VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS WITH NONUNIFORM CONSTRAINTS,ELASTIC BED AND ADDED MASS; PART I: EMPTY AND FLUID-FILLED SHELLS

Circular cylindrical shells with non uniform edge constraints (with zero radial and circumferential displacement) are investigated, including riveted shells. The linear modes of simply supported shells vibrating in vacuo are used as admissible functions, and the solution is obtained with the artificial spring method. The Flügge theory of shells is used and in-plane inertia is retained. Any shell constraint other than simple supports can be studied with the proposed method. Complicating effects due to the contained inviscid fluid, elastic bed of partial axial and angular dimensions, intermediate constraints and added mass are considered. The convergence of the method is numerically investigated and the effect of the number of rivets (clamped arcs) on shell modes is studied.     

Oscillating laminar fluid flow in a cylindrical elastic pipe of annular cross-section

The coupled elastohydrodynamic problem based on the dynamic equations for a viscous incompressible fluid and for two closed finite-length cylindrical elastic shells, inner and outer, described using the Kirchhoff-Love hypotheses is formulated and solved with the corresponding boundary conditions for harmonic variation of the pressure at the inlet and outlet of an elastic annular pipe. From the solution of this problem the flow parameters and the elastic shell displacements are found. The amplitude and phase frequency characteristics and resonant frequencies of the shells are found. The cases of shells simply supported and with fixed ends are considered. The effect of the support mode and the fluid characteristics on the resonant frequencies and the amplitude frequency characteristics of the shells is investigated.     

Vibration of open circular cylindrical shells with intermediate ring supports

This paper is concerned with the free vibration of open circular cylindrical shells with intermediate ring supports. An analytical procedure for determining the free vibration frequencies of such shells is developed based on the Flügge thin shell theory. An open circular cylindrical shell is assumed to be simply supported along the two straight edges and the remaining two opposite curved edges may have any combinations of support conditions. The shell is divided into multiple segments along the locations of the intermediate ring supports. The state-space technique is employed to derive the exact solutions for each shell segment and the domain decomposition method is applied to enforce the geometric and natural boundary/interface conditions along the interfaces of the shell segments and the curved edges of the shell. Comparison studies are carried out to verify the correctness of the proposed method. Exact vibration frequencies are obtained for open circular cylindrical shells with multiple intermediate ring supports.The influence of the number of intermediate ring supports, the locations of the ring supports, the boundary conditions and the variation of the included angle of the shells on the natural frequencies are examined. The exact vibration solutions can be used as important benchmark values for researchers to check their numerical methods and for engineers to design such shell structures.     

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.     

双层加筋圆柱壳在不同舷间连接形式下的声辐射性能分析

论文用解析法推导得出了双层加筋圆柱壳的两种舷间连接形式-实肋板和托板的反力表达式,其中实肋板的振动形式分别采用三种振动方程近似表示-考虑板的面内面外振动、仅考虑板的面内振动、仅考虑板的面内准纵波振动,托板的振动形式也分别采用三种振动方程近似表示-考虑板的面内振动、仅考虑板的面内准纵波振动、近似成杆的纵向振动,数值分析对...     

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

We analyze the steady-state response of a functionally graded thick cylindrical shell subjected to thermal and mechanical loads. The functionally graded shell is simply supported at the edges and it is assumed to have an arbitrary variation of material properties in the radial direction. The three-dimensional steady-state heat conduction and thermoelasticity equations, simplified to the case of generalized plane strain deformations in the axial direction, are solved analytically. Suitable temperature and displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are then solved by the power series method. In the present formulation, the cylindrical shell is assumed to be made of an orthotropic material, although the analytical solution is also valid for isotropic materials. Results are presented for two-constituent isotropic and fiber-reinforced functionally graded shells that have a smooth variation of material volume fractions, and/or in-plane fiber orientations, through the radial direction. The cylindrical shells are also analyzed using the Flügge and the Donnell shell theories. Displacements and stresses from the shell theories are compared with the three-dimensional exact solution to delineate the effects of transverse shear deformation, shell thickness and angular span.     

VIBRO-ACOUSTIC BEHAVIOR OF SUBMERGED CYLINDRICAL SHELLS: ANALYTICAL FORMULATION AND NUMERICAL MODEL

We propose both an analytical formulation and a numerical model to study the hydroelastic or vibroacoustic behaviour of cylindrical thin shells immersed in an unbounded, inviscid and heavy fluid. The analytical solution allows us to calculate the dynamic response and the pressure radiated in the far field by a baffled cylinder. This formulation uses the truncated modal basis of the dry structure to expand the displacements of the submerged shell. The analytical model is used as a reference in order to validate a numerical model which couples the finite element method (FEM) to the boundary element method (BEM). As opposed to the analytical formulation which is dedicated to baffled circular cylinders only, the numerical model allows us to treat any axisymmetric shell, such as cylindrical and spherical shells, or more complex shells of revolution. The structure is idealized by two-node ring finite elements and the boundary equation is solved using the method of singularities.     

柱面扁壳的非线性数值分析

本文研究了柱面扁壳在均布荷载作用下的大变形弯曲问题。首先导出了位移型非线性控制微分方程,然后结合两种边界情况(简支与固定)给出了用正交配点法进行解算的详细公式。     

Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads

In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated. The linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations.     

有限长圆柱壳中轴对称弹性瞬态波

有限长的计及剪切变形和转动惯性的弹性圆柱壳的轴对称运动方程经过Laplace变换后转化为一组相空间中的方程。对该方程组作了一些适当的处理后,应用广义射线法,得到了相空间中位移和内力的射线法表达式。采用快速Fourier变换作Laplacl逆变换,即可得到圆柱壳受轴对称冲击载荷时的弹性瞬态波解。     

Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.     

夹层FGM圆柱壳在扭转载荷作用下的弹性稳定性

采用半解析方法研究了两端简支的功能梯度夹层圆柱壳在端部扭转载荷作用下的弹性稳定性.考虑圆柱壳的里外表层为均匀材料,中间层为材料性质沿厚度方向连续变化的功能梯度材料,并且在界面处的材料性质保持连续. 基于Flügge薄壳理论,建立了位移形式的结构静态屈曲控制方程.根据边界条件将位移表示为三角级数形式,获得包含柱壳端部扭转载荷参数的近似线性代数特征值问题,并通过数值方法求得了表征结构失稳特征的临界载荷. 数值结果表明,临界载荷随着半径与厚度比的增加而减小,随着功能梯度中间层的弹性模量的平均值的增加而增加.      

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

A closed-form solution procedure for circular cylindrical shell vibrations

A systematic procedure for obtaining the closed-form eigensolution for thin circular cylindrical shell vibrations is presented, which utilizes the computational power of existing commercial software packages. For cylindrical shells, the longitudinal, radial, and circumferential displacements are all coupled with each other due to Poissons ratio and the curvature of the shell. For beam and plate vibrations, the eigensolution can often be found without knowledge of absolute dimensions or material properties. For cylindrical shell vibrations, however, one must know the relative ratios between shell radius, length, and thickness, as well as Poissons ratio of the material. The mode shapes and natural frequencies can be determined analytically to within numerically determined coefficients for a wide variety of boundary conditions, including elastic and rigid ring stiffeners at the boundaries. Excellent agreement is obtained when the computed natural frequencies are compared with known experimental results.     

圆柱薄壳稳定性的一个修正理论

著名的唐乃尔(Donnell)——穆什塔利的简化壳体理论只能较精确地适用于较短圆柱壳稳定性计算.其近似性误差随长度与半径之比的增加而增大.本文考虑了横向切力的影响,对非完善型圆柱壳体推导了几何非线性理论的基本方程,建立了对各种长度半径比的圆柱壳体稳定性均适用的修正理论.     

Free Vibrations of Cylindrical Shells with Non-Axisymmetric Mass Distribution on Elastic Bed

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.     

非惯性参考系中弹性壳的非线性振动分析

给出了弹性壳处于非惯性参系中的运动描述，基于Ｈａｍｉｌｔｏｎ原理建立了中厚壳在非惯性参考系中的非线性运动控制方程，应用多尺度法及谐波平衡法具体地分析了圆柱壳的非线性振动问题     

Thermomechanical vibration analysis of a functionally graded shell with flowing fluid

This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. The new features in this paper are helpful for the application and the design of functionally graded cylindrical shells containing fluid flow.     

静力预加载环向加筋圆柱壳的轴向流-固冲击屈曲

将初缺陷放大准则应用于静力预加载环向加筋圆柱壳结构受轴向流-固冲击加载作用时的几何非线性动力屈曲研究中。运用Galerkin方法推导出壳体-肋骨系统的动力屈曲控制方程,并且采用Runge-Kutta法进行数值求解。着重分析了静力预加载荷对结构屈曲性态及抗轴向冲击能力的影响。