An analytical method for thermal stresses of a functionally graded material cylindrical shell under a thermal shock

In this paper, the thermal stresses of a thin functionally graded material (FGM) cylindrical shell subjected to a thermal shock are studied. An analytical method is developed. The studied problem for an FGM cylindrical shell is reduced to a plane problem. A perturbation method is used to solve the thermal diffusion equation for FGMs with general thermal properties. Then, the transient thermal stresses are obtained. The results show that the thermal shock is much easier to result in failure than the steady thermal loading. The present method can also be used to solve the crack problem of an FGM cylindrical shell with general thermal properties.     

Wave propagation in a bifurcated impedance-lined cylindrical waveguide

The radiation of a cylindrical-surface-wave mode which propagates towards the mouth of a semi- infinite cylindrical waveguide which supports surface waves is considered. This semi-infinite cylindrical waveguide is symmetrically located inside an infinite cylindrical waveguide whose surfaces are lined with an absorbent material. The whole system constitutes a new bifurcated cylindrical-waveguide boundary-value problem that has application in acoustics and electromagnetism. The mathematical model results in a scalar Wiener–Hopf problem which can be rigorously solved to give a closed-form solution.     

On the gradient elastic wave propagation in cylindrical waveguides with microstructure

The present work describes the development of a complete theoretical framework of wave propagation in cylindrical waveguides possessing microstructure. In parallel, a thorough investigation of the full 3-D model of wave propagation in cylinders is presented. The first step is the spectral decomposition of the boundary value problem emerging via wave propagation analysis. The spectral representation of the specific gradient elasticity problem reflects the ability to construct all the possible propagating modes in cylindrical geometry. Several byproducts arise along the present work, which constitute generalizations of well known important features of classical elasticity and are indispensable for modeling the gradient elasticity problem. We note the construction of the set of dyadic Navier eigenfunctions which constitute the generalization of the Navier eigenvectors. The restriction of the Navier eigendyadics on cylindrical surfaces gives birth to the dyadic cylindrical harmonics, which constitute the generalization of the well known vector harmonics. This set is also a basis in the sense that the trace of every dyadic field on a cylindrical surface can be represented as a countable superposition of dyadic cylindrical harmonics. The method aims at providing the necessary theoretical establishment for the determination of the dispersion curves emerging in cortical bones.     

管桩屏障在柱面波源下近场隔振效应的解析求解

基于波函数展开法表示柱面波源自由场,首次提出了一种求解柱面波源下管桩屏障对弹性波隔振效应的解析方法。方法首先考虑柱面波源与管桩屏障的位置关系,采用波函数展开法对入射柱面波进行了0阶Hankel展开表示,并采用任意坐标系间变换的Graf加法定理在任意桩体坐标系中表示,将入射波场和散射波场叠加后通过满足所有桩体的边界条件以求解所有桩体的散射波场。该解析方法分析了柱面波源入射下群桩屏障的隔振效果,首次在排桩隔振问题中考虑了入射波曲率的影响,为柱面波的散射问题提供了理论解答。该文重点讨论了入射波曲率、管桩个数和桩排数等因素对管桩隔振效果的影响,结果表明:整体上管桩屏障对柱面P波的隔振效果优于柱面SV波;柱面波源距离管桩屏障更近时排桩后场地的位移反应显著增大;相比平面波,柱面波源作用下排桩数量的提升对隔振效果的影响较小;三排管桩屏障比两排管桩屏障隔振效果更强,更宜采用三排管桩屏障进行柱面波源的隔振。     

Exact Solutions of Finite Deformation for Everted Compressible Hyperelastic Cylindrical Tubes

The eversion problem for a class of compressible hyperelastic thinwalled cylindrical tubes is examined. The mathematical model is formulated as a second-order nonlinear ordinary differential equation based on the theory of nonlinear elasticity. The exact solution that describes the mechanism of the finite deformation of the everted cylindrical tube is obtained. Using numerical simulations, it is shown that the initial thickness of the tube plays a significant role in the eversion.     

带圆孔复合材料板壳的有限元分析

本文把高精度三角形元用于复合材料板、柱壳结构的一般线性静力、稳定、振动问题,导出了有限元分析中的基本公式;并提出了自动生成高精度三角形元单元矩阵的方法,从而避免了繁琐的单元矩阵公式推导.文中重点分析了带有圆孔的复合材料柱形曲板的振动特性,算例表明:计算结果精度是好的.     

Dynamic stability of a viscoelastic cylindrical panel with concentrated masses

We discuss the problem of the dynamic stability of a viscoelastic cylindrical panel with concentrated masses in a geometrically nonlinear formulation that is based on the Kirchhoff-Love hypothesis. The effect of the action of concentrated masses is introduced into the equation of motion of a cylindrical panel using the Dirac δ-function. The problem is solved by the Bubnov-Galerkin method based on a polynomial approximation of deflections together with a numerical method based on the use of quadrature formulas. The choice of the Koltunov-Rzhanitsyn singular kernel is justified. Comparisons between the results obtained from different theories are presented. The Bubnov-Galerkin method convergence is investigated for all problems. The effect of the material viscoelastic properties and concentrated masses on the process of the dynamic stability of a cylindrical panel is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 132–147, July–August, 2008.     

A non-axisymmetric cylindrical contact problem

The contact problem under investigation is one whereby a solid circular elastic cylinder of infinite length is rigidly indented by a two piece collar of finite length, each piece being diametrically opposed and extending only partially around one half of the circumference. This case is practically significant in relation to the axisymmetric cylindrical contact problem since in many cases attachment of a component to a cylindrical shaft is achieved by means of a two piece clamp.Shear stresses on the contact interface are taken zero and a radial displacement influence coefficient technique is used to model the integral equation governing this contact problem. Adopting the Papkovich-Neuber solution for the non-axisymmetric cylindrical coordinate case and substituting the appropriate boundary conditions leads to a combined Fourier series, Fourier integral representation for the desired displacements. Convergence of this series—integral is studied and results of interference contact pressure are presented for an illustrative range of the various parameters involved.     

Dynamic response of an FGM cylindrical shell under moving loads

This paper presents an analytical study on the dynamic behavior of the infinitely-long, FGM cylindrical shell subjected to combined action of the axial tension, internal compressive load and ring-shaped compressive pressure with constant velocity. It is assumed that the cylindrical shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The problem is studied on the basis of the theory of vibrations of cylindrical shells. Derived formulas for the maximum static and dynamic displacements, dynamic factors and critical velocity for the FGM cylindrical shell subjected to moving loads. Numerical calculations have been made for fully metal, fully ceramic and FGM (Si₃N₄/SUS304) cylindrical shells. A parametric study is conducted to demonstrate the effects of the material property gradient, the radius to thickness ratio and the velocity of the moving load on the dynamic displacements and dynamic factors of the inner and ring-shaped pressures for FGM cylindrical shells.     

Fast calculation method for computer-generated cylindrical holograms

Since a general flat hologram has a limited viewable area, we usually cannot see the other side of a reconstructed object. There are some holograms that can solve this problem. A cylindrical hologram is well known to be viewable in 360 deg. Most cylindrical holograms are optical holograms, but there are few reports of computer-generated cylindrical holograms. The lack of computer-generated cylindrical holograms is because the spatial resolution of output devices is not great enough; therefore, we have to make a large hologram or use a small object to fulfill the sampling theorem. In addition, in calculating the large fringe, the calculation amount increases in proportion to the hologram size. Therefore, we propose what we believe to be a new calculation method for fast calculation. Then, we print these fringes with our prototype fringe printer. As a result, we obtain a good reconstructed image from a computer-generated cylindrical hologram.     

单层柱面网壳结构的找形

该文研究刚性网壳结构的合理找形问题,将柔性结构中广泛应用的找形概念引入刚性结构,提出基于力密度法的单层柱面网壳结构的找形方法。通过在找形过程中引入自重,解决了高斯曲率为零的柱面网壳的找形问题,且通过合理找形可基本消除自重引起的弯矩和剪力。找形得到的网壳结构与传统柱面网壳在曲面外形上比较相近,但可大幅度提高单层柱面网壳结构的承载能力。该文提出的找形方法效率高、收敛性好,为单层柱面网壳结构的设计开拓了新的方法和思路。     

Cylindrical phase change approximation with effective thermal diffusivity

No exact, general, solution exists for phase change in a cylindrical geometry. In fact, even approximate solutions are rare and limited in applicability. The use of the effective thermal diffusivity concept has allowed a closed form approximate solution to be generated for phase change around a circular cylinder in an infinite medium. The effective diffusivity method permits solutions to be found for phase change problems merely by solving the usually linear, zero latent heat problem analogous to the phase change problem. Phase change problems are often intractable with the usual mathematical methods. The cylindrical formulae given here are shown to be of acceptable accuracy, for most engineering purposes, over a wide range of parameters. No other simple, closed form, approximation is known for the cylindrical system. Although the accuracy of the effective diffusivity method has been demonstrated for the cylindrical geometry, application to other geometries must be verified.     

Vibration characteristics of fluid-filled cylindrical shells based on elastic foundations

In this paper, vibrations of fluid-filled isotropic circular cylindrical shells are studied based on elastic foundations. The wave propagation approach is employed to solve the shell problem. This approach is formulated by approximating the eigenvalues of the characteristic beam functions. Vibrations of natural frequencies for both empty and fluid-filled cylindrical shells based on elastic foundations are evaluated and their comparisons are performed to confirm the validity and accuracy of the present method. An excellent agreement has been found between the present and previous ones available in the literature. It is observed that frequencies are strongly affected when a cylindrical shell is attached with elastic foundations.     

波在考虑热载荷和转动惯量效应的非线性大变形多层压电层合壳内的传播研究

研究了非线性大变形、层合壳的铺设形式、转动惯量及热载荷效应对波在压电层合壳中传播的影响。首先利用Hamilton最小势能变分原理推导了波在大变形压电层合壳内传播的非线性动力学平衡方程;通过求解方程特征值得到了波传播特征曲线;数值算例表明波在压电层合壳内传播与壳体大变形、转动惯量以及热载荷有关,并与线性小变形理论(Cooper-Naghdi壳体理论)进行了比较。     

On a rigid inclusion pressed between two elastic half spaces

A solution to the problem of a rigid cylindrical inclusion pressed between two elastic half spaces is obtained using the distributed dislocation technique. The solution is compared with previously published analytical and numerical results for a rigid cylindrical inclusion bounded by two parabolic arcs with rounded corners. A simplified solution to the problem based on the classical contact theory and well-known results for crack problems is also suggested and validated. The simplified solution agrees well with analytical results in the case when the length of the opening around inclusion is much larger than the length of the contact zone.     

Dynamic elastic response of an infinite discrete multi-layered cylindrical shell subjected to uniformly distributed pressure pulse

A discrete multi-layered cylindrical shell (DMC) consists of a thin inner cylindrical shell and helically cross-winding flat steel ribbons. The dynamic elastic response of such cylindrical shell under uniformly distributed pressure pulse is studied in this paper. Under the axisymmetric plane strain assumption, the solution of the problem is divided into two parts: a quasi-static part satisfying inhomogeneous stress boundary conditions and a dynamic part complying with homogeneous stress boundary conditions. The quasi-static part is determined by homogeneous linearity method and boundary conditions, and the dynamic part was worked out by means of finite Hankel transform and Laplace transform. The dynamic response of a DMC is compared with the response of monobloc cylindrical shell. Parametric analyses with the consideration of major influential factors, such as thickness ratio of the inner shell to that of the complete shell, material parameters and winding-angle, are discussed.     

一端周向激励的圆柱壳声辐射特性研究

针对一端受周向均布激励的圆柱壳建立了新的理论模型,结合线激励下平板的有效传递导纳理论对圆柱壳表面的振动响应及声辐射功率进行仿真计算和分析,结果表明一端受均布激励作用的圆柱壳表面的声辐射功率在中低频段随频率的增大而增加,在临界频率处出现较大的波动,在环频处达到最大值,之后仍有较小波动并略有下降。实验测量结果证明了理论模型的有效性。     

Optimization of plasmon excitation at structured apertures

Surface plasmon excitation that is due to a single or a structured circular aperture in a flat metallic screen is investigated theoretically and numerically with a view to enhancing the electric field close to the metallic surface. A systematic study of the homogeneous solution of the electromagnetic scattering problem is made with cylindrical coordinates, expanding Maxwell equations on a Fourier-Bessel basis. A perturbation analysis devoted to simple physical analyses of different types of cylindrical nanostructure is developed for the optimization of plasmon excitation by a normally incident linearly polarized monochromatic plane wave. The conclusions drawn from this analysis agree well with the results of rigorous electromagnetic calculations obtained with the differential theory of diffraction in cylindrical coordinates.     

A circumferential crack in a cylindrical shell under torsion

The fully anti-symmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.     

A global finite-dimensional attractor and coherent vortex structures in one particular problem of magnetohydrodynamics

The exact solution of a stationary problem of magnetohydrodynamics is obtained for an incompressible cylindrical conductor possessing constant electric conductivity and shear viscosity. It is shown that a global finite-dimensional attractor in this problem represents a stable focus and has a dimensionality of two. The coherent spatial structures appear as two periodic systems of interacting hydrodynamic and current vortices.