基于混合变量条形传递函数方法的圆柱壳屈曲分析

提出了一种分析交各向异性圆柱壳和阶梯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Fluegge薄壳理论，通过定义广义位移变量和对应的广义力变量，建立了圆柱壳混合变量能量泛函；然后通过引入条形单元，定义混合状态变量和采用传递函数方法对超级壳单元求解，得到具有多种边界条件圆柱壳屈曲问题的半解析解；最后通过位移连续和力平衡条件，可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。     

An application of theoretical solutions about cylindrical shells with small openings

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Nonlinear dynamical behavior of shallow cylindrical reticulated shells

By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral tri- angle cell are founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support.The tensile force is solved out from the compati- ble equations,a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin.The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.The existence of the chaotic motion of the single-layer shallow cylin- drical reticulated shell is approved by using the digital simulation method and Poincarémapping.     

The displacement solution of conical shell and its application

In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the     

New solutions of Novozhilov's equation of toroidal shells

New solutions are obtained for Novozhilov’s equation of toreidal shells having general slenderness ratio 0<a<1 (a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.     

The exact solution for the general bending problems of conical shells on the elastic foundation

The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell^[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem.     

New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.     

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.     

Theoretical and Experimental Investigations of the Stress Concentration in Nonthin Cylindrical Shells with Rectangular Openings

The problem on the stress state of cylindrical shells with rectangular openings under axial compression is considered based on the theory of shells of average thickness. For a shell with two diametrical openings, numerical calculations are carried out by the finite-difference method for anisotropic and isotropic materials. The anisotropy of the material and the sizes of the openings are shown to affect the displacements and stresses on the opening periphery. An experiment is implemented for a cylindrical shell with rectangular openings under axial compression. The experimental and numerical data are compared     

功能梯度压电、压磁柱对称问题的振动分析

本文在不考虑体力、体电流和体电荷的情况下, 假定压电、压磁柱壳的材料参数沿圆柱厚度方向呈幂函数分布时, 研究了径向载荷作用下功能梯度压电、压磁空心柱壳的空间柱对称径向振动问题. 首先在柱坐标系下, 由功能梯度材料的参数、本构、梯度和平衡方程推导得出外激励作用下以Bessel函数表示圆柱壳的应力、电势、磁势等物理量的稳态解, 进而对空间柱对称的压电、压磁功能梯度材料动力控制问题进行了理论分析. 可以看出, 当梯度参数时, 即完全退化为横观各项同性压电、压磁柱对称的振动问题, 与文献[16]的基本方程为柱坐标下得出的结果一致. 最后给出数值算例, 结果表明材料不均匀性对沿径向振动各物理量的显著影响, 且用一个特定不均匀性参数值可以优化电磁力耦合的性能, 这在现代工程设计中尤为重要.     

功能梯度压电、压磁柱对称问题的振动分析

本文在不考虑体力、体电流和体电荷的情况下, 假定压电、压磁柱壳的材料参数沿圆柱厚度方向呈幂函数分布时, 研究了径向载荷作用下功能梯度压电、压磁空心柱壳的空间柱对称径向振动问题. 首先在柱坐标系下, 由功能梯度材料的参数、本构、梯度和平衡方程推导得出外激励作用下以Bessel函数表示圆柱壳的应力、电势、磁势等物理量的稳态解, 进而对空间柱对称的压电、压磁功能梯度材料动力控制问题进行了理论分析. 可以看出, 当梯度参数时, 即完全退化为横观各项同性压电、压磁柱对称的振动问题, 与文献[16]的基本方程为柱坐标下得出的结果一致. 最后给出数值算例, 结果表明材料不均匀性对沿径向振动各物理量的显著影响, 且用一个特定不均匀性参数值可以优化电磁力耦合的性能, 这在现代工程设计中尤为重要.     

Effects of exponential volume fraction law on the natural frequencies of FGM cylindrical shells under various boundary conditions

In the present work, vibration characteristics of thin functionally graded cylindrical shells are studied under the influence of various boundary conditions. Fabrication of FGM cylindrical shell is carried out by using exponential volume fraction law. Strain- and curvature-displacements relationships are taken from Love’s thin shell theory. The frequency equation in the form of eigenvalue problem is obtained by adapting the Rayleigh-Ritz method. Characteristic beam functions are assumed to approximate the axial modal dependence. Effects of exponential volume fraction law on the natural frequencies of the FGM cylindrical shells for various boundary conditions are studied against circumferential wave number, length to radius ratio and thickness to radius ratio for different values of power law exponents. Results evaluated show good agreement with those available in the literature.     

电活性聚合物圆柱壳静态与动态电压下的响应及稳定性

摘要：在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场。这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏。本文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题。采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程。给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏。同时,也讨论了厚度和边界条件对临界电压的影响。圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动。给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性。采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏。最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论。     

Weak formulation of mixed state equation and boundary value problem of laminated cylindrical shell

IntroductionBasedonthree-dimensionalelasticitytheory,exactsolutionofhomogeneousisotropic,orthotropic,andlaminatedplatesandshellshasbeenstUdiedll]-[61,respeChvely.Butallofabovepapersadoptedrigorousequilibriumandboundarycondihons,andtheirsolutioncanbereliedonlyonspecialtechnique.Thusthosemethodswouldbedifficulttobepopularized.Ref.[7]clarifiedtheimportanceofdriedstateequationofelasticity,andfirStgaveHndltoncanonicalequationbymodifyingHellinger-Reissuervariationalprinciple.AtthesametimeTangL'I…     

RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.     

Interaction of an infinite thin elastic cylindrical shell and a pulsating spherical inclusion in potential flow of ideal compressible liquid: internal axisymmetric problem

The paper proposes a method to analyze the behavior of a mechanical system consisting of an infinite thin cylindrical shell filled with a flowing compressible liquid and containing a pulsating spherical inclusion. This coupled problem is solved using linear potential flow theory and the theory of thin elastic shells based on the Kirchhoff–Love hypotheses. Use is made of the possibility to represent the general solutions of equations of mathematical physics in different coordinate systems. This makes it possible to satisfy the boundary conditions on both spherical and cylindrical surfaces and to obtain a solution in the form of a Fourier series. Some numerical results are given     

Harmonic Vibrations of Shells with Cutouts Under Kinematic Conditions at Their Periphery

Problems on harmonic vibrations of shells with openings are considered for the case where displacements and angles of turn are specified at their periphery. A technique for determination of the natural frequencies and modes of vibrations is stated. The technique replaces the unknown peripheral forces and moments by a system of local statically equivalent loads. The intensity of these loads is found from the boundary conditions at the opening periphery. The solutions of the equations of shell theory for local loads are constructed by expanding the sought-for quantities into series in terms of the natural modes of the shell without openings. The performance of the approach developed is illustrated by calculating the natural frequencies and modes of shallow shells with a rectangular planform and various Gaussian curvatures     

A theoretical solution of cylindrical shells for axisymmetric plain strain elastodynamic problems

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface. Contributed by Ding Hao-jiang Foundation item: the National Natural Science Foundation of China (10172075) Biography: Ding Hao-jiang (1934-)     

层合闭口厚柱壳的温度应力

基于层合柱壳混合状态方程和边界条件的弱形式，建立了两端固支层合闭口柱壳的温度应力混合方程，给出了任意厚度合闭口柱壳在温度荷载和机械荷载共同作用下的解析解。     

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory (FSDT) of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young’s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.