复合材料层合圆柱壳的动力响应与层间应力

采用分层壳理论和厚度方向的二次插值函数推导出正交铺设层合圆柱壳的动力响应方程,并得出简支层合圆柱壳自由振动问题的解。对于给定算例,计算出的自振频率与三维分析的结果吻合良好,说明所推导的二维解具有足够精度。计算了前四阶模态对应的壳中应力。计算结果说明,对于高阶模态,层间应力相对于面内应力的比值远高于低阶模态的对应比值,高的层间正应力是高阶模态导致脱层破坏的主要原因。     

基于多元L-P法的复合材料圆柱壳内共振分析

以不同材料构成的复合材料圆柱壳作为研究模型,考虑几何非线性,动态弹性模量等因素,根据Donnell’s简化壳理论及经典层合壳理论建立其非线性振动方程。采用Galerkin 方法对振动方程进行离散化,应用多元L-P法求解了系统包含两个相邻轴向模态的非线性振动响应,得到了反映复杂内共振的幅频特性曲线,表明能量在两个模态之间相互传递,彼此影响牵制,系统存在1:1 内共振现象。最后利用多尺度法与多元L-P 法所得结果进行比较,得到了相同的结论。     

热环境中功能梯度圆柱壳内共振非线性模态

研究热环境中无限长功能梯度薄壁圆柱壳内共振非线性模态,给出系统发生内共振条件;采用多尺度法建立系统具有内共振的非线性调谐方程;讨论梯度指数、温度变化及振动能量对系统非线性模态频响特性影响。研究表明,随调谐参数的变化,系统非线性模态会发生分岔;调谐参数分岔值取决于梯度指数、温度及振动能量。     

高速旋转薄壁圆柱壳的行波共振特性研究

基于传递矩阵法研究了不同边界条件下高速旋转薄壁圆柱壳的行波共振特性。首先,基于Love 壳体理论,考虑离心力、科氏力和惯性力的影响,建立了旋转态薄壁圆柱壳的振动微分方程;然后,引入传递矩阵方法,根据壳体子段间的状态向量表达式,推导了结构的整体传递矩阵;最后,通过高精度的精细积分法进行求解,得到了两端简支、两端固支和固支-自由边界条件下的共振特性。算例结果表明,传递矩阵方法适合于求解高速旋转薄壁圆柱壳的行波共振特性,在三种边界条件下以周向模态的振动为主;在工作转速和1倍频激振力作用下,共振裕度小于10%的共振转速点仅有一个,而在其它倍频激振下的共振转速点不在安全裕值范围内。     

圆柱壳的轴向动力屈曲、参数共振与混沌运动

首先利用线性的动力屈曲方程,对受压的理想圆柱壳稳定性进行了动力分析。接着利用随时间周期变化的轴压载荷,导出Mathieu方程,讨论了轴压柱壳的参数共振。在Donnell-K偄rm偄n大挠度方程中引入惯性力和阻尼力给出圆柱壳的非线性运动方程,借助Bubnov-Galerkin法,将其转化为含有三次非线性的常微分方程。在定性分析的基础上,利用次谐轨道Melnikov函数和同宿轨道的Melnikov函数分别给出了前屈曲和后屈曲情况下发生Smale马蹄型混沌的临界条件。在此基础上,选用适当参数借用MATLAB数学软件,计算运动时程曲线、相图和Poincar啨映射,给出了混沌运动的数字特征。     

复合材料层合厚圆柱壳高阶理论的改进及其应用

建立了一个改进的LCW型的精化高阶理论,以分析厚圆柱壳的振动。提出u,v为三次多项式、w为二次多项式的位移模式,并利用上、下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,将三阶剪切变形理论的未知数缩减为7个,在此基础上建立了相应的有限元列式。通过一个典型算例,与Soldatos和Lam的高阶剪切变形理论的解析解作了比较,说明笔者的精化高阶理论是可行的,而且具有较高的精确性,比LCW高阶理论更具有实用性。还通过频率参数随长度半径比L/R的变化,说明由于考虑了法向应力和法向应变,本文方法更适用于长度半径比较小的结构。     

薄壁圆柱壳在流体脉动激励下的振动特性分析

摘要：为深入研究薄壁圆柱壳在流体脉动激励下的运动特性,应用Donnell简化壳理论,考虑阻尼、结构非线性和附加质量的影响,建立了薄壁圆柱壳在流体脉动激励下的非线性振动方程。基于Galerkin方法将偏微分方程转化为方便求解的常微分方程,利用多尺度法求解了系统主共振的一次近似解,得到了系统稳态响应的转迁集与分岔图,并通过奇异性分析,得到了系统工作稳定性和可靠性的结构参数区域。对薄壁圆柱壳在流体作用下的振动特性进行了数值模拟和实验研究,考察了阻尼系数、脉动频率、液体深度等对系统动力学特性的影响。研究表明,考虑阻尼、结构非线性和附加质量的非线性振动方程更能体现薄壁圆柱壳在流体脉动激励下完整的动力学特性,同时系统中存在多种分岔行为。     

几何参数对旋转薄壁圆柱壳振动特性的影响

摘 要: 本文基于Love壳体理论对旋转薄壁圆柱壳的自由振动特性进行分析,讨论几何参数对圆柱壳振动特性的影响。针对五种边界条件,分别分析厚度与半径之比、半径与长度之比对旋转薄壁圆柱壳固有频率特性的影响;探讨半径与长度之比对系统振型比的影响。分析结果表明：圆柱壳固有频率随着厚度与半径之比的增加而单调增加,增加幅度较小。半径与长度之比对圆柱壳固有频率与振型比的影响显著,且随其增大固有频率及振型比均不单调变化。由此可知,细长圆柱壳的振动特性与短粗圆柱壳的振动特性差异显著,研究结果为圆柱壳的动力学分析提供理论依据。     

基于混合分层理论的粘弹层合圆柱壳的阻尼振动和层间应力研究

应用混合分层理论,并在壳厚方向采用位移和应力插值函数推导出粘弹层合圆柱壳的动力学方程。计算了两层粘弹层合圆柱壳的振动频率和结构损耗因子,与Okazaki A的结果吻合良好。针对不同模量和厚度的粘弹性材料,计算出层合圆柱壳的层间横向应力的幅值。结果表明:过大的层间法向正应力是导致自由阻尼层合壳脱层破坏的主要因素,采用环向加强的粘弹性材料将有效地降低层间法向正应力的幅值。     

轴向极化的层合压电圆柱壳的自由振动

从轴向极化的三维圆柱型正交各向异性压电弹性力学基本方程出发,建立了状态方程。采用细分近似方法,得到了状态变量解。分析了两端简支的层合压电圆柱壳的自由振动问题,给出了频率方程的精确形式,并作了具体计算。     

粘弹性复合材料层合板壳的动力稳定性分析

分析面内周期激励下粘弹性层合平板以及轴向周期荷载作用下粘弹性层合圆柱壳的动力稳定性。设粘弹性复合材料服从Boltzmann积分型本构关系，其松弛模量由Prony—Dirichlet级数表示，基于薄板与薄壳理论，分别得到对称正交铺设层合板与层合圆柱壳的微分-积分型动力学方程，并应用谐波平衡法直接求解，忽略积分运算所产生的衰减项，导出确定动力不稳定区域边界的特征方程。分析结果表明，主要动力不稳定区域的缩小与材料的粘性参数以及结构横向振动的基频密切相关。     

Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories

The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory.     

Buckling of moderately thick laminated cylindrical shells: a review

The present paper is a review article on the problem of buckling of moderately thick, laminated, composite shells subjected to destabilizing loads. The loads consist of uniform axial compression, uniform lateral pressure and torsion applied individually or in combination. In all the works reported in the literature, the analysis is based on higher-order shear deformation (HOSD) shell theory and/or first-order shear deformation (FOSD) shell theory with or without a shear correction factor. Results obtained by these two shell theories and by employing classical thin shell theory are compared to determine the range of applicability of each in predicting critical conditions. The effect of stacking sequence, radius-to-thickness ratio and length-to-radius ratio is assessed. Typical numerical results are presented in tabular form. Moreover, some limited results, which are based on limit point analysis are also presented (imperfection sensitivity studies).     

受轴压黏弹性层合圆柱壳的极值点蠕变失稳

基于Donnell薄壳理论, 采用准弹性方法, 分析了含初始几何缺陷黏弹性层合圆柱壳极值点形式的延迟失稳特征。由轴向缩短量的突然增加定义失稳临界时间, 对玻璃纤维/环氧树脂层合圆柱壳进行了数值计算。结果表明: 圆柱壳存在临界时间趋于无穷的持久临界荷载; 表征延迟失稳程度的瞬时弹性临界荷载与持久临界荷载之差值随着初始几何缺陷的增加而减小; 边界条件、 铺设方式对延迟失稳的影响机制可通过对应弹性层合圆柱壳的缺陷敏感性分析来考察。      

Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells

A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis–Lagrange (M–L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part II: Numerical results

In this Part, the extensive parametric studies performed are reported and numerical results are presented for the buckling and postbuckling of fiber reinforced polymer matrix and metal matrix composite laminated shells subjected to axial compression or external pressure under different sets of environmental conditions. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The numerical results show that the buckling loads as well as postbuckling strength of the shell can be increased as a result of functionally graded fiber reinforcements. The results reveal that the effect of functionally graded fiber reinforcements on the buckling loads and postbuckling strength of shell with polymer matrix is more pronounced compared to the shell with metal matrix in the case of axial compression. In contrast, in the case of external pressure, the functionally graded fiber reinforcements may have a significant effect on the buckling pressure and postbuckling strength of the shell with metal matrix.     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. The non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths of FRC laminated cylindrical shells.     

叠层复合材料圆柱壳的细-宏观阻尼特性预测

研究了叠层复合材料圆柱壳的细-宏观阻尼特性.基于Reissner-Naghdi薄壳理论,给出了圆柱壳的振动微分方程,在分量变量的过程中,采用Haar小波级数表示轴向振型,Fourier级数表示环向振型,通过边界条件求解积分过程中出现的未知系数,进而得到用于分析圆柱壳自由振动特性的特征方程;基于单层混杂材料的细观力学阻尼...     

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined axial compression and torsion

A postbuckling analysis is presented for an anisotropic laminated cylindrical shell of finite length subjected to combined loading of axial compression and torsion. The governing equations are based on classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including the extension–twist, extension–flexural and flexural–twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells for different values of load-proportional parameters. The results show that the postbuckling characteristics depend significantly upon the load-proportional parameter. The results reveal that in combined loading cases the postbuckling equilibrium path is unstable and the shell structure is imperfection-sensitive.     

A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells

In this study a higher‐order shell theory is proposed for arbitrary shell geometries which allows the cross‐section to rotate with respect to the middle surface and to warp into a non‐planar surface. This new kinematic assumption satisfies the shear‐free surface boundary condition (BC) automatically. A new internal force expression is obtained based on this kinematic assumption. A new functional for arbitrary shell geometries is obtained employing Gâteaux differential method. During this variational process the BC is constructed and introduced to the functional in a systematic way. Two different mixed elements PRSH52 and CRSH52 are derived for parabolic and circular cylindrical shells, respectively, using the new functional. The element does not suffer from shear locking. The excellent performance of the new elements is verified by applying the method to some test problems. Copyright © 2000 John Wiley & Sons, Ltd.