Free vibration analysis of circular cylindrical shells

A general analytical method is presented for evaluating the free vibration characteristics of a circular cylindrical shell with classical boundary conditions of any type. The solution is obtained through a direct solution procedure in which Sanders' shell equations are used with the axial modal displacements represented as simple Fourier series expressions. Stokes' transformation is exploited to obtain correct series expressions for the derivatives of the Fourier series. An explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions. The accuracy of the method is checked against available data. The method is used to find the modal characteristics of the thermal liner model of the U.S. Fast Test Reactor (FTP). The numerical results obtained are compared with finite element method solutions.     

Axisymmetric vibration of prestressed non-uniform cantilever cylindrical shells

The extended Galerkin method has been used in the investigation of axially loaded clamped-free homogeneous, isotropic and elastic cylindrical shells. Both mass and stiffnesses are considered to vary along the longitudinal direction. Legendre polynomials have been used as shape functions which lead to a simple and systematic procedure in determining the natural frequencies and mode shapes. Some numerical results are presented.     

Simplified equations and solutions for the vibration of orthotropic cylindrical shells

Starting with Love type equations of motion for orthotropic circular cylindrical shells, the theory is simplified by assumptions similar to those in the Donnell-Mushtari-Vlasov development for isotropic shells. Closed form solutions for simply supported cases are then obtained. Results of two example cases are compared with finite element results and are shown to agree well. It is argued that this simplified approach allows easy assessment of the influence of design parameter changes.     

Free vibration of non-circular cylindrical shells with variable circumferential profile

An analysis is presented of the free vibration of non-circular cylindrical shells with a variable circumferential profile expressed as an arbitrary function. The applicability of thin-shell theory is assumed and the governing equations of vibration of a non-circular cylindrical shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the transfer matrix has been determined by numerical integration of the matrix equation, the natural frequencies and mode shapes of vibration are calculated numerically in terms of the matrix elements. The method is applied to cylindrical shells of three or four-lobed cross-section, and the effects of the length of the shell and the radius at the lobed corners on the vibration are studied.     

Free vibration of non-circular cylindrical shells with longitudinal interior partitions

An analysis is presented for the free vibration of a simply supported non-circular cylindrical shell with longitudinal interior partitions. For this purpose, the governing equations of vibration of a non-circular cylindrical shell including a plate as special case are written in a matrix differential equation by using the transfer matrix in the circumferential direction. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrix of the shell and the point matrix at the joint of the structure matrix. The method is applied to approximately elliptical cylindrical shells with an interior plate, and the natural frequencies and the mode shapes of vibration are calculated numerically, giving the results.     

Purely axial vibration of thin cylindrical shells with shear-diaphragm boundary conditions

This work presents the free vibration characteristics of a thin walled cylindrical shell at the zeroth axial mode number. The cylindrical shell has shear-diaphragm boundary conditions at each end. The thin shell equations by Flügge are used as these equations of motion lead to more accurate results at low frequencies. The zeroth axial mode number is found to occur at the cut-on of the second class of waves. The mode shapes at these natural frequencies result in a purely axial displacement of the middle surface of the shell. High modal density for the first class of waves occurs before the cutting-on of the second class of waves. Beyond this frequency, the dynamic response is dominated by the latter modes.     

Free vibration study of layered cylindrical shells by collocation with splines

The free vibration of circular cylindrical thin shells, made up of uniform layers of isotropic or specially orthotropic materials, is studied using point collocation method and employing spline function approximations. The equations of motion for the shell are derived by extending Love's first approximation theory. Assuming the solution in a separable form a system of coupled differential equations, in the longitudinal, circumferential and transverse displacement functions, is obtained. These functions are approximated by Bickley-type splines of suitable orders. The process of point collocation with suitable boundary conditions results in a generalized eigenvalue problem from which the values of a frequency parameter and the corresponding mode shapes of vibration, for specified values of the other parameters, are obtained. Two types of boundary conditions and four types of layers are considered. The effect of neglecting the coupling between the flexural and extensional displacements is analysed. The influences of the relative layer thickness, a length parameter and a total thickness parameter on the frequencies are studied. Both axisymmetric and asymmetric vibrations are investigated. The effect of the circumferential node number on the vibrational behaviour of the shell is also analysed.     

轴向振动对圆柱形液体自由表面流的影响

通过光学实时观察法研究了轴向振动对恒温圆柱形容器内液体自由表面流动行为的影响。该地面实验是在一个频率为100赫兹的电磁振动台上进行的，水－甘油的混合溶液作为模型体系。结果发现，小于100mm的振动振幅能够使自由表面产生稳定的流动。这种流动主要是由沿自由表面传播的毛细波与斯托克斯边界层效应的共同作用驱动的。随着振动振幅的变化，稳态流会呈现不同的流动花样。高振幅作用下，稳态流动趋向于周期性流甚至成为湍流，这个过程可以通过临界无量纲雷诺数(Nre)c来表征，实验中得到的(Nre)c值在10-2 ～ 10-1范围内。此外，利用示踪粒子散射技术对自由表面的流动速度进行了测量，结果显示流速随粘度的增大而减小，并且随振幅的增加呈抛物线形增长。     

Simplified prediction of the modal characteristics of ring-stiffened cylindrical shells

Two simplified means of predicting the modal characteristics of ring-stiffened circular cylindrical shells are developed. These approaches are based on the receptance method and use the modal characteristics of the unstiffened cylinder and of the rings as inputs. In the first approach simplicity is achieved while retaining accuracy by confining the geometry to a cylindrical shell with simply supported ends stiffened by identical, equally-spaced rings. For this not uncommon configuration, a single non-matrix frequency equation is developed which can be solved surely and rapidly by a numerical method. The second approach is more general and provides insight into the effects of ring stiffeners. The results are not as precise as the first approach, but the calculations are simple enough to be carried out at one's desk given the modal characteristics of the unstiffened cylindrical shell and of the rings.     

Underwater sound scattering characteristics of three paralleling flexible cylindrical shells

To investigate the sound scattering characteristics of three paralleling flexible cylindrical shells with the plane incident wave,a mathematical model is established with Fourier series expansion method which involves the flexible vibration,the sound radiation and the rigid scattering of each shell and their coupling through the sound field.With the model,the difference between the flexible radiation term and the rigid scattering term of the sound field of three combined cylindrical shells is ca...     

三弹性圆柱壳体多重耦合声辐射计算方法

为研究多圆柱壳组合结构的声辐射特性,采用模态叠加法建立了3个并排无限长弹性圆柱壳的振动声散射耦合物理模型,充分考虑了三圆柱壳的表面振动与散射声场的耦合,其中散射声场可分解为各圆柱壳刚性散射声场和弹性辐射声场的叠加,数学上将各壳间的声场耦合关系通过柱函数加法公式描述。利用该物理模型,分析了多重散射对稳态声场求解结果的影响,比较了三圆柱壳耦合系统与单个圆柱壳系统的辐射声场指向性、声压级及辐射声功率级的差异及其产生机理,结果表明:结构弹性耦合声辐射不仅在低频对总声场有显著影响,在高频范围也不可忽略;另外,针对本文设定参数的组合圆柱壳,在150 Hz以上频段,两旁圆柱壳对中间圆柱壳在正横方位产生了声辐射遮蔽效应,垂直方位则体现声泄漏作用。本文建立的方法可推广到三维空间任意多壳结构的声振耦合建模。     

水下三弹性柱壳耦合声散射特性研究

为研究3个并排无限长弹性圆柱壳受垂直于柱轴方向的平面声波作用的声散射特性,采用Fourier级数展开法建立了圆柱壳声散射数学物理模型,考虑了三圆柱壳弹性振动声辐射和刚性声散射,建立了3个壳体辐射声场和刚性散射声场的耦合作用关系,比对了等效散射强度的刚性散射分量与弹性散射分量,并分析了三壳体等效散射强度特性。计算结果表明:当ka₂>40,在频率f=3000 Hz以上频段,弹性分量对等效散射强度变化趋势的贡献可以忽略。当ka₂>30,在频率f=2400 Hz以上频段,弹性散射分量对等效散射强度影响不超过3 dB;三壳与单壳的等效散射强度在0°入射角方位相当,其它方位三壳体等效散射强度明显大于单壳体。本文的理论公式可推广到任意数量阻抗柱的声透射和声反射问题。     

Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations

In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge–Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency–amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.     

带缺口加强圈的圆柱壳屈曲特性分析

以低温液体罐车外筒体为原型,采用有限元方法研究了带缺口加强圈的圆柱壳的屈曲特性。着重考察了加强圈缺口间的夹角、加强圈之间的间距、边界条件对此类结构屈曲载荷的影响。计算结果表明:圆柱壳的屈曲载荷与加强圈缺口间夹角不是简单的线性关系,当加强圈缺口间夹角增大到一定程度后,圆柱壳的屈曲载荷几乎不再变化;加强圈布置的均匀度不但会影响到圆柱壳的屈曲载荷,同时也对其屈曲模态产生影响;在不同的边界条件下,圆柱壳也表现出不同的屈曲特性。     

水中有限长加肋圆柱壳体振动和声辐射近似解析解

加肋圆柱壳体是水下航行器的主要结构形式。将肋骨对壳体的作用简化为只有法向力,本文导出了水中有限长加肋圆柱壳体的振动和声辐射的近似解析解。其中肋骨的作用表现为在无肋的耦合振动方程中增加附加阻抗,因此壳体的振动和声辐射由壳体的机械阻抗、流体的辐射声阻抗和肋骨的附加阻抗所决定。数值计算例子表明,在低频情况下,加肋对辐射声功率影响不大,但将降低表面平均振速,从而增加声辐射效率。     

考虑铺层角的复合材料圆柱壳自由振动三维弹性准确解

为了获得任意角度铺层的多层复合材料圆柱壳的自由振动准确解,在三维弹性理论的基础上,结合分层理论和状态空间法,建立横向位移和应力的传递矩阵,轴向和环向位移采用双螺旋模式的位移函数,对任意角度铺层复合材料圆柱壳简支边界条件下的自由振动进行了理论推导,得到了自由振动方程的精确形式。与文献理论解和有限元计算结果对比,结果表明,关注频率在2倍的环频率以下时,薄壳的固有频率计算精度能控制在1%以内,厚壳的固有频率计算精度能控制在2%以内。对于厚壳的计算可将壳体沿厚度方向划分为多层来处理,这样能有效提高计算精度。计算分析了铺层角对壳体固有频率的影响,环向模态数较低时,固有频率随着铺层角的增加呈抛物线变化趋势;环向模态数较高时,固有频率随着铺层角的增大单调递增。该理论方法同样适用于均质各向同性壳和正交各向异性圆柱壳。     

Vibration characteristics of thin rotating cylindrical shells with various boundary conditions

An analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of Fourier series expansion method. Based on Sanders’ shell equations, the governing equations of motion which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotating are derived. The displacement field is expressed as a product of Fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements. Stokes’ transformation is employed to derive the derivatives of the Fourier series expressions. Then, through the process of formula derivation, an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type. Once the frequency equation has been determined, the frequencies are calculated numerically. To validate the present analysis, comparisons between the results of the present method and previous studies are performed and very good agreement is achieved. Finally, the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries, and the results are presented.     

Static cylindrical matter shells

Static cylindrical shells composed of massive particles arising from matching of two different Levi–Civita space-times are studied for the shell satisfying either an isotropic or an anisotropic equation of state. We find that these solutions satisfy the energy conditions for certain ranges of the parameters.