(deg/s)。      

On the propagation of long thickness-stretch waves in piezoelectric plates

We study the propagation of thickness-stretch waves in a piezoelectric plate of polarized ceramics with thickness poling or crystals of class 6 mm whose sixfold axis is along the plate thickness. For device applications we consider long waves with wavelengths much longer than the plate thickness. A system of two-dimensional equations in the literature governing thickness-stretch, extensional, and symmetric thickness-shear motions of the plate is further simplified. The equations obtained can be used to analyze piezoelectric plate acoustic wave devices operating with thickness-stretch modes.     

Temperature self-compensated lithium tantalate piezoelectric gyroscope for higher sensitivity and stability

A new H-type gyroscope using a single LiTaO3 crystal that combines the H-type vibrational mode with a tuning fork type vibrational mode is proposed. This greatly suppresses leakage output from the piezoelectric gyroscope and also improves stability. The operation in the drive mode non-resonant condition and detection mode resonance condition is also proposed. It is possible to increase the sensor sensitivity remarkably because the drive voltage can be increased. In addition, an equivalent circuit constant including the leakage output could be accurately deduced. Automatic compensation of temperature characteristic for angular velocity detection sensitivity and drift is examined with the simple equivalent circuit. By adding a new sensor that detects the drive vibrational mode, we can produce a stable reference signal for the phase detection of output. This shows that it is possible to greatly improve the temperature characteristic of sensitivity and drift.     

Application of piezoelectric transient response in transducer acoustic power measurement

To explore a more convenient method for measuring the focused ultrasound power,a piezoelectric ceramic plate was used to receive ultrasonic signal directly.Due to an acoustic force acts on the surface of piezoelectric ceramic plate,the piezoelectric response was obtained by means of electromechanical analogy,which was composed of voltage response caused by forced vibration and high frequency attenuation response caused by natural vibration.The conversion relationship between output signal of piezoelectric ceramic plate and acoustic power of transducer was analyzed.The envelope of output piezoelectric signal was extracted in twice,and a voltage amplitude curve with sinusoidal distribution that could describe the changes of acoustic power was obtained.Under different drive voltage of transducer,the maximum peak voltage of envelope curve was found respectively.Their squared values were made a linear fitting with acoustic power measured by acoustic power meter,and then the proportional coefficient of theoretical relational expression was calibrated.The experimental results are in good agreement with the theory.The relative error between calibrated theoretical acoustic power and that measured by acoustic power meter was less than 8.7%.The paper can provide a guideline for measuring acoustic power of transducer by using piezoelectric signal.     

Energy trapping in high-frequency vibrations of piezoelectric plates with partial mass layers under lateral electric field excitation

We study coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate of monoclinic crystals with mass layers on the central parts of the plate surfaces. The plate is driven by a lateral electric field. Mindlin’s first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and the vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimension of the mass layers and the number of trapped modes is examined.     

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals (PCs), a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper. This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform. Firstly, the vibration of the model is analyzed theoretically, the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established, and the resonance frequency equation is derived. The effects of the length, width, and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method, the effective electromechanical coupling coefficient is also analyzed. The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate. The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method. The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated. The results show that the theoretical results are in good agreement with the simulation results. When the resonance frequency is in the band gap, the decoupling phenomenon occurs, and then the vibration mode in the thickness direction is purer.     

Electroacoustic lamb waves in piezoelectric crystal plates

The main characteristics of various types of plate electroacoustic waves propagating in piezoelectric single-crystal plates of various thickness are numerically studied. A number of piezoelectric plates and orientations in them with record high values of the electromechanical coupling coefficient for transverse plate waves are proposed.     

压电瞬态响应在换能器声功率测量中的应用

探索一种简便的聚焦超声功率测量方法,利用压电陶瓷片直接接收超声信号,通过机电类比得到压电瞬态响应由压电片在声波作用力下引起受迫振动产生的电压响应与固有振动产生的高频衰减响应叠加而成,分析输出压电信号与换能器声功率之间的换算关系。对输出压电信号进行二次包络提取,获得表征声功率变化的电压幅度曲线,分别找出不同换能器驱动电压下包络曲线的最大峰值电压,将其平方值与声功率计所测声功率进行线性拟合,并对理论关系式中的比例系数进行标定。实验结果所得线性拟合度较高,且标定后所得声功率与声功率计所测值相对误差低于8.7%,证明了通过压电瞬态响应测量换能器声功率具有可行性。      

Optimization of the piezoelectric transducer response by means of electrical correcting circuits

A method of shortening the transient response of a piezoelectric transducer is described. It can be applied to thickness mode piezoelectric transducers of arbitrary electromechanical coupling. The system incorporates electrical correcting circuits and can produce a transient response with a duration much shorter than the transit time of an ultrasonic wave travelling through the piezoelectric plate.     

一种高灵敏压电平面水声换能器

设计并制作了一种高灵敏压电平面水声换能器。该换能器敏感元件是对1-3-2型压电复合材料结构的改进,即在带基底的压电陶瓷小柱阵列间不注入聚合物,并在其上表面直接覆盖金属板,构成“带基底的压电小柱阵列+金属盖板”结构敏感元件(称为“空气填充型”敏感元件)。对“空气填充型”敏感元件的谐振频率进行了理论计算和有限元仿真,与实测结果较吻合。为便于对比性能,同时制作了同尺寸“1-3-2型压电复合材料+金属盖板”结构敏感元件(称为“聚合物填充型”敏感元件)换能器。分别对“空气填充型”和“聚合物填充型”敏感元件换能器的有效机电耦合系数、发送电压响应和接收灵敏度进行有限元仿真和实测,结果均显示,“空气填充型”敏感元件换能器具有较高的接收灵敏度,相较于“聚合物填充型”敏感元件换能器可提高21 dB。该敏感元件换能器能有效提高灵敏度,可为研制高灵敏换能器提供参考。      

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Localized bending vibrations of piezoelectric plates

This paper investigates the existence and propagation of electro-elastic bending waves localized at the free edge of a piezoelectric plate. The problem is considered within the framework of the high-order refined plate theory introduced by Ambartsumian. The condition for existence of a localized bending wave is obtained, and the dispersion equation solved with respect to a dimensionless frequency. It is shown that the piezoelectric effect can increase the attenuation coefficient for a localized wave by up to 70% compared with that for a purely elastic plate, thus significantly decreasing the depth of penetration. The problem is also solved within the classical Kirchhoff theory. A comparison of results is carried out between two theories.