同轴圆柱壳流固耦合附加质量研究

论文根据堆本体内窄间隙同轴设备支承筒的结构特征、边界条件和窄间隙环腔内流体流速,将结构简化为一端固定一端自由的同轴圆柱壳,将圆柱壳内外的流体简化为无旋、无黏、不可压缩流体.同轴圆柱壳通过流体压力场实现耦合,其径向位移模态决定了窄间隙流体域的压力场,故采用级数形式的圆柱壳径向正交位移模态构建既满足一端固定一端自由边界条件...     

Method of successive approximations for solving boundary-value problems of plasticity with allowance for the stress mode

A method for solving boundary-value problems of plasticity with allowance for the stress mode is developed. To describe the elastoplastic deformation of an isotropic material, use is made of constitutive equations that include two nonlinear functions dependent on the stress mode and determined experimentally. The elastoplastic state of a thin cylindrical shell under axisymmetric loading is calculated as a numerical example. The numerical results demonstrate good convergence of the method. The effect of the stress mode on the strain distribution in a cylindrical shell is assessed     

Dynamics of a Semi-Infinite Cylindrical Shell with a Liquid Containing a Vibrating Spherical Segment

A semi-infinite cylindrical shell filled with a perfect incompressible liquid is considered. A vibrating rigid spherical segment placed on the shell axis excites the shell. The Laplace equation is solved under appropriate boundary conditions on the spherical, cylindrical, and flat surfaces bounding the liquid. Possibility is used to reexpand a spherical harmonic function in terms of a system of cylindrical harmonic functions and vice versa. The potential constructed is used to compute the shell deflections and the liquid pressure and velocity.     

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to ana-lyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With themethod of complex variable function, a series of conformal mapping functions are obtained from dif-ferent cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And,the general expressions for the equations of a cylindrical shell, including the solutions of stress concen-trations meeting the boundary conditions of the large openings' edges, are given in the mapping plane.Furthermore, by applying the orthogonal function expansion technique, the problem can be summa-rized into the solution of infinite algebraic equation series. Finally, numerical results are obtained forstress concentration factors at the cutout's edge with various opening's ratios and different loadingconditions. This new method, at the same time, gives a possibility to the research of cylindrical shellswith large non-circular openings or with nozzles.     

Calculation for cylindrical shell under local vertical loadings

In this paper, we use the method of mixed-type series to derive the analytical solutions of cylindrical shell, which is simply supported along the transverse edges and subjected to the local vertical loads, and give the analytical expressions of the solutions for this kind of shell under five types of local vertical loading. A numerical example for a cylindrical shell roof, which is simply supported along the transverse edges and is free along the longitudinal edges, is given in this paper and from the calculated results it may be seen that the convergence of the solutions is considerably satisfactory. Using the solutions of this paper, we can deal with some practical problems of underground structure.Project Supported by the National Natural Science Foundation of China and by Scientific and Technical Fund of Ministry of Urban and Rural Construction and Environmental Protection.We are grateful to Mr. Lu Ping who has completed partial numerical calculations.     

Superior aeroelastic behaviors of axially functional graded cylindrical shells in supersonic airflow

It is well known that mode localization occurs in the panel flutter structural systems. Therefore, it is reasonable to expect the aeroelastic stability of the structure to be enhanced by changing the geometrical sizes and material properties of the structure along the airflow direction. In this investigation, an axially functionally graded (AFG) cylindrical shell is designed and its super aeroelastic behaviors in supersonic airflow are studied. The enhanced aeroelastic stability and the excellent capability in the passive flutter suppression are achieved by the present AFG design. For the thickness of the cylindrical shell, three types of functions are analyzed. Numerical results show that all these three functions can increase the flutter bound of the cylindrical shell to some extent. It is also noted that in some situations, local mode coalescence happens. In this study, an effective method is proposed to eliminate the local mode coalescence by adding the lumped mass. For the material properties, two groups of functions are considered. It is found that under suitable parameters of the functions, even if the effective stiffness of the whole structural system decreases, the flutter bound of the structure can still be increased due to the AFG design. In addition, the flutter stability of the AFG cylindrical shell is much better than that of the traditional transversely functionally graded shell. The present study is significant in the aeroelastic design of aerospace vehicles.     

TiNi合金圆柱薄壳静压屈曲失稳特性的实验研究

对马氏体相变支配的伪弹性TiNi合金圆柱薄壳进行了准静态屈曲实验研究和分析,结果表明,TiNi柱壳的屈曲模态以非轴对称钻石型为主,卸载时可恢复,与马氏体相变和相变铰的行为相关,明显不同于传统弹塑性柱壳。还讨论了长径比和边界条件对屈曲模态、比能、临界失稳阈值等的影响。研究发现：随着长径比和边界条件的变化,TiNi圆柱薄壳呈现出多样化的屈曲模态发展。相同长径比下,两端简支的TiNi圆柱薄壳比能Se较大;随着长径比增大,边界条件的影响有逐步弱化趋势。相同边界条件下,长径比较小的TiNi圆柱薄壳比能较大。     

Interaction Between an Oscillating Sphere and a Thin Elastic Cylindrical Shell Filled with a Compressible Liquid. Internal Axisymmetric Problem

The problem on the interaction between a spherical body that oscillates in a prescribed manner and a thin elastic cylindrical shell filled with an ideal compressible liquid is formulated. It is assumed that the geometrical center of the sphere is located on the cylinder axis. The problem is solved based on the possibility of representing a partial solution of the Helmholtz equation written in cylindrical coordinates in terms of partial solutions in spherical coordinates, and vice versa. By satisfying the boundary conditions on the surfaces of the sphere and the shell, we obtain an infinite system of linear algebraic equations to determine the coefficients of expansion of the liquid-velocity potential into a Fourier series in terms of Legendre polynomials. The hydrodynamic characteristics of the liquid filling the cylindrical shell are determined and compared with the cases where a sphere oscillates in an infinite liquid and in a rigid cylindrical vessel     

An Exact Analysis for Free Vibration of a Composite Shell Structure-Hermetic Capsule

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纵横加肋圆柱壳的应力分析

建立了一种纵横加肋圆柱壳有限元分析的正确的力学模型,通过大量数值计算,论证了纵骨尺寸,纵骨间距对壳体应力状态的影响,提出了一种等效各向同性壳的近似解析公式,为开展纵横加肋圆柱壳的结构设计打下了良好的基础。     

Vibration characteristics of a spherical–cylindrical–spherical shell by a domain decomposition method

A domain decomposition method is used to analyze the free and forced vibration characteristics of a spherical–cylindrical–spherical shell, based on Reissner–Naghdi's thin shell theory. The joined shell is divided into some cylindrical and spherical shell segments along the meridional (longitudinal) direction. Double mixed series, i.e., Fourier series and Chebyshev polynomials, are employed as the admissible displacement functions to obtain the discretized equation of motion for the joined shell. Numerical comparisons with the results derived by FEM and those available in the previous literature are made to validate the present method. Moreover, the effects of length-to-radius and radius-to-thickness ratios on the natural frequencies are also investigated.     

Flow around a flexible cylindrical shell by a plane stream of an ideal liquid

The flow by a plane stream of an ideal liquid around a cylindrical shell of zero flexural stiffness (a soft cylindrical shell), or a gas bubble on the boundary of which forces of tension act, was studied in [1–6]. The flow around an elastic plate in a linear formulation was considered in [7, 8]. We consider the flow, around a flexible cylindrical shell which possesses a flexural stiffness and at the same time admits large displacements, by a plane system of an ideal incompressible liquid. An application of methods of the theory of functions of a complex variable leads to an effective solution of the problem. The shape of the shell, the forces in it, the forces acting on the shell, and the field of velocities of the flow of the liquid are determined.     

任意边界条件下环肋圆柱壳振动特性的建模与求解

边界条件对环肋圆柱壳的振动特性有重要影响。基于能量法,把环肋看作离散模型,构建了任意边界条件下加环肋圆柱壳的动力学模型。采用一种改进的傅里叶级数作为位移容许函数,通过瑞利里兹程序求解结构的拉格朗日方程,得到环肋圆柱壳的振动模态和频响特性。通过与实验和有限元(FEM)方法的计算结果进行对比,验证了论文方法的准确性,在此基础上分析了环肋偏心方式、截面尺寸、位置分布和边界弹簧刚度等参数对环肋圆柱壳振动特性的影响。     

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.     

带初始几何缺陷FGM固支圆柱壳的非线性动力学分析

本文主要研究了带初始几何缺陷的功能梯度固支圆柱壳在不同体积分数下的非线性动力学行为。假定该功能梯度圆柱壳材料的组分是沿厚度的方向呈梯度几何变化的。运用经典板壳理论、von-Karman几何非线性应变位移关系以及Hamilton原理,推导出两端固支FGM圆柱壳的偏微分非线性运动控制方程。本文考虑了圆柱壳的对称模态,利用Galerkin法对上述非线性动力学方程进行截断,得到常微分形式的非线性动力学方程。主要运用Runge-Kutta法进行数值仿真,并且画出了其最大lyapunov指数图,主要研究了面内载荷对振动响应的影响,并对比了不同体积分数对系统非线性动力学的影响。     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

Free vibration analysis of open thin deep shells with variable radii of curvature

In the present paper, free vibration of a thin open curved shell with parabolic curvature was studied. This shell has a curvature with variable radius in one direction. The equations of motion of this shell were inferred by first order shell theory. According to perpendicular nature of loading on shell of marine structures, the assumptions of Donnell–Mushtari–Vlasov can be used with an acceptable level of accuracy and the in-plane displacement along shell straight direction “x” can be neglected as compared to the displacement in two other directions. The natural frequencies and mode shapes related to the first five vibrational modes were extracted using semi-analytical methods including power series method, Galerkin method and beam function method. The results of the semi-analytical methods were validated against those obtained by using the finite element method. Out of the studied semi-analytical methods, Galerkin method was found to have an appropriate convergence in both natural frequency and mode shape. Adopting eight terms of the response series, Galerkin method has an appropriate convergence compared with the results of finite element.     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

The free bending vibration of cylindrical tank partially filled with liquid and submerged in water

This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.     

含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法

提出了一种分析含内埋矩形脱层正交各向异性圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。