An Axisymmetric Electrothermoviscoelastic Problem for a Partially Depolarized Piezoceramic Sphere Under Quasistatic Harmonic Loading

The analytical solution is obtained for the vibrations and dissipative heating of a hollow piezoceramic sphere polarized across the thickness, with thermal depolarization taken into account. The sphere is subjected to a quasistatic potential difference varying harmonically with time. The inside surface is heat-insulated and the outside surface is involved in convective heat exchange with the environment. A numerical analysis is made and the depolarization conditions and the effect of the depolarized region on the stress–strain state and heating temperature are analyzed.     

Natural frequencies of submerged piezoceramic hollow spheres

An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained. The project supported by the National Natural Science Foundation of China (No. 19872060)     

Nonaxisymmetric electroelastic vibrations of a hollow sphere made of functionally gradient piezoelectric material

The nonaxisymmetric problem of natural vibrations of a hollow sphere made of functionally gradient piezoelectric material is solved based on 3D electroelasticity. The properties of the material change continuously along a radial coordinate according to an exponential law. The external surface of the sphere is free of tractions and either insulated or short-circuited by electrodes. After separation of variables and representation of the components of the displacements and of the stress tensor in terms of spherical functions, the initially three-dimensional problem is reduced to a boundary-value problem for the eigenvalues expressed by ordinary differential equations. This problem is solved by a stable discrete-orthogonalization technique in combination with a step-by-step search method with respect to the radial coordinate. Moreover, a numerical investigation is performed based on the algorithm used for solving the problem. In particular, we investigate the influence of the geometric and electric parameters on the frequency spectrum at the nonaxisymmetry of natural vibrations of an inhomogeneous piezoceramic thick-walled sphere.     

3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Summary  The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces. Received 28 February 2001; accepted for publication 26 June 2001     

On the dynamics of locally resonant sonic composites

The sound attenuation in a sonic composite is studied using a new method that combines the features of the piezoceramic theory, cnoidal method and genetic algorithms. A sonic composite consists of an array of acoustic scatterers embedded in an epoxy matrix. Acoustic scatterers are piezoceramic hollow spheres made from functionally graded materials – the Reddy and cosine graded hollow spheres. We show that stable attenuation bands may coexist with different patterns of dynamics, including chaos. In order to extend the method towards a tool for analyzing the sound attenuation in sonic composites, the behavior of a real sonic composite is simulated. The results concerning the full band-gaps have been validated by experimental data.     

Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere

Summary  The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also presented. Received 30 October 2001; accepted for publication 21 February 2002 The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016)     

Finite elastoplastic deformation of an internally pressurized hollow sphere

This paper considers large elastoplastic deformations of an internally pressurized hollow sphere of dilatant soil. A complete analytical solution for the expansion of a hollow sphere is developed. The soil is modelled as an elastic-perfectly plastic material obeying the Mohr-Coulomb yield criterion. A non-associated plastic flow rule is used and therefore the dilation of the material is fully taken into account. Closed form solutions are obtained for the stresses and the elastic-plastic deformations of arbitrary magnitude when a hollow sphere of soil is subjected to constant external pressure and monotonically increasing internal pressure. A selection of numerical results is presented to indicate the effects of various key parameters     

Hollow sphere of randomly bonded material subjected to internal pressure

A hollow sphere of an elastic binding material of slight stiffness, bonded randomly by “fiber” segments of a stiffer material, is considered. Polymer material, for example, can be the binder. Such a bonding permits obtaining a material with improved properties, where the material on the whole is quasi-isotropic [1]. The stress distribution in a hollow sphere is obtained.     

Free vibrations of axially polarized piezoceramic hollow cylinders of finite length

The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed for a wide range of their geometric characteristics     

Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere

For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow sphere are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping, and frequency shift.     

Radially polarized functionally graded piezoelectric hollow cylinders as sensors and actuators

An axisymmetric electroelastic problem of hollow radially polarized piezoceramic cylinders made of functionally graded (FG) materials is analyzed. For the material properties of power-law profile, a closed-form solution is derived. For a general gradient variation, an analytic approach is suggested, which reduces the problem to a Fredholm integral equation. Solving the resulting equation, the response of the electroelastic field can be determined. No severe limitation is required for varying material properties in this method. Numerical results of a cylindrical FG piezoelectric tube with PZT-5H as the inner surface ceramic are evaluated, and the distribution of the radial and circumferential stresses as well as the electric potential for piezoelectric sensors and actuators are presented graphically under electric and mechanical stimuli, respectively. Our results indicate that the electroelastic response in an FG piezoceramic tube with material properties decreasing when the radius increases becomes more obvious than that with material properties increasing. Moreover, the gradient index strongly affects the stress distribution and electric response. The obtained results are helpful for the design of annular cylindrical FG piezoelectric sensors/actuators.     

Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.     

Resonant Vibrations and Dissipative Heating of an Infinite Piezoceramic Cylinder

The monoharmonic radial vibrations and dissipative heating of an infinite hollow piezoceramic cylinder are studied in dynamic formulation, taking into account the temperature dependence of the complex electromechanical characteristics over a wide range of temperatures, including depolarization temperatures. The influence of the heat exchange conditions, the level of electric load, and geometry on the thermoelectromechanical characteristics is studied in the case of forced vibrations at the first resonance__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 101–107, March 2005.     

用库仑-莫尔屈服准则对厚壁球的极限分析

用库仑－莫尔屈服准则对厚壁球进行了极限分析。该分析能够较好地反映出考虑材料的拉压屈服强度不同而对结构极限承载能力的影响。结果表明,厚壁球的极限承载能力随坟拉比Ｋ的增大而增大。本文导出的公式,对于理论研究和工程设计都具有参考价值。     

缩径焊接空心球压弯下节点刚度研究

以缩径焊接空心球节点为研究对象,运用正交设计法设计了9个试件,试验研究了压弯受力状态下节点的名义抗弯刚度。利用ABAQUS软件建立缩径焊接空心球节点分析模型,采用线性强化应力-应变关系,考虑几何和材料非线性的影响,对压弯受力状态下的缩径焊接空心球节点的抗弯刚度进行了有限元分析,绘制了节点弯矩-转角曲线,得到了节点名义抗弯刚度,验证了有限元模拟的准确性。进而参数化分析了不同因素对节点抗弯刚度的影响。以虚功原理为基础,推导了压弯作用下缩径焊接空心球节点抗弯刚度简化计算公式。结果表明:在本文研究范围内,节点的破坏模式为球凹陷破坏;锥管小径端直径与球径比d/D对节点抗弯刚度的影响最大,球壁厚与球径比t/D的影响次之,锥管长度L的影响最小;本文提出的缩径焊接空心球节点刚度简化计算公式具有一定的精度。     

Low-velocity viscous incompressible fluid flow around a hollow porous sphere

The problem of a viscous incompressible fluid flow around a hollow porous sphere in the Stokes approximation, in which the filtration flow through the sphere shell obeys the Darcy law, is solved. The force acting on the sphere from the fluid is calculated. The limiting cases are considered. The stream function is constructed.     

Stress Analysis of Rotating Inhomogeneous Transversely Isotropic Hollow Spheres

An approach is proposed to the stress–strain analysis of hollow, arbitrarily inhomogeneous, transversely isotropic, either closed or open spheres that rotate about the axis of symmetry with a constant angular velocity. The stress problem for a rotating single-layer sphere and a segment of a sphere is solved as an example. The distribution of radial stresses and displacements along the radius of the sphere is analyzed depending on thickness variation at arbitrary points of the sphere     

含空心球涂层粒子复合材料界面的脱粘应力分析

在球对称拉伸载荷作用下针对空心球涂层复合材料分析了空心球涂层粒子增强复合材料的局部应力场，得到了界面临界脱粘应力的解析表达式．讨论了各相几何参数对非均匀涂层空心球粒子临界脱粘应力的影响，比较了均匀涂层和非均匀涂层的脱粘应力．结果表明：在球对称拉伸下界面脱粘更容易发生在涂层相与基体相界面间，空心球的壁厚和涂层厚度是影响界面临界脱粘应力的重要因素，因而选择适当的空心球、涂层厚度和提高界面粘结能将有利于提高界面的临界脱粘应力．     

Free nonaxisymmetric vibrations of radially polarized hollow piezoceramic cylinders of finite length

The three-dimensional problem of free nonaxisymmetric vibrations of hollow piezoceramic cylinders with axial polarization is considered. An efficient numerical analytic method to solve boundary-value problems is proposed. The original three-dimensional problem of electroelasticity is reduced to a two-dimensional problem by representing the displacement components as standing circumferential waves. Spline collocation with respect to the axial coordinate is used to reduce this two-dimensional problem to an eigenvalue boundary-value problem with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental-search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed in a wide range of their geometric characteristics     

Acoustic radiation from a submerged hollow FGM sphere

An exact study based on the linear theory of elasticity is presented for the steady-state sound radiation characteristics of an arbitrarily thick radially inhomogeneous elastic isotropic hollow sphere, immersed in and filled with ideal compressible fluids, and subjected to an arbitrary axisymmetric time-harmonic driving force at its internal surface. A modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics by means of the laminated approximation approach. Taylor’s expansion theorem is subsequently employed to solve the modal state equation, ultimately calculating a global transfer matrix. Numerical results are presented for a water-submerged/air-filled steel/zirconia FGM hollow sphere under an axisymmetric distributed internal pressure force. The effects of shell wall thickness, the material compositional gradient, frequency, and subtended polar angle of the internal pressure force on the far-field radiated pressure directivity patterns as well as the total radiated power are examined. It is demonstrated that the material gradient can significantly change the acoustical characteristics of hollow inhomogeneous sphere, especially for thick shells at high excitation frequencies. Limiting cases are considered and good agreements with available results as well as with the computations made by using a finite element package are obtained.