Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

Bending versus membrane theory in the design of fluid filled, circular cylindrical shells

The note discusses the solutions which result from using Flügge's simpler membrane equations in the analysis of thin walled, fluid filled beam-type, circular cylindrical shells, simply supported over large spans. Comparisons are made with the more comprehensive bending equations in terms of the normal (longitudinal) stresses occurring at the center of the beam.A simple error analysis applied to each stress profile indicates that the variations are not merely a function of sectional slenderness, h²/12a², where h and a are thickness and radius of shell respectively. It is shown that length is also important in weighing the relative merits of the two systems of equations. Instead of referring to longitudinal and circumferential half waves, as is done by Flügge, a simpler parameter, K, incorporating longitudinal and sectional slenderness, is seen to be significant.     

Edge reinforced circular elastic inclusions in cylindrical shells

The effect of having an edge reinforcement around a circular elastic inclusion in a cylindrical shell is studied. The influence of various parameters of the reinforcement such as area of cross section and moment of inertia on the stress concentrations around the inclusion is investigated. It is found that for certain inclusion parameters it is possible to get an optimum reinforcement, which gives minimum stress concentration around the inclusion. The effect of moment of inertia of the reinforcement of SCF is found to be negligible. The results are plotted in a non-dimensional form and a comparison with flat plate results is made which show the curvature effect. In the limiting case of a rigid reinforcement the results tend to those of a rigid circular inclusion. Results are also presented for different values of μ_e the ratio of extensional rigidity of shell to that of the inclusion.     

Linear and nonlinear stability analysis of cylindrical shells

The paper describes the application of a curved isoparametric shell element to large displacement analyses including instability phenomena. A total Lagrangian formulation has been adopted using the standard incremental/iterative solution procedure. The linear stability analyses usually performed for the initial position were repeated at several advanced fundamental states on the nonlinear prebuckling path. Thus a current estimate of the final failure load is given. The method has been applied to several perfect and imperfect cylindrical shells under uniform pressure or wind load. Finally the example of a cylindrical panel under one concentrated transverse load is discussed.     

Effect of geometry on the stability of cylindrical clamped shells subjected to internal fluid flow

In this paper, the nonlinear stability of circular cylindrical shells subjected to internal incompressible flow is studied by means of the Donnell nonlinear shallow shell equations and a linear fluid–structure interaction model. Specifically, the effect of varying the thickness-to-radius (h/R) and length-to-radius (L/R) ratios is investigated. In general, the system loses stability by a subcritical pitchfork bifurcation, leading to a stable divergence of increasing amplitude with flow; no oscillatory solutions are found. Increasing the value of the circumferential wavenumber for shells with the same h/R ratio reduces the natural frequency and enhances the subcritical behaviour of the shell. Interesting results are found for different L/R cases in which the solution changes from subcritical to supercritical nonlinear behaviour.     

Instability phenomena during the conical expansion of circular cylindrical shells

Pushing a conical die into a tube is a forming process that is suitable for changing the shape of a thin cylindrical tube into that of a conical shell. The degree of expansion that is achievable without destroying the tube is limited by two mechanisms: (a) loss of global stability due to elasto-plastic ‘Concertina’ buckling of the straight part of the tube, and (b) diffuse necking caused by local loss of material stability in the conical part of the tube. The former mechanism is characterized by a periodic buckling pattern, that is similar to the one observed in typical crash elements, while the latter mechanism leads to the formation of periodic necks and subsequent failure by strain localization and rupture.In this study experimental evidence for both kinds of instabilities is presented along with corresponding simulation results obtained with the finite element method. For long tube specimens ‘Concertina’ buckling was found to be the dominant instability mode while for short tube specimens failure by necking and rupture occurred. The critical circumferential strain for the onset of necking at the expanding tube end was markedly higher than the one expected from uniaxial tension results. This finding is attributed to the supporting effect of the tube sections that are subjected to lower strains.     

Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid

The finite element method is applied to analyze a stationary or rotating cylindrical shell containing a co-rotating compressible fluid. The motion of the rotating fluid is described in the framework of the potential theory. The behavior of shells is analyzed using the classical shell theory. It has been found that the loss of stability in the stationary shells occurs in the form of a flutter. It has been shown that in the case of rotating shells the loss of stability is prevented by taking into account the initial circumferential tension caused by the centrifugal forces.     

旋转Timoshenko输流管道的固有频率和稳定性分析

基于Timoshenko梁模型,本文研究了旋转输流管道在自由振动状态下的流固耦合振动特性.考虑流体压力、重力、初始轴应力作用,基于Hamilton原理和欧拉角转换,推导得到了旋转Timoshenko输流管道的偏微分方程.根据Galerkin截断法将运动方程进行离散,通过求解系统的特征方程即可得到输流管一阶复频率的实部和虚部,实部代表固有频率,虚部代表能量变化.在流速较高时,研究发现必须考虑4阶及以上Galerkin截断,才能得到稳定的结果.通过与EulerBernoulli梁模型对比,验证了本文的结果正确性.研究发现针对短粗型管道,Timoshenko梁模型更加精确.此外研究了多种参数对旋转Timoshenko输流管道固有频率和振动稳定性的影响.研究结果表明质量比、流速、剪切系数对Timoshenko输流管道流固耦合振动的稳定性影响显著,而转动惯量、重力、流体压力和初始轴应力在一定程度上也会影响管道振动的频率和稳定性.转速的出现将管道频率分为两个量值,但转速并不影响系统能量变化.     

Asymmetric vibration analysis of thick composite circular cylindrical shells with variable thickness

Thick isotropic and composite shells of revolution are analyzed for vibration characteristics. The theory used is that proposed by Naghdi, which includes the thickness normal strain and shear deformation. A curved-semianalytical finite element is used to solve the problem. Parametric studies are conducted to study the effect of various parameters on the vibration behavior of shells. The effect of thickness variation along the axial direction with a constraint on mass is also studied.     

Parametric studies of coupled vibration of cylindrical pipes conveying fluid with the wave propagation approach

The wave propagation approach is extended to the coupled frequency analysis of finite cylindrical pipes conveying dense fluid. The downstream, upstream and mixed frequencies of the pipe are defined and discussed. The effects of fluid and shell parameters on the coupled frequencies are investigated. The difference between the coupled and uncoupled frequencies decreases with the circumferential mode n, but increases with the mode n after the number n where the fundamental frequency is obtained. The fundamental frequency can change from one circumferential mode to another circumferential mode with the h/R ratios. However for a shorter shell the fundamental frequency may keep with the same mode n in the interested h/R ratios. For different boundary conditions the transition of fundamental frequency between circumferential modes occurs at different h/R ratios. The downstream frequency increases with increasing fluid velocity, whereas the upstream frequency decreases as the fluid velocity increases. However, the mixed frequency of the pipe decreases with the increase of the fluid velocity. For a given flow velocity all the three frequencies decrease with decreasing h/R ratios. However the mixed frequency drops more with increasing fluid velocity at small h/R ratios than at large h/R ratios. Therefore negative frequencies may occur for small h/R ratios if the fluid velocity is large enough, which means that instability occurs first for thinner pipes.     

主动约束层阻尼圆柱壳的环向占优模态控制

基于作者最近对主动约束层阻尼（ACLD）圆柱壳的建模研究基础,通过数值算例进一步研究了电压分布方式对ACLD圆柱壳减振效果的影响,重点放在控制方式以及驱动电压的施加方案上.大量的数值计算表明,在多种外激励下的ACLD圆柱壳,采用环向占优模态控制方案,具有最佳的振动抑制效果,进而提出了环向占优模态控制策略的概念.     

Optimal design of cylindrical shells

In this paper, two types of problems of the optimal design of cylindrical shells with arbitrary axisymmetrical boundary conditions and distributed load, under the condition of the volume being constant, are discussed. These problems involve the minimax deflection and minimal compliancy of a cylindrical shell. Expressions of the objective function can be obtained by a stepped reduction method. In minimizing the maximum deflection, the position of the maximum deflection from the previous iteration is used as the next one. This procedure converges (Avriel 1976). Several examples are provided to illustrate the method.     

Effects of the slip boundary condition on dynamics and pull-in instability of carbon nanotubes conveying fluid

This paper addresses the effects of the slip boundary condition on dynamics and pull-in instability of carbon nanotubes (CNTs) containing internal fluid flow. Both the clamped–clamped and the cantilever boundary conditions are considered. The structure of CNTs is modelled using the size-dependent strain gradient theory (SGT) of continuum mechanics. It is shown that the Knudsen number (Kn) has a significant effect on the static and dynamic CNT response due to pull-in voltage loading and the existence of the instability region.     

Nonlinear analysis of reinforced concrete cylindrical shells

In this paper, analysis of reinforced concrete cylindrical shells is performed using a strain-based finite element. The shell element employed is bidimensional, cylindrical circular and has four-nodes and five nodal degrees of freedom. The nonlinearities due to concrete cracking and yielding of the steel are taken into account. The constitutive models for the materials employ the smeared cracking concept and a finite element layered approach. Concrete is modeled by a strain-induced orthotropic-elastic model under plane state of stress. A bilinear steel model is used and the stress/reversal with Baushinger effect is included. Examples show the good accuracy provided by this analysis.     

Pulsatile vibrations of viscoelastic microtubes conveying fluid

In this paper, the pulsatile coupled vibrations of a viscoelastic microtube conveying pulsatile fluid is examined for the first time. The problem is grouped into the class of parametrically excited, internally damped, gyroscopic where both Coriolis and parametric forces are present in the presence of viscosity. The Kelvin–Voigt approach of the viscosity, the Euler–Bernoulli for the deformation, the modified couple stress theory for the small size, and Hamilton’s principle for deriving differential equations are used. Parametric frequency–response curves are obtained in the vicinity of the parametric resonance near the critical speed for both subcritical and supercritical regimes. The effect of the flow pulsation on the oscillations is investigated.

     

Buckling analysis of ring-stiffened oval cylindrical shells

An energy principle is employed to derive the equations governing the stability of a simply-supported, eccentrically ring-stiffened, oval, orthotropic cylindrical shell. The kinematic relations used are those of Love-type shell theory and the effect of reinforcing rings is accounted for by a distributed stiffness approach. The cylinder is subjected to a combination of uniform axial and lateral pressures.

It is determined that the domain of stability of such a stiffened cylinder is bounded by two distinct solutions, herein denoted as corresponding to ‘long’ and ‘short’ axial wavelengths, with the extent of the short wavelength solution being dependent upon the degree of stiffening afforded by the rings.

The analysis of the effects of ring eccentricity shows that ovals are affected in a similar manner to circular cylinders in that outside rings provide the greatest capacity for sustaining axial compression, while inside rings are capable of supporting the greatest lateral pressure.

Finally, it is found that the buckling load of an oval cylinder under uniform lateral pressure slightly exceeds the corresponding value for an equivalent circular cylinder. As a further verification of this phenomenon, a Rayleigh-Ritz procedure is employed to determine the buckling load of an oval ring under uniform radial load. The results of this analysis corroborate those obtained for the cylinder.     

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Non-linear analysis of shells of revolution under arbitrary loads

A new finite element formulation is presented for the non-linear analysis of elastic doubly curved segmented and branched shells of revolution subject to arbitrary loads. The circumferential variations of all quantities are described by truncated Fourier series with an appropriate number of harmonic terms. A coupled harmonics approach is employed, in which coupling between different harmonics is dealt with directly rather than by the use of pseudo-loads. Key issues in the formulation, such as non-linear coupling and growth of harmonic modes, are carefully and systematically explained. This coupled harmonics approach allows an easy implementation of the arc-length method. As a result, post-buckling load–deflection paths can be traced efficiently and accurately. The formulation also employs a non-linear shell theory more complete than existing classical theories. The results from the present study are independently verified using ABAQUS, while those from other studies are found to be inaccurate in general.     

变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．     

扁锥面单层网壳的非线性动力学特性

用拟壳法建立了正三角形网格三向扁锥面单层网壳的轴对称非线性动力学基本方程．通过分离变量函数法,用Galerkin法得到了一个含二次、三次的非线性微分方程．为了研究混沌运动,对一类非线性动力系统的自由振动方程进行了求解,给出了单层扁锥面网壳非线性自由振动微分方程的准确解．通过求Melnikov函数,给出了发生混沌运动的临界条件．数字仿真证实了混沌运动的存在．