复合材料波纹夹层圆柱壳设计及轴压性能

结构轻量化是航空航天发展的永恒主题, 波纹夹层圆柱壳作为常见的轻质结构形式, 在航空航天领域具有很大的发展空间。采用模具热压法, 制备出纵向和环向碳纤维复合材料波纹夹层圆柱壳, 其中芯子整体成型, 面板分瓣制备。采用经典板壳屈曲理论, 分析纵向和环向波纹夹层圆柱壳的轴压力学性能, 得到了欧拉屈曲、整体屈曲、局部屈曲和面板压溃4种失效模式下的极限载荷理论公式。绘制出结构的失效机制图, 直观显示出了失效模式与试件尺寸之间的关系。通过对纵向和环向波纹夹层圆柱壳的轴向压缩试验, 获得了结构的载荷-位移曲线及局部屈曲和面板压溃2种失效模式。结果表明:纵向波纹夹层圆柱壳的轴向承载能力及载荷/质量效率优于环向波纹夹层圆柱壳, 在一定范围内增加圆柱壳面板的厚度、减小圆柱壳的高度可提高结构的载荷/质量效率。      

非均匀加筋圆柱薄壳圆截面内振动的径向模态机械阻抗分析

提出圆柱薄壳的圆截面内运动假设,从声学角度将环肋对壳体的作用等效为径向作用力,根据Hamilton原理建立了简支非均匀加筋圆柱壳的振动控制方程,利用驻波形式解对其径向模态机械阻抗进行了研究。分析表明:对于加筋圆柱壳,环肋与圆柱薄壳的径向模态机械阻抗具有串联连接方式,通过调整环肋的几何参数增大环肋自身的径向模态机械阻抗,可以达到壳体减振降噪的目的,并指出了利用环肋的反共振特性进行加筋圆柱壳结构减振的设计方向。     

复杂边界条件圆柱壳自由振动特性分析

提出一种半解析法来分析圆柱壳结构自由振动特性。将圆柱壳壳结构在轴向方向分解为若干壳段,用沿轴向的Jacobi多项式和沿周向的Fourie r级数来表示各个壳段的位移函数,并采用罚参数法对圆柱壳结构的边界条件和壳段间的连续性条件进行模拟;最后,基于Rayleigh-Ritz法求得圆柱壳结构的自由振动频率。研究表明,该方法具有较好的收敛性,与公开发表文献一致性较高,研究成果可为复杂边界条件下圆柱壳结构自由振动特性分析提供数据积累和方法依据。     

On the stability of thin-walled, corrugated, circular cylindrical shells under external pressure

Summary Thin-walled, corrugated, circular cylindrical shells under external pressure have repeatedly buckled at much lower values than has been predicted from simple orthotropic shell theory, where a flexural mode of buckling is assumed, in-plane to the cross-section of the tube. In the present paper it is shown that there exists always a combined, torsional–flexural, out-of-plane mode of buckling, frequently corresponding to an extremely low critical pressure. The need to design these tubes also with respect to torsional stiffness is emphasized, and a formula for the buckling pressure is proposed. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Stress-Strain State of a Corrugated Cylindrical Shell

By using the relations of the Kirchhoff–Love theory of shells and the method of distortion of the shape of the boundary in the process of axisymmetric heating through the thickness of shells according to a linear law, we construct a solution of the problem of statics for a corrugated cylindrical shell in an axially symmetric temperature field under the action of internal pressure.     

The transient responses of two-layered cylindrical shells attacked by underwater explosive shock waves

An approximation solution is introduced for the dynamic response of a two-layered cylindrical shell of circular cross-section subjected to an underwater explosive shock wave. The solution is obtained within the framework of the Flugge thin shell theory and the reflected-afterflow-virtual-source (RAVS) method is used to account for the fluid–structure interaction. Detailed numerical computations are carried out, in dimensionless form, for the cases of infinitely long two-layered cylindrical shells. Time histories of nondimensional radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity are presented in graphical form and the effects of elastic modulus, shell radius and thickness on the transient response characteristics of the shells are investigated.     

弹性薄壳的大变形分析

本文给出了弹性薄壳大变形时应变与位移之间的精确关系。经过合理的简化,给出了壳的挠度与厚度同级的大变形基本公式。当薄壳为柱形且作柱状弯曲时,精确地求得了壳的挠度与长度同级的大变形基本公式。这些公式符合实际和便于应用。用解析法求得了无限长园柱壳一边固定,另一边受力偶作用的精确解。用能量法求得了无限长条板的近似解。     

A finitely long circular cylindrical shell of piezoelectric/piezomagnetic composite under pressuring and temperature change

The problem of a finitely long circular cylindrical shell of cylindrically orthotropic piezoelectric/piezomagnetic composite under pressuring loading and a uniform temperature change is analytically investigated in detail. The analytical solution is obtained through the power series expansion method and the Fourier series expansion method. Numerical results are presented and compared for two-layered piezoelectric/piezomagnetic composite circular cylindrical shells with different stacking sequences under inner pressuring loading.     

A generalized self consistent model for effective elastic moduli of human dentine

Closed-form expressions are presented for effective material properties of human dentine in this paper. The derivation is based a Generalized Self Consistent Method and the strain energy principle. The Generalized Self Consistent Model for cell model of fiber-reinforced composites is extended to the case of hollow cylinder model and the corresponding cell model is chosen to consist of a circular hollow cylinder filled with liquid or gas phase, which surrounded by a circular cylindrical shell of matrix phase. Each layer of cylindrical shell is here considered as a kind of composite consisting of collagen fibrils, with mineralized hydroxyapatite, loosely connected to their neighbours, and water (or gas in the case of dry dentine composite). Using the cell model, the effect of Poisson’s ratio and volume fraction of intertubular dentine on effective mechanical constants is analyzed. Results obtained from the proposed model are compared with those from other models such as nano-indentation method.     

不同参数下的单、双层圆柱壳体速度场研究

研究圆柱壳体表面速度场的重构：疗法对潜艇水下辐射噪声的预报具有重要的意义。采用了分区段重构轻外壳速度场的思想，在此基础上建立无限流体中的有限长单、双层加肋圆柱壳模型，分析了壳体表面速度场随不同结构参数的变化规律，并对单、双层圆柱壳体，以及双层圆柱壳体内、外壳的振动响应性能作了一定的比较。得到了单区段壳体长度的选取、模型刚度特性以及不同频段内壳体间耦合作用等对壳体速度场的影响，为研究潜艇轻外壳速度场重构方法提供了理论依据。     

波纹管壳结构中振动波的传播

研究了波纹管壳结构中的振动波。运用摄动方法与结构振动的波动方法得到了波纹管结构波动解的形式;在此基础上考察了振动波的频散特性。结果表明：摄动波是以传播波和衰减驻波形式存在;研究了振动波通过圆柱壳－波纹壳不连续截面时的传播特点,从频散特性角度对弯曲波传播进行了解释。本文为工程实际中波纹管接头的降噪预报提供了一种理论方法。     

Analysis of simply-supported laminated circular cylindrical shell roofs

An elasticity solution has been presented for the analysis of a laminated circular cylindrical shell roof with simply-supported edges, and the displacements and stresses of the solution are expressed in terms of infinite series. A solution according to the classical shell theory (CST) is also developed. Computations are made for various ratios of midsurface radii to thicknesses and the results of the CST have been examined in the light of the elasticity solution results.     

几何参数对旋转薄壁圆柱壳振动特性的影响

摘 要: 本文基于Love壳体理论对旋转薄壁圆柱壳的自由振动特性进行分析,讨论几何参数对圆柱壳振动特性的影响。针对五种边界条件,分别分析厚度与半径之比、半径与长度之比对旋转薄壁圆柱壳固有频率特性的影响;探讨半径与长度之比对系统振型比的影响。分析结果表明：圆柱壳固有频率随着厚度与半径之比的增加而单调增加,增加幅度较小。半径与长度之比对圆柱壳固有频率与振型比的影响显著,且随其增大固有频率及振型比均不单调变化。由此可知,细长圆柱壳的振动特性与短粗圆柱壳的振动特性差异显著,研究结果为圆柱壳的动力学分析提供理论依据。     

Vibration characteristics of a circular cylindrical panel piezoelectric transducer

We study the theory of the basic vibration characteristics of a circular cylindrical shell piezoelectric transducer. The linear theory of piezoelectricity is used. Both the free-vibration solution for resonant frequencies and modes as well as the electrically forced-vibration solution for admittance are obtained. Numerical results are presented.     

Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells

A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis–Lagrange (M–L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.     

流体作用下正交各向异性圆锥壳的自由振动

给出了流体载荷作用下正交各向异性圆锥壳体的自由振动理论模型。通过波传播法和Galerkin法得到了流体载荷作用下截锥壳体自由振动的解。流体载荷作用下的锥壳被划分为好几段,并且每个小圆锥段被当作一个小圆柱段。通过确定每个小圆柱段的流体载荷,来确定锥壳的流体载荷。这样,作用在锥壳上的流体载荷逐段加载。流体载何以及没有流体载荷作用的各向同性和正交各向异性圆锥壳的数值结果被计算出来阐述求解过程的有效性。     

Stability similarities between shells, cells and nano carbon tubes

The similarity in stability characteristics between multiscale circular cylindrical structures is revealed. Two detailed structures are explored. One is the circular cylindrical shell on an engineering scale, and another is the circular cylindrical lipid bilayer vesicle on a micro- or nanoscale. The critical stability of the vesicle acted on by uniformly distributed radial pressure is analysed. The critical load of the vesicle is derived and compared with that of the thin shell. The astonishing similarity between them is disclosed. The possible applications of such similarity to biophysics, biology and biomedicine are presented.     

Boundary value problems in thin shallow shells of arbitrary plan form

Summary This paper is concerned with a general method of analysis of boundary-value problems in thin shallow shells of arbitrary plan form. Two specific shell configurations are considered. General solutions to the governing partial differential equations are obtained in complex form, containing a sufficient number of arbitrary elements to satisfy the four boundary conditions permitted by classical thin shell theory. An algorithm for the determination of these arbitrary elements from a general form of boundary condition is presented. The method of solution is based on I.N.Vekua's theory of elliptic partial differential equations.Part 1 of the paper is devoted to shallow spherical shells. An example calculation is given for a circular planform shell, for which a closed form of solution may be obtained. The computed results show close agreement with the exact solution.Part 2 of the paper deals with shallow circular cylindrical shells, including the calculation of a shell the planform of which is a square with rounded corners. Graphs of deflection and stress function are given.     

Free vibration of composite circular cylindrical shells with random material properties. Part II: Applications

In the second part of this study the approach developed in Part I has been used to analyse free vibration of three composite circular cylindrical shells with random scatter in the material properties. The cases considered are – specially orthotropic symmetric shells in axisymmetric and asymmetric oscillations, and antisymmetric cross ply laminated shell in axisymmetric oscillations. With known statistics of the material properties the mean and the variance of the natural frequencies have been obtained. Numerical results have been presented for graphite–epoxy composite shells.     

Static path jumping to attain postbuckling equilibria of a compressed circular cylinder

The postbuckling behavior of an axially compressed circular cylindrical shell is exceedingly complicated due to an infinite number of closely spaced postbuckling branches and bifurcation points. The minimum strength existing in the deep bottom of the postbuckling region may serve as a design limit. The primary concern in this present paper is to compute this stable postbuckling equilibrium solution by two different approaches: One is to repeat the procedures of tracing unstable branches, pinpointing bifurcation points and branch-switching in order to carefully approach to the target. The other is to trigger a static jump to the target by two-parametric loading. As a numerical example, a perfect circular cylindrical panel is analyzed to show that a direct jump from the undeformed state to a stable postbuckling solution is possible with a proper choice of the load perturbation.