考虑压电效应时压电陶瓷圆形振子的耦合振动

在考虑压电效应的情况下，本文对压电陶瓷圆形振子的耦合振动进行了研究。根据压电陶瓷圆形振子的运动方程及压电方程，通过引入振子不同振动模式之间的机械耦合系数，分析了振子轴向及径向振动之间的耦合关系，得出了振子耦合振动的电导纳表达式，并导出了共振频率方程。与一维理论的结果相比，由本文理论得出的振子共振频率与实际测量值更加符合。     

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。     

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。     

低Qm压电振子机电耦合系数的标准计算方法的原理误差分析

压电材料的机电耦合系数通常由谐振及反谐振频率之间的相对间隔确定。常用的ＩＥＥＥ标准计算公式,是由描述理想无损压电振子的电行为方程推导得出的。本文结出了压电材料的固有损耗产生的谐振及反谐振频率的偏移及由此引起的标准公式的误差。代替以往分析时常用的等效电路方法,本文采用把损耗考虑在内的严格的压电振子导纳或阻抗模型。分析结果表明：由测得的谐振子及反谐振频率用标准公式得出的耦合系数小于材料的固有耦合系数;     

低Qm压电振子机电耦合系数的标准 计算方法的原理误差分析

压电材料的机电耦合系数通常由谐振及反谐振频率之间的相对间隔确定。常用的IEEE标准计算公式,是由描述理想无损压电振子的电行为方程推导得出的。本文给出了压电材料的固有损耗产生的谐振及反谐振频率的偏移及由此引起的标准公式的误差。代替以往分析时常用的等效电路方法,本文采用把损耗考虑在内的严格的压电振子导纳或阻抗模型。分析结果表明由测得的谐振及反谐振频率用标准公式得出的耦合系数小于材料的固有耦合系数;误差随固有损耗的增加及耦合的减弱而增加。文中给出了较为详细的分析结果,确定了常用耦合系数标准公式的精确性及适用范围。     

压电陶瓷矩形振子的三维等效电路及其在振子频率特性分析中的应用

在忽略剪切振动、弯曲振动及扭转振动的近似条件下,分析了压电陶瓷矩形振子长度、宽度及厚度振动模式之间的耦合振动,推导出了振子三维耦合振动的等效电路.在此基础上研究了矩形振子耦合振动的共振频率特性并得出了振子的共振频率方程.理论分析表明,压电陶瓷细长条的横向及纵向振动模式是矩形振子在一定几何尺寸条件下的振动模式.按照导出的耦合振动频率方程设计的压电陶瓷矩形振子,其实测共振频率与理论计算值基本符合.     

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。     

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。     

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。     

电极配置对悬臂梁压电振子发电能力的影响

研究了带末端质量块的悬臂梁压电振子多模态振动时的应变分布特点,针对压电陶瓷表面电极配置对压电振子输出电压的影响关系进行压电-电路耦合有限元分析,并建立悬臂梁压电振子发电测试系统,对工作在一阶和二阶谐振频率附近处的压电振子分段电极和连续电极输出功率进行对比分析。研究结果表明,一阶谐振时分段电极的峰值输出功率与连续电极相接近,二阶谐振时分段电极的峰值输出功率增加了900%。相比于连续电极配置法,分段电极配置法可有效提高压电振子在高频振动时的发电能力。     

Dynamic focusing-effect of piezoelectric fibers subjected to radial impact

This paper presents a simple analytical method to solve the response histories of dynamic stresses and transient electric potential in piezoelectric fibers subjected to radial impact. From analytical expressions and calculation results for two kinds of piezoelectric fibers, PZT-4 and BaTiO₃ it is found that dynamic focusing-effects of dynamic stresses and transient electric potential at the center of piezoelectric fibers are dependent on different piezoelectric material. Because electroelastic waves accumulate at the center, and reflect at the external boundary the dynamic stresses and transient electric potential at the center (r = 0) or near the center (r = 0.01) of piezoelectric fibers appear in dynamic focus-phenomena. The results carried out can be used as a reference to piezoelectric sensor and actuator and to solve other transient coupled problems of thermo-electroelasticity in piezoelectric structures.     

阶梯型径向振动环形变幅器的振动特性

文中首先对各向同性弹性薄圆环的径向振动进行了研究,得出了其等效电路。在此基础上,对由双金属圆环组成的阶梯型径向振动变幅器进行了探讨,推出了其径向振动的复合等效电路及其共振频率方程。分析了此类径向振动变幅器的共振频率及径向位移振幅放大系数与其几何尺寸之间的依赖关系。利用数值方法,对变幅器的径向振动特性进行了数值模拟,结果表明,数值结果与解析结果符合很好。     

Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method

Three-dimensional nonlinear thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. The strain–displacement relations are based on the nonlinear Lagrangian strain–displacement relations; that is, nonlinear terms containing derivatives of the displacement in the radial direction are included. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson’s ratio is assumed to be constant. Cylindrical shells are assumed to be under the effect of pressure loading in cosine form, ring pressure loads, electric and temperature fields. Numerical results of stress, displacement, electric and thermal fields are obtained by using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. The convergence of the solution is studied, and results of the axisymmetric loadings are verified with reported results for a cylindrical shell with material properties obeying a power law. Effects of the grading index of material properties, the temperature difference, the ratio of the mean radius to the thickness of the shell, boundary conditions, the thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented.     

A shear lag model of Piezoelectric composite reinforced with carbon nanotubes-coated Piezoelectric fibers

A novel hybrid piezoelectric composite in which the microscopic piezoelectric fiber reinforcements are coated with radially aligned carbon nanotubes (CNTs) is analyzed in this study. A shear-lag model is developed to analyze the load transferred to such coated fibers from the aligned-CNT reinforced matrix in a hybrid composite application in the absence and the presence of the electric field along the length of the fiber. It is found that if the aligned CNTs are radially grown on the surface of the piezoelectric fiber then the axial load transferred to the fiber is reduced in the absence of the electric field while the axial stress in the fiber increases in the presence of the electric filed only. The radial stress in the active piezoelectric fiber significantly increases due to the radial growth of aligned CNTs on the surface of the fibers. This indicates a probable critical window for engineering the surface of the piezoelectric fiber for improving the effective piezoelectric properties. Effects of the variation of the aspect ratio of the piezoelectric fiber and the CNT volume fraction on the load transferred to such CNT-coated piezoelectric fibers are also investigated.     

Bending analysis of piezoelectric exponentially graded fiber-reinforced composite cylinders in hygrothermal environments

The closed-form solutions of a piezoelectric exponentially graded fiber-reinforced hollow cylinder in hygrothermal environment conditions are investigated. The interaction of electric displacement and electric potentials as well as the elastic deformations is discussed. The present piezoelectric fiber-reinforced circular cylinder is subjected to a mechanical load as well as an electric potential at its lateral surfaces. The resultant constitutive equations of the piezoelectric fiber-reinforced composite cylinder are analytically investigated. The thermal conductivity and the moisture diffusivity coefficient are supposed to change continuously in the radial direction by a simple exponential law. The hygrothermoelastic responses of piezoelectric exponentially graded fiber-reinforced hollow circular cylinders are presented. The significant of influence of the graduation of material, temperature, moisture, pressures and electric parameters is investigated. Concluding remarks and appropriate discussions are presented.     

Study on a new type of radial composite piezoelectric ultrasonic transducers in radial vibration

In this paper, a new type of radial composite ultrasonic transducers in radial vibration is presented and studied. The radial composite ultrasonic transducer consists of a solid piezoelectric ceramic thin disk and a hollow metal thin, circular ring in radial vibration; and they are connected together in the radial direction. The radial vibrations of a piezoelectric ceramic thin disk and a hollow, metal, thin, circular ring are analyzed, respectively. Their radial electromechanical equivalent circuits are obtained. Based on the electromechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin disk and the hollow, metal, thin ring, the electromechanical equivalent circuit of the radial composite ultrasonic transducer is derived and the resonance frequency equation is obtained. The theoretical results from the resonance frequency equation are in good agreement with the measured radial resonance frequencies, and they also are in a good agreement with the results from the numerical method.     

TRANSIENT RESPONSE OF A CRACKED INFINITE PIEZOELECTRIC STRIP UNDER ANTI-PLANE IMPACT

By using the well-established integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under anti-plane impact. The dynamic intensity factors of stress and electric displacement are obtained analytically. The results show that the dynamic electric field will promote or retard the propagation of the crack at different stages of the loading process. On the other hand, the response of the electric field is coherent with the applied electric load and independent of the external mechanical load. The result obtained for the anti-plane impact of a cracked infinite piezoelectric ceramic can be regarded as a special case of the present work when the width of the strip tends to infinity.     

A theoretical model on piezoelectric fibre pullout with electric input

A theoretical model of a single piezoelectric fibre pullout from an elastic matrix was developed to study the effect of an input electric field. The stress distributions in the fibre under both mechanical and electric loads are obtained. The relationships between pullout force, induced electric potential and deformation are evaluated by computer simulation. The effects of electric input, piezoelectric parameters and fibre volume fraction on the load- displacement curve for fibre pullout are discussed. Numerical results obtained in this study indicate that the pullout force can be adjusted by changing the value or the direction of the applied electric field. Also, the results show that piezoelectric parameters and fibre volume fraction play important roles on the pullout force in the piezoelectric fibre.     

A hybrid radial boundary node method based on radial basis point interpolation

The hybrid boundary node method (HBNM) retains the meshless attribute of the moving least squares (MLS) approximation and the reduced dimensionality advantages of the boundary element method. However, the HBNM inherits the deficiency of the MLS approximation, in which shape functions lack the delta function property. Thus in the HBNM, boundary conditions are implemented after they are transformed into their approximations on the boundary nodes with the MLS scheme.This paper combines the hybrid displacement variational formulation and the radial basis point interpolation to develop a direct boundary-type meshless method, the hybrid radial boundary node method (HRBNM) for two-dimensional potential problems. The HRBNM is truly meshless, i.e. absolutely no elements are required either for interpolation or for integration. The radial basis point interpolation is used to construct shape functions with delta function property. So unlike the HBNM, the HRBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables, and boundary conditions can be applied directly and easily, which leads to greater computational precision. Some selected numerical tests illustrate the efficiency of the method proposed.     

Antiplane Permeable Edge Cracks in a Piezoelectric Strip of Finite Width

A piezoelectric strip with permeable edge cracks normal to the strip boundaries is analyzed. Under uniform antiplane mechanical shear and inplane electric loading, the distribution of the entire electroelastic field in a cracked piezoelectric strip is determined in explicit analytic form via the conformal mapping technique. It is found that the strain and the electric displacement exhibit the same singularity as the stress near the crack tips, while the electric field is always uniform. The field intensity factors and the energy release rate are independent of the applied electric load for prescribed stress, and related to the applied electric load for prescribed strain.