A circular cylindrical, radially polarized ceramic shell piezoelectric transformer

We propose a circular cylindrical shell piezoelectric transformer of radially polarized ceramics operating in thickness-stretch modes. Two theoretical analyses involving different approximations are performed on the proposed transformer using the 3-D equations of linear piezoelectricity. The transforming ratio, input admittance, and efficiency of the transformer are calculated and compared with those of a previously analyzed circular cylindrical shell transformer of axially polarized ceramics operating in shear modes.     

Frequency-dependent open-circuit acoustic sensitivity of fluid-filled, coated, radially polarized piezoelectric ceramic cylindrical shells of arbitrary thickness and infinite length

The frequency-dependent free-field open-circuit voltage generated by radially polarized piezoelectric ceramic fluid-filled shells of infinite length coated with an elastic layer and excited by a plane acoustic wave is studied. The shell and the coating are of arbitrary thickness and are anisotropic. It is shown that the charge density in the piezoelectric shell is zero by using the electrostatic and open-circuit conditions. General expressions for the pressures and radial velocities in the interior and exterior fluids are obtained by using the finiteness and radiation conditions, respectively. General expressions for the radial stresses and velocities in the piezoelectric shell and elastic coating are also determined by using two-dimensional equations of state and axisymmetric equations of motion. The coefficients in the general expressions are then determined by using the continuity conditions at the various interfaces. Finally, an expression for the open-circuit sensitivity is obtained by using a piezoelectric equation of state. Numerical results are presented for air, water, and vacuum in the interior, two types of elastic coating, and piezoelectric shells with various thicknesses. The effect of neglecting anisotropy on the sensitivity is also illustrated     

Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories

Summary The dynamic stability of thin, laminated cylindrical shells under combined static and periodic axial forces is studied here using three common thin shell theories, namely Donnell's, Love's and Flügge's shell theories. A normal-mode expansion of the equations of motion yields a system of Mathieu-Hill equations the stability of which is examined using Bolotin's method. The present study examines and compares the effects of the use of the various shell theories on the dynamic stability analysis.     

一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元

基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。      

Stability analysis of cylindrical shells using refined non‐conforming rectangular cylindrical shell elements

The accuracy of stability analysis depends on the accuracy of both the element stiffness matrix and geometry stiffness matrix. Therefore, when carrying out the stability analysis of thin cylindrical shells using the finite element methods will require, firstly, a refined non‐conforming rectangular curved cylindrical shell element RCSR4 is proposed according to the refined non‐conforming FE method, in which both the C¹ and C⁰ weak continuity conditions are satisfied and as a result, can ensure the convergence of computation. At the same time, a refined geometrical stiffness matrix is introduced to replace the standard consistent geometrical stiffness matrix. Simple expressions of the refined constant strain matrices with adjustable constants are introduced with respect to the weak continuity conditions. Numerical examples are presented to show that the present method can indeed improve the performance and the accuracy in stability analysis. Copyright © 2001 John Wiley & Sons, Ltd.     

Thermoelastic solution for static deformations of functionally graded cylindrical shell bonded to thin piezoelectric layers

We study infinitesimal axisymmetric deformations of a functionally graded shell with piezoelectric layers perfectly bonded to its inner and outer surfaces, and the hybrid structure subjected to thermo-electro-mechanical loads. The material properties of the shell are assumed to be graded in the radial direction according to a power law but Poisson’s ratio is assumed to be constant. For simply-supported and grounded edges kept at a constant temperature, the problem is analyzed analytically by assuming a Navier type solution for the governing equations and the state space method for solving the resulting ordinary differential equations. Numerical results are given to illuminate influences of the mechanical and the electrical boundary conditions, the exponent of the power law variation, and the radius to thickness ratio.     

A solution of laminated cylindrical shells using an unconstrained third-order theory

An unconstrained third-order shear deformation theory is presented for the analysis of laminated anisotropic cylindrical shells. Based on the realistic through-thickness distribution of the in-plane displacements, a zig-zag function is used to approximate the piece-wise nature of the displacements. The zero-shearing condition on the laminate surfaces and continuous conditions for the transverse shear stresses on the inter-laminar surfaces have been considered for the final stresses calculation, the displacement functions remain to be unconstrained. This theory is very useful for the finite element analysis because it requests only C⁰ continuity for the assumed displacement fields. By comparing with three-dimensional elasticity theory for laminated orthotropic cylindrical shell, the performance of the present theory is verified. The problems solved in this paper illustrate that the present theory is very accurate for the thin and moderately thick shells.     

Vibration control of a simply supported cylindrical shell using a laminated piezoelectric actuator

Summary This paper develops a novel laminated piezoelectric actuator (LPA) to control the vibration of a cylindrical shell structure, which is fabricated through bonding multiple piezoelectric layers of the same property together. The electromechanically coupled equations of the system are derived based on the classic shell theory. A parametric study is then conducted to evaluate the effects of geometric and physical properties of the actuator on actuating forces. The results show that as the number of layers increases, the actuating forces per voltage produced by LPA in the axial, circumferential and radial directions of the shell all increase noticeably. The active vibration control of a simply supported cylindrical shell using LPA of different layer numbers is simulated as well under a velocity feedback scheme. It is indicated that with the same control voltage the LPA can obtain a better control performance than the conventional single layer piezoelectric actuator as expected and the targeted radial modal vibration of the shell is attenuated significantly.     

Torsional oscillations of a finite inhomogeneous piezoelectric cylindrical shell

Torsional wave motion of a finite right circular cylindrical shell of inhomogeneous piezoelectric material of (622) crystal class under time dependent electric potential on the boundary is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as expf((r)) where f is a suitable function of the radial distance. Two related problems, investigated by the author, in the papers [1, 2] are shown to be particular cases of the present problem.     

Vibration characteristics of a corrugated cylindrical shell piezoelectric transducer

We study coupled extensional and flexural cylindrical vibrations of a corrugated cylindrical shell piezoelectric transducer consisting of multiple pieces of circular cylindrical surfaces smoothly connected along their generatrices. Using the classical shell theory, a theoretical solution is obtained. Based on the solution, basic vibration characteristics of resonant frequencies, mode shapes, and internal forces are calculated and examined for the corrugated transducers, consisting of a few circular pieces each about 50 μm thick, with radius of 5 mm and span angle of 120°. For these transducers the first resonance is of the order of 10-100 Hz.     

Fabrication of thin wall cylindrical shells by sputtering

In this paper we describe the process used to grow thin wall cylindrical shells by sputtering. The shells are grown on both sacrificial aluminum and reusable stainless steel mandrels. The post-deposition process used to remove the shells from the mandrels is described. The effects of deposition conditions and post-deposition treatment on crystallographic structure are presented. Comparisons of sputtered shells are made with conventionally machined shells with respect to crystallography, dimensional uniformity and performance. Some test results of sputtered thin wall cylindrical shells used as pressure-sensing elements are given.     

A global-local higher order theory for multilayered shells and the analysis of laminated cylindrical shell panels

Based on the global-local superposition technique proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212.], a global-local higher order laminated shell model is proposed for predicting both displacement and stress distributions through the thickness of laminated shells. This shell model satisfies transverse shear stress continuity conditions at interfaces as well as free surface conditions of transverse shear stresses. The merit of this model is that transverse shear stresses can be accurately predicted directly from constitutive equations without smoothing techniques. Cylindrical bending of laminated and sandwich shell panels is chosen to assess the present model wherein the results from several 2D laminated shell models and three-dimensional elasticity solution are available for comparison. In addition, thermal bending and thermal expansion of laminated cylindrical shell panels are also considered in this paper.     

Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method

Three-dimensional solution for static analysis of functionally graded (FG) cylindrical shell with bonded piezoelectric layers is presented using differential quadrature method (DQM) and state-space approach. Applying the DQM to the governing differential equations and to the edges boundary conditions, new state equations about state variables at discrete points are derived. The stress, displacement, and electric potential distributions are obtained by solving these state equations. The convergence and accuracy of the present method is validated by comparing numerical results for the hybrid FG cylindrical shell with simply-supported edges with the analytical solution that has been published in the literature. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers and gradient index on the mechanical behavior of shell is studied.     

Torsional wave motion of a finite inhomogeneous piezoelectric cylindrical shell

Torsional oscillations of a finite right circular eylindrical shell of inhomogeneous piezoelectric material of (622) crystal class under a time dependent electric potential on the boundary is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as a certain power of the radial distance. Under certain conditions, the amplitudes of torsional oscillations are found to be high for small values of the inner radius of the shell.     

Multipole theory for tight focusing of polarized light, including radially polarized and other special cases

A multipole expansion, based on spherical harmonics, provides an efficient method for calculating the field in the focal region of a lens for radially polarized illumination, or other illumination polarization and phase distributions, including vortex beams. The multipole approach also has the benefit of providing a simple measure of the purity of the longitudinal field mode. The method is also convenient for calculation of fields scattered by particles and calculation of optical trapping forces.     

Formation of a sub-wavelength longitudinally polarized beam using a radially polarized controllable dark-hollow beam

On the basis of vector diffraction theory, the tightly focusing properties of radially polarized controllable dark-hollow (CDH) beams are examined theoretically. Calculation results demonstrate that by choosing the initial parameters of the proposed light beams suitably, a sub-wavelength (0.422λ) longitudinally polarized light beam with high beam quality (82.2%) can be formed without any filters. Meanwhile, we find that a relatively long depth of focus benefits from larger beam order. The dependence of the focal spot size on the parameters such as truncation parameter, variation constant, and beam order is also explored in detail. Moreover, an alternative method to generate the CDH beams is proposed.     

The general theory of thin elastic shells

Variationsl methods can consistently be used to derive the equations of shell theory, by introducing a finite number of internal constraints. A systematic derivation of particular nonlinear and linear theories becomes then possible. Variational methods serve also to prove the existence and in some cases the uniqueness of the solution. They provide also with error estimates.     

Three dimensional analysis of piezoelectric circular cylindrical shell of finite length

Summary An exact elasticity solution for a simply supported piezoelectric circular cylindrical shell of finite length is presented. Different boundary conditions are considered, which correspond to the respective situations when it is acted as sensor or actuator. The stresses, displacements and electric potential distributions are shown. Our results show that the distributions depend strongly on the boundary conditions and can not be justified by purely elastic structures. The presented results can be used not only to assess various approximate theories but also to enhance the understanding of the response behavior of piezoelectric structures.     

Tri-axial sensors and actuators made of a single piezoelectric cylindrical shell

Electromechanical transducers for sensing and actuating disturbances or vibrations have been used in many fields of applications. There have been transducers of different configuration developed for the unidirectional transduction. This paper demonstrates a single element transducer for tri-axial components made of a piezoelectric cylindrical shell. The separation of the tri-axial transductions is achieved by devising a proper electrode arrangement. The structure and the fundamental idea are first presented, and then the numerical analysis by means of the finite element modeling follows, and their characteristics and behaviors are then experimentally verified.