计及压电效应时矩形振子的三维振动研究

在计及压电效应的情况下，本文利用解析方法对有限尺寸压电陶瓷矩形振子的三维振动进行了研究，推出了振子耦合振动的频率方程，并对振子的振动模式进行了分析。理论研究表明，利用本文中的解析法研究振子的耦合振动，计算简单、物理意义明显。与传统的一维理论分析方法及数值方法相比，由于本研究考虑了振子的压电效应以及不同振动模式不同的相互耦合，因此，振子的理论计算频率与测量值更加符合。     

计及高次径向模式时短圆柱压电振子的耦合振动特性

先前笔者曾就方形板及圆柱压电振子从实验和等效耦合电路理论两个方面研究了在极化方向及其垂直方向上两个基本纵向振动相耦合情况下的耦合振动特性(共振频率和机电耦合系数与尺寸比的关系)。但在那种情况下,如果垂直方向的尺寸比极化方向的尺寸大,耦合系数的理论值与实测值几乎看不出有一致性。因此,我们又在考虑高次径向模式的情况     

逆压电效应的压电常数和压电陶瓷微位移驱动器

本文介绍了由过压电效应的应变-电场曲线测得弱场和强场下的压电常数d₃₃、d₃₁．测量发现S～E曲线上呈现应变和压电系数突增的阈值场强E_b,用铁电陶瓷固有的90°畴转向对应变的贡献进行了分析和讨论．该方法与以往常用的正压电效应的压电常数测试相比,方便、简单,尤其对过压电效应的压电微位移驱动器应用更具有实际意义．     

圆柱形压电振子的多维耦合换能器理论

利用表观弹性法讨论了有限长实心和空心压电圆柱振于的三维耦合振动理论,并给出了各振子的总导纳方程、频率方程和多维耦合下的机电转换系数等。由总导纳方程计算了频率常数随振子几何尺寸的变化曲线,所得结果与用里兹变分法得到的结果相当一致,也与实验结果相吻合。此方法可用于圆柱形压电陶瓷参数的修正以及复合压电振子和非压电振子耦合振动的计算。     

压电材料及压电效应的应用

压电效应技术以其特有的优势在能源紧缺的今天发挥了显著的作用。自该技术使用以来,开发出了包括压电晶体、Pb Ti O3系压电材料、压电陶瓷及高聚物复合材料等新型压电材料。目前压电效应技术在换能器、驱动器、传感器等方面得到了广泛应用。     

矩形压电振子的多维耦合换能器理论

利用表观弹性法推导了矩形断面压电陶瓷长条和矩形压电薄板振子的二维耦合振动理论并给出了各振子的总导纳方程、多维耦合下的机电转换系数等,由总导纳方程计算了频率常数随振子几何尺寸的变化曲线。所得结果与有限差分法和有限元法的结果相当满意地符合。 这种方法比其他方法简单,可用于压电陶瓷参数的修正,复合压电振子和非压电振子的耦合振动的计算。     

多次压电效应对压电石英物性系数的影响

为改善石英器件与产品的性能以适应并推动微/纳机电系统技术的发展,从理论和实验两方面系统地研究了多次压电效应对压电石英弹性系数、压电系数和机电耦合系数等物性系数的影响.理论分析表明,外应力作用下多次压电效应对压电石英弹性系数及压电系数的影响分别是多次逆和多次正压电效应综合作用的体现.采用与压电石英晶体并联一个远大于其等效电容量的电容器的实验方法,测试了多次压电效应对石英物性系数的影响,获得了三次压电效应时石英的压电系数为0.04 pC/N,比未考虑多次压电效应时提高了1.75%,所对应的机电耦合系数亦增加了1.75%.     

切向极化压电陶瓷细长圆棒的扭转振动研究

利用压电材料的压电及运动方程，本文研究了切向极化压电陶瓷细长棒的扭转振动，分析了扭转振动压电陶瓷细棒中扭转角及扭矩的分布规律，推出了扭转振动压电陶瓷振子的机电等效电路，并得出了振子的共振及反共振频率方程，为扭转振动超声换能器的设计及计算奠定了一定的理论基础。     

压电陶瓷振动振幅的测量

采用激光多谱勒法测量了P4、P8和P5压电陶瓷元件的振动振幅,进而确定压电陶瓷振幅最大时的频率,并且与导纳电桥法测得的频率进行了比较。实验证实采用激光多普勒法可以准确测量压电陶瓷的振动振幅和谐振频率,并且机械品质因数Qm越大,测得的谐振频率越准确,这为评价压电陶瓷元件的质量提供了一种新的手段。     

压电陶瓷圆环与金属圆环复合振动系统的径向振动

对由压电陶瓷圆环与金属圆环组成的复合振动系统的径向振动特性进行了研究。首先分析了压电陶瓷圆环和金属圆环的径向振动,推出了其各自的机电等效电路。在此基础上,得出了压电陶瓷圆环与金属圆环复合振动系统的机电等效电路及其共振频率方程。探讨了系统的共振及反共振频率、有效机电耦合系数与其几何尺寸之间的关系。研究表明,当复合振动系统的壁厚比增大时,其共振及反共振频率升高。对于换能器的第一阶径向振动,其有效机电耦合系数随壁厚比的增大而单调减小;对于换能器的第二阶径向振动,其有效机电耦合系数随壁厚比的增大会出现一个极大值,而且,在一定的壁厚比范围内,换能器第二阶径向振动的有效机电耦合系数大于第一阶径向振动的有效机电耦合系数,这一规律与传统的有关压电换能器的分析理论及结果是有所不同的。     

三叠片压电复合换能器弯曲振动的比较研究

用瑞利法对三叠片弯振圆盘换能器在三种不同边界条件下的振动特性进行理论研究,推导了谐振频率及有效机电耦合系数的表达式,通过数值计算分析了复合换能器的谐振频率及有效机电耦合系数随换能器各结构参数的变化规律并进行比较研究,同时将计算结果与有限元模拟结果比较,结果表明不同边界条件下换能器的结构参数对谐振频率和有效机电耦合系数影响不同:在换能器结构参数一定时,自由边界条件下谐振频率最大,简支边界条件下最小,固定边界条件下次之;有效机电耦合系数随着金属片厚度、陶瓷片厚度和陶瓷片半径变化时,分别有一个最大值;其他参数一定时,有效机电耦合系数在简支边界条件下最大,自由边界条件下的值稍大于固定边界条件下的值。上述研究结果可为三叠片弯曲振动换能器的设计和实际应用提供一定的理论支持。     

Developments of piezoelectric ultrasonic actuators operating under bending hybrid vibration modes

The exciting methods for the sandwich type piezoelectric ultrasonic actuators used bending hybrid modes are investigated. Five exciting methods are discussed and compared in detail, in which the polarizations and the partitions of the ceramic rings are different. Harmonic analyses are developed to obtain the effects of the exciting methods on the electromechanical coupling factors and the vibration amplitudes. At last, five prototypes are manufactured to verify their differences. Both the simulation and experiment results prove that the exciting method using ceramic rings with four separated partitions achieves great improvements on the efficiency, velocity and force, synchronously.     

Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

This paper investigates the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory. The piezoelectric nanobeam is subjected to an applied voltage and a uniform temperature change. The nonlinear governing equations and boundary conditions are derived by using the Hamilton principle and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the piezoelectric nanobeams. A detailed parametric study is conducted to study the influences of the nonlocal parameter, temperature change and external electric voltage on the size-dependent nonlinear vibration characteristics of the piezoelectric nanobeams.     

A 3-D Ritz solution for free vibration of circular/annular functionally graded plates integrated with piezoelectric layers

This paper addresses three-dimensional (3-D) free vibration characteristic of thick circular/annular functionally graded (FG) plates with surface-bonded piezoelectric layers on the basis of 3-D Ritz solution. Three displacement components along with electrical potential field of the plate are expressed by a set of Chebyshev polynomials multiplied by geometry boundary functions. Both open-circuit and closed-circuit surface conditions are taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey either exponent or power law distribution of the volume fraction of the constituents. The effect of thickness-to-radius ratio, inner-to-outer radius ratio, piezo-to-host thickness ratio and gradient index on the natural frequencies of coupled piezoelectric FG circular/annular plates is investigated for different electrical and mechanical boundary conditions. It is observed that, unlike isotropic homogeneous circular/annular plates, frequency parameters of their piezoelectric coupled FG counterparts significantly increase with an enhancement in the host plate thickness to radius ratio. Results also show that the frequency parameters for open-circuit condition are higher than those for closed-circuit condition.     

On free vibration of piezoelectric nanospheres with surface effect

Surface effect responsible for some size-dependent characteristics can become distinctly important for piezoelectric nanomaterials with inherent large surface-to-volume ratio. In this paper, we investigate the surface effect on the free vibration behavior of a spherically isotropic piezoelectric nanosphere. Instead of directly using the well-known Huang-Yu surface piezoelectricity theory (HY theory), another general framework based on a thin shell layer model is proposed. A novel approach is developed to establish the surface piezoelectricity theory or the effective boundary conditions for piezoelectric nanospheres employing the state-space formalism. Three different sources of surface effect can be identified in the first-order surface piezoelectricity, i.e. the electroelastic effect, the inertia effect, and the thickness effect. It is found that the proposed theory becomes identical to the HY theory for a spherical material boundary if the transverse stress components are discarded and the electromechanical properties are properly defined. The nonaxisymmetric free vibration of a piezoelectric nanosphere with surface effect is then studied and an exact solution is obtained. In order to investigate the surface effect on the natural frequencies of piezoelectric nanospheres, numerical calculations are finally performed. Our numerical findings demonstrate that the surface effect, especially the thickness effect, may have a particularly significant influence on the free vibration of piezoelectric nanospheres. This work provides a more accurate prediction of the dynamic characteristics of piezoelectric nanospherical devices in nano-electro-mechanical systems.     

基于传递矩阵法分析ACLD圆柱壳振动控制问题的一种完全力电耦合模型

目前在ACLD薄壳结构的动力学分析中,通常采用一种忽略压电约束层面内电场强度,仅考虑在厚度方向为常量分布的法向电场强度的简化力电耦合模型。文中首先从理论上分析了简化力电耦合模型的局限性,进而提出了一种新的完全力电耦合模型,以此为基础导出了该模型下ACLD圆柱壳的一阶常微分矩阵状态方程,并结合传递矩阵法和齐次扩容精细积分法求解该方程。相对于传统三维模型方法,所建立的新模型和求解方法不仅大幅度简化了计算,而且适用于分析部分覆盖和任意支承条件下ACLD圆柱壳的振动控制问题。最后通过数值算例对完全力电耦合模型和简化力电耦合模型进行了比较,结果表明：简化力电耦合模型仅适用于低频分析;完全力电耦合模型具有更宽的频率适应性