Free vibration of piezoelectric annular plate

General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated. Project (No. 10002016) supported by the National Natural Science Foundation of China     

Analytical modelling and free vibration analysis of piezoelectric bimorphs

INTRODUCTION Piezoelectric bimorphs (or benders), a special type of piezoelectric device, which can produce flexural deformation significantly larger than the length or thickness deformation of the individual piezoelectric layers, have been widely used as elec- troacoustic transducers, medical devices and micro- robot due to their characteristics of easy miniaturiza- tion, high positioning accuracy, sensitive response, and large displacement (e.g., Shirley and Hampton, 1978; Ha and Kim, 2…     

Three-dimensional vibration of thick plate

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3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.     

Active control of structural vibration by piezoelectric stack actuators

INTRODUCTION Passive methods have played an important role for a long time (Snowdon, 1973; Nelson, 1982; Pan et al., 1992) in vibration and noise control. However, with inrush of some novel engineering structures and machines, such as super high-speed machine tools, long-span bridges, thin shell structures, micro elec- tromechanical systems and so on, traditional passive control approaches are not efficient enough for con- trolling structure noise and vibration from these novel systems an…     

Nonlinear vibration of circular plate with variable thickness

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Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates

INTRODUCTION In quartz crystal resonator design, the mass effec of the electrodes must be considered to achieve ac curate prediction of the fundamental thickness-shea frequency, as analyzed and demonstrated b Bleustein and Tiersten (1968), which is considered t be the exact frequency solutions in making necessar comparisons with solutions from two-dimensiona plate equations and deriving the correspondent cor rection factors (Mindlin, 1972). When the crysta plate is relatively thick or the…     

Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media

INTRODUCTION The traditional method of solving solutions of the transversely isotropic piezoelectric media belongs to Lagrange formulation so that the method of sepa- ration of variables cannot be applied due to the in- volvement of high order partial differentiation in the Euclidian space and is difficult for some problems. New theoretical system or method is a key for the investigation of piezoelectric materials. Since the foundational equations (Sosa and Pak, 1990) in transversely iso…     

A generalized plane strain theory for transversely isotropic piezoelectric plates

INTRODUCTION For moderate thickness plate containing notches or holes, neither plane stress nor plane strain theory can describe its true deformation states (Jin and Hwang, 1989). This well known drawback has mo- tivated many analytical and numerical studies carried out to determine the effect of plate thickness on the in-plane stress distribution. Pioneering work on the along depth stress components, i.e. the K-M gener- alized plane strain theory was proposed by Kane and Mindlin (1956)…     

A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media

INTRODUCTION Since the phenomenon of piezoelectricity in natural crystals was discovered in 1880, it has been applied in many fields, such as smart structure, sensing devices and active control, because of its special properties. Combining electrical behavior with mechanical deformation is the special property which attracted great interest of researchers. Many models have been developed for studying piezoelec- tric effects. Dunn and Wienecke (1996) used Green’s functions for transverse…     

Resonant frequencies of a piezoelectric drum transducer

This paper presents a piezoelectric-metal structure called a drum transducer. An equation for calculating the resonance frequency of the drum transducer is obtained based on thin plate elastic theory of piezoelectric and metal material combined with the Rayleigh-Ritz method. The finite element method （FEM） was used to predict the excitation frequency of the drum transducer. To verify the theoretical analysis, the input impedance characteristic of the drum transducer was measured using an experimental method. The results obtained from theoretical analysis were in very good agreement with those from the FEM and experimental results. The effect of geometrical changes to the thick-walled steel ring of the drum transducer at the first resonance frequency is also described. The calculated results were found to be in good agreement with the FEM results. The results indicate that the first resonance frequency of the drum decreases with the increasing inner diameter of the thick-walled steel ring.     

弹性地基上四边自由矩形大挠度薄板的自由振动

考虑具有粘滞阻尼的Winkler地基上四边自由受简谐激励的矩形板的偏微分方程组,找到了满足所有边界条件的近似挠度函数,利用Galerkin方法把偏微分方程表示的非线性动力学方程转化为用常微分方程表示的非线性动力学方程。在KBM法的基础上,引入谐波平衡的观点研究了弹性地基上四边自由无阻尼矩形板自由振动,应用Hamiltonion函数研究了系统能量与周期的关系。     

高温压电材料的概况及发展趋势

介绍了高温压电材料的研究现状,综述了钙钛矿、钨青铜型、铋层状、碱金属铌酸盐结构体系4种不同压电陶瓷的结构及研究情况,并指出了高居里点压电陶瓷的研究方向和发展趋势。     

Stochastic optimal control of first-passage failure for rectangular thin plate vibration model under gaussian white-noise excitations

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito? stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method.     

研究环形光阑的衍射场

由波前相因子判断法并考虑到孔径的影响,来揭示环形光阑的夫琅禾费衍射场所含成分。分别给出衍射场的积分表达式,进而导出像面衍射场振幅分布公式,并显示出像面衍射场光强分布图。为光阑的夫琅禾费衍射场的分析提供了一种新的分析方法。     

Modeling of sensor function for piezoelectric bender elements

An analytical sandwich beam model for piezoelectric bender elements is derived based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution for coupled electric potential in piezoelectric layers. Shear coefficient is introduced to correct the effect of transverse shear strain on shear force and the electric displacement integration. Static and free vibration analyses of simply-supported bender elements are carried out for the sensor function. The results illustrate the high accuracy of the present model compared with the exact 2D solutions.     

半群x*的一族极大自由幺子半群的构造性证明

分析自由幺半群X﹡的一族特殊幺子半群,并以X﹡为顶点集构造了一个语言图,利用它证明了该族子半群是半群X﹡的一族极大自由幺子半群。     

高层建筑框架结构与基础地基共同工作的半解析自由振动分析

将高层建筑框架结构与其基础等效连续化为一个半无限大弹性地基上的闭口薄壁筒体,并以此三维模型,用半解析法对其动力特性进行计算.计算结果表明:简化模型合理,分析方法正确,为高层建筑框架结构的自由振动计算提供了一种合理可行的简化计算方法,并得出了一些结论.     

Dynamic responses of a multilayer piezoelectric hollow cylinder under electric potential excitation

INTRODUCTION Recently, more and more investigations have been conducted on multilayer piezoelectric media. Kharouf and Heyliger (1994) and Heyliger and Ra- mirez (2000) dealt with the free vibration problems of laminated piezoelectric cylinders and discs, respec- tively. Chen (2000) considered the free vibration of (multilayer) nonhomogeneous piezoceramic hollow spheres by employing a separation formulation for displacements. Chen (2001) developed a state-space method for free vibration …     

弹性地基上四边自由矩形大挠度薄板复杂运动研究

考虑具有粘滞阻尼的Winkler地基上四边自由受简谐激励的矩形板的偏微分方程组,找到了满足所有边界条件的近似挠度函数,利用Galerkin方法把偏微分方程表示的非线性动力学方程转化为用常微分方程表示的非线性动力学方程。应用多尺度法求得了系统的主共振解,并对主共振解的静态分岔方程进行了奇异性分析。应用Floquet理论和Melnikov方法分析了系统的全局特性。