Axisymmetric vibration of piezocomposite hollow circular cylinder

Summary The axisymmetric vibration of a piezoelectric laminated hollow circular cylinder has been studied for an imperfect interface model. The frequency equation is derived for traction free inner and outer surfaces of the hollow cylinder with continuity conditions at the bonding interfaces. The composite cylinder is composed of two different piezoelectric materials belonging to 6 mm class and a hypothetical Linear Elastic Material with Voids (LEMV) as bonding layer. Numerical solutions of the frequency equation are obtained for the composite cylinder ceramic(1)/LEMV/ceramic(2). Computational results are presented as dispersion curves as well as in tables to characterize the attenuation of axial waves for three layered cylinders with and without voids in the thin LEMV layer.     

Three-dimensional BEM for piezoelectric fracture analysis

A boundary element approach with quadratic isoparametric elements, quarter-point elements and singular quarter-point elements for three-dimensional crack problems in piezoelectric solids under mechanical and electrical loading conditions, is presented in this paper for the first time. The procedure is based on Deeg's fundamental solution for anisotropic piezoelectric materials, and the classical extended displacement boundary integral equation. Stress and electric displacement intensity factors are directly evaluated as system unknowns, and also as functions of the computed nodal displacements and electric potentials at crack faces. Special attention is paid to the fundamental solution evaluation. Several three-dimensional crack problems in transversely isotropic bodies under mechanical and electrical loading conditions are analysed. Numerical solutions computed for prismatic cracked 3D plate problems with a plane strain behaviour are in very good agreement with their corresponding 2D BE solutions. Results for a penny shape crack in a piezoelectric cylinder are presented for the first time. The proposed approach is shown to be a simple, robust and useful tool for stress and electric displacement intensity factors evaluation in piezoelectric media.     

Equilibrium of Elastic Hollow Inhomogeneous Cylinders of Corrugated Elliptic Cross-Section

The approach to the solution of a three-dimensional boundary-value stress problem for elastic hollow inhomogeneous cylinders of corrugated elliptic cross-section is proposed. The boundary conditions make it possible to separate variables along the length at the cylinder ends. It is proposed to include additional functions into the resolving system of differential equations. These functions enable the variables to be separated along a directrix using discrete Fourier series. The boundary-value problem derived for the system of ordinary differential equations is solved by the stable numerical method of discrete orthogonalization over the cylinder thickness. Results in the form of plots and tables are presented.     

Diameter estimation of cylinders by the rigorous diffraction model

The Fraunhofer diffraction formula is commonly used for estimating the diameter of thin cylinders by far field diffractometry. However, an experimental systematic overestimation of the value of the cylinder diameter by this diffraction model and other three-dimensional models has been reported when this estimation is compared with those obtained from interferometric techniques. In this work, a rigorous electromagnetic diffraction model is analyzed to determine the cylinder diameter by using the envelope minima of the far field diffraction pattern. The results of this rigorous model are compared with those from the Fraunhofer diffraction formula. The overestimation by the Fraunhofer model is predicted theoretically, presenting a dependence on the wavelength, the polarization state of the incident wave, and the cylinder diameter. The discrepancies are shown to be due to the three-dimensional geometry.     

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.     

Integral formulations and bounds for two phase Stefan problems initially not at their fusion temperature

Summary The classical two phase Stefan problems for spheres, cylinders and slabs do not, in general, admit exact solutions. For a number of genuine two phase moving boundary problems involving these geometries integral formulation are obtained which generalize known results for idealized one phase Stefan problems and can be utilized to obtain upper and lower bounds on the motion of the moving boundary, even though the analysis is complicated considerably by the presence of a nontrivial second phase. The problems considered are the inward thawing of an initially subcooled solid contained within a finite sphere, cylinder or slab, or within a region bounded by concentric spheres, cylinders or planes, as well as the outward thawing of an initially subcooled solid in the finite region surrounding a sphere, cylinder or plane. The relation of the integral for the boundary motion to the enthalpy is noted, and the bounds obtained for the cases of inward thawing of spheres, cylinders and slabs are compared with exact numerical solutions, generated by the enthalpy method. From these comparisons it becomes apparent that the bounds are adequate when the latent heat is the dominant thermal factor, that is, when more heat is required to produce the change of phase than to warm the substance. However, when this is not the case, that is, when the sensible heat is the dominant thermal factor, further analysis is needed.With 5 Figures     

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method

In this paper, dynamic analysis of nanocomposite cylinders reinforced by single-walled carbon nanotubes (SWCNTs) subjected to an impact load was carried out by a mesh-free method. Free vibration and stress wave propagation analysis of carbon nanotube reinforced composite (CNTRC) cylinders are presented. In this simulation, an axisymmetric model is used. Four types of distributions of the aligned carbon nanotubes (CNTs) are considered; uniform and three kinds of functionally graded (FG) distributions along the radial direction of cylinder. Material properties are estimated by a micro mechanical model. In the mesh-free analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Effects of the kind of distribution and volume fractions of carbon nanotubes and cylinder thickness on the natural frequencies and stress wave propagation of CNTRC cylinders are investigated. Results obtained for this analysis were compared with FEM and previous published work and good agreement was seen between them.     

Stresses in cross-ply laminated circular cylinders of axially variable thickness

Summary This paper presents the results from an analytical investigation of the behavior of composite circular cylinders subjected to internal and external surface loading. The present cylinder consists of a number of homogeneous ply groups of axially variable thickness. Each ply group forming a layer is treated as an individual thin elastic cylinder of generally orthotropic material with interfacial stresses on the inner and outer surfaces of the layer as boundary loading. The deformation and stresses in each layer can be expressed in terms of interfacial stresses along the exterior surfaces of each layer. All displacement and stresses throughout the composite cylinder can be determined subsequently after satisfying boundary conditions at the inside and outside surfaces of the cylinder in conjunction with the recurrence relationship among interfacial stresses. Numerical results are presented for different values of the inner-to-outer ratio, number of layers, stacking sequence, axially-variable-thickness parameter, and load factor. Based on the presented results, conclusions can be drawn concerning the cylinder behavior and its sensitivity to different parameter variations.     

功能梯度压电压磁圆柱轴对称的静力学响应

针对无限长功能梯度压电压磁空心圆柱,研究轴对称空心圆柱电磁弹耦合静力学问题。在柱坐标系下,假定材料参数沿径向为幂函数分布,推导出在外激励作用下空心圆柱体中位移、应力、电势以及磁势等物理场的解析解。数值讨论中,针对BaTiO₃-CoFeO₄复合材料空心柱体,在不同边界条件下得到了不同梯度参数及不同厚度下空心圆柱应力、电势和磁势的分布规律。结果表明,对于功能梯度压电压磁空心圆柱,材料的失效主要是由于环向应力引起的,且圆柱厚度对环向应力有着显著影响。此外,梯度参数强烈影响功能梯度压电压磁传感器/制动器的电/磁输出和力学性能。结果对压电压磁圆柱型传感器/制动器的设计和分析具有一定的指导作用。     

Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements

Natural frequencies for free vibration of infinite piezoelectric cylinders are computed using finite elements that are formulated in cylindrical coordinates. The finite-element method is used to model the cross-section of the cylinder in r, theta coordinates using circular sectors. Material constants that are functions of theta are allowed to vary in each circular sector and are computed using standard tensor transformations. The accuracy of the finite-element formulation is verified using previous results for isotropic cylinders and axisymmetric piezoelectric cylinders. New results are tabulated for frequencies of free vibration of solid and hollow piezoelectric cylinders of LiNbO(3) of crystal class 3m. Displacements for typical mode shapes are illustrated graphically.     

Three-dimensional analysis of an antiparallel piezoelectric bimorph

Summary Three-dimensional electromechanical responses of a piezoelectric bimorph are studied. The bimorph is antiparallel in the sense that it consists of two identical, plate-like piezoelectric elements with opposite poling directions. Both the top and bottom surfaces of the bimorph are fully covered with negligibly thin conductive electrodes. By introducing a small parameter and using the transfer matrix method it is shown that a three-dimensional solution of the problem can be readily constructed, provided the solution to a set of two-dimensional equations very similar to those in the classic plate theory is obtainable. The three-dimensional solution satisfies all the field equations as well as the boundary conditions on the major surfaces and at the interface between the two piezoelectric plates. In many special cases, the electric edge condition can be fulfilled point by point, and thus the solution is exact in Saint-Venant's sense. The formulation and new analytical results for a strip-shaped cantilever bimorph under the action of applied voltage and end moment are presented.     

平面应变轴对称压电圆柱壳的随机响应

提出求解随机激励轴对称压电圆柱壳响应的一种方法，并导出相应的解析表达式。首先给出压电圆柱壳在边界随机激励下的基本方程；然后通过位移与电势的变换，将随机激励变换到运动方程中；再利用Legendre多项式展开位移，应用Galerkin法化偏微分的运动方程为常微分方程组；最后根据随机振动理论，得到压电圆柱壳位移与加速度响应的均方值，由此可计算随机响应、分析有关因素的影响与机电耦合关系等。分析说明了存在的机电耦合项，及由此产生广义刚度的非对称性。     

充填聚氨酯泡沫的薄壁金属筒的力学性能研究

通过充填聚氨酯泡沫的薄壁金属圆筒的力学性能试验,研究薄壁金属圆筒内充填聚氨酯泡沫的作用和效果。试验比较了空心薄壁金属圆筒和充填聚氨酯的薄壁金属圆筒的轴向抗压荷载一位移曲线和破坏模式．试验结果表明充填聚氨酯后可大大改善薄壁金属筒的力学性能,提高其抗变形和吸收能量的能力．     

The transient heaving motion of floating eylinders

Summary The transient heave response of a freely floating cylinder with given initial conditions is obtained by a simultaneous time-domain solution of the fluid-motion and rigid-body dynamics problems. Volterra's method is used to derive the integral equation associated with the fluid motion. It is shown that the unit initial-velocity response is simply the time-derivative of the unit initial-displacement response multiplied by one half of the infinite-fluid virtual mass of the cylinder. Numerical evaluation of integrals related to the unsteady waterwave Green function is facilitated by expressing them in terms of the complex error function. Results for the transient motion of semi-circular, triangular, and rectangular cylinders are presented and discussed. Experimental measurements for the case of a semi-immersed circular cylinder agree excellently with the theoretical calculations.     

Magnetoelastodynamic stress and perturbation of magnetic field vector in an orthotropic laminated hollow cylinder

An analytical method is presented to solve magneto-elastic wave propagation and perturbation of the magnetic field vector in an orthotropic laminated hollow cylinder with arbitrary thickness. The magnetoelastodynamic equation for each separate orthotropic hollow cylinder is solved by making use of finite Hankel transforms and Laplace transforms. The unknown constants involved in the solution for each separate layer are determined by using the interface continuity conditions between layers and the boundary conditions at the internal and external boundaries of the laminated hollow cylinders. Thus, an exact solution for magnetoelastodynamic stresses and perturbation response of an axial magnetic field vector in laminated hollow cylinder is obtained. From sample numerical calculations, it is seen that the present method is suitable to solve magnetoelastodynamic problems of laminated hollow cylinders subjected to a radial shock load and an axial magnetic field.     

The eigenvalue problem for hollow circular cylinders

In three-dimensional elasticity the solution of the biharmonic equation for a hollow circular cylinder can be presented in terms of Bessel functions. If there are no surface tractions on either of the radial faces and no thermal effects, an eigenvalue problem arises. A method of establishing these eigenvalues and tables of them for various types of hollow cylinders are presented. Two special cases are investigated, namely, as the ratio of radii tends to unity, that is, a ‘thin shell’, and as the ratio tends to infinity, which can either be regarded as the inner radius tending to zero for a fixed outer radius or as the outer radius tending to infinity for a fixed inner.The eigenvalues are subsequently used for the calculation of the effect of end loading on a semi-infinite length cylinder. From this a quantitative comparison can be made with thin shell theory in the transition region between thin and thick shells of this type.     

Stokes flow past a swarm of porous circular cylinders with Happel and Kuwabara boundary conditions

The problem of creeping flow past a swarm of porous circular cylinders with Happel and Kuwabara boundary conditions is investigated. The Brinkman equation for the flow inside the porous cylinder and the Stokes equation outside the porous cylinder in their stream function formulations are used. The force experienced by each porous circular cylinder in a cell is evaluated. Explicit expressions of stream functions are obtained for both the inside and outside flow fields. The earlier results reported by Happel and Kuwabara for flow past a solid cylinder in Happel’s and Kuwabara’s cell model, have been deduced. Analytical expressions for the velocity components, pressure, vorticity and stresstensor are also obtained     

Finite element analysis of vortex shedding oscillations from cylinders in the straight channel

In this paper a GCL (Geometry Conservation Law) – preserving finite element model is developed to simulate the fluid-structure interaction phenomena. The boundary locations are part of the solution procedures. Within the moving grid framework, the employed numerical method involves the operator splitting technique, balance tensor diffusivity (BTD), Runge-Kutta time-stepping method, and an element-by-element conjugate gradient iterative solver. Flows around a self-vibrating cylinder and elastically supported cylinders are investigated to validate the present method. The simulated results agree well with available data in the literature. The lock-in phenomenon that may cause the unstable motion of cylinders is also revealed. It is significant from the simulated 2×2 four cylinders result that the rear two cylinders approach to each other at a time earlier than the front two ones.     

Transient solution of temperature field in functionally graded hollow cylinder with finite length using multi layered approach

In this paper by using a multi-layered approach based on the theory of laminated composites, the solution of temperature in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions are presented. The material properties are assumed to be temperature-independent and radially dependent. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Employing Laplace transform techniques and series solving method for two-dimensional heat conduction equation in the cylinder, solutions for the variation of temperature with time as well as temperature distribution through the cylinder are obtained.     

A three-dimensional elasticity solution for functionally graded rotating disks

A semi-analytical three-dimensional elasticity solution for rotating functionally graded disks for both of hollow and solid disks is presented. The aim is to generalize an available two-dimensional plane-stress solution to a three-dimensional one. Although for the thin disks problems the two-dimensional solution provides appropriate results, for the thick disks, a three-dimensional elasticity solution should be considered to avoid poor results. It is shown that although the plane-stress solution satisfies all the governing three-dimensional equations of motion and boundary conditions, it fails to give a compatible three-dimensional strain field. A valid three-dimensional solution has been introduced by modifying the plane-stress solution.