轴向荷载下功能梯度材料圆柱壳的动力屈曲

基于Donnell壳体理论和经典板壳理论,利用Hamilton变分原理得到轴向荷载作用下材料属性呈幂律分布的功能梯度材料圆柱壳的动力屈曲控制方程。根据圆柱壳周向连续性设出径向位移的函数表达,利用分离变量法求解得到功能梯度材料圆柱壳在轴向荷载作用下的动力屈曲临界荷载的解析表达式和屈曲解。利用MATLAB软件编程计算,讨论了径厚比、梯度指数、环向模态数、轴向模态数等对功能梯度材料圆柱壳动力屈曲临界荷载的影响。结果表明:圆柱壳的临界荷载随临界长度的增加而减小;冲击端为夹支的临界荷载比冲击端为简支的临界荷载大,说明约束条件对临界荷载有较大影响;圆柱壳的临界荷载随着模态数的增加而增大,说明临界荷载越大,高阶模态越易被激发;屈曲模态图随着模态数的增加而复杂化。     

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。      

滑移和同步脉冲载荷下圆柱壳瞬态响应的对比分析

为定量分析滑移和同步脉冲载荷下圆柱壳瞬态响应的差异,以不同尺寸的圆柱壳为对象,分别加载滑移和同步脉冲载荷进行数值模拟,研究了平均应变差异随几何特征参数的变化规律。结果表明:对于圆柱壳结构,平均应变差异随径厚比d/t变化的情况与长度相关,厚度变化对圆柱壳的平均应变差异影响较小;对于不同厚度的圆柱壳,平均应变差异随细长比d/l的增大而减小,当d/l≤0.45时,平均应变差异在20%以内。分析结果为相关试验设计和结果评估提供了有价值的参考。     

虚拟网格法模拟静止或运动并列布置双圆柱绕流现象

基于自主开发的虚拟网格浸入边界法求解器,数值模拟并列布置双圆柱绕流问题,分析了不同圆柱间距和振荡频率下双圆柱的水动力载荷和尾涡特性。数值算法采用时间半隐式有限差分虚拟网格法,在固定笛卡尔交错网格上求解不可压缩黏性Navier-Stokes方程。在虚拟网格法中,为了考虑任意多体边界对流场的影响,通过设置物体内的虚拟网格单元,采用适当的插值模块及技术重构虚拟网格,以施加浸入动边界条件。首先,数值模拟不同间距下并列布置双圆柱静止绕流问题,分析了不同间距对圆柱表面载荷和水动力特性的影响,捕捉到单涡脱落、偏斜流和双涡脱落等典型流动形态。其次,数值模拟自由流中并列布置圆柱振荡问题,验证了本文方法的精度和模拟多体动边界的准确性和可靠性。最后,分析了不同间距和不同振荡频率下双圆柱的水动力载荷变化规律,观察到不同振荡频率下偏斜流、双涡对称脱落和涡列融合等典型流动干扰现象。     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

轴压柱壳在连续波激光辐照下的屈曲破坏

介绍轴向预压柱壳侧表面在连续被ＣＯ＿２激光辐照下的屈曲破坏实验。结果表明，辐照面的材料热软化将诱发预压柱壳的屈曲破坏，并且柱壳预压的屈曲；临界载荷将随激光入射能量的增高而降低，考虑到持续轴压载荷和柱壳的后屈曲特性，可能引起柱壳屈曲的灾难性塌陷破坏。     

轴向冲击载荷作用下双壁碳纳米管的动力屈曲

应用改进的有限元方法,建立考虑层间范德华力作用的壳-弹簧非线性有限元模型,基于B-R运动准则,系统地研究了双壁碳纳米管的动力屈曲问题,得到了轴向冲击载荷作用下双壁碳纳米管的临界动力屈曲载荷和临界动力失效载荷. 研究结果表明,在动力屈曲过程中,双壁碳纳米管层间距的变化非常小,各管的变形相互协调;碳纳米管中应力波的传播导致碳纳米管出现非对称屈曲模态,可明显观测到四个环向波瓣,沿着碳纳米管的轴线方向,四个波瓣的波峰和波谷交替变化. 对碳纳米管动力屈曲问题的研究表明,冲击载荷的大小和持续时间对碳纳米管的动力屈曲有 关键词： 碳纳米管 动力屈曲 冲击载荷     

填充介质圆柱壳在侧向爆炸冲击作用下的变形型面研究

对填充介质圆柱壳在侧向爆炸冲击作用下的变形型面进行了实验研究,获得了圆柱壳的最终变形型面。基于刚塑性动力学中的塑性铰理论建立了相应的分析模型,将圆柱壳划分为多个首尾相连的刚性方杆,利用方杆的平动、转动描述圆柱壳的变形过程,详细推导了相邻方杆间弹簧力、弯矩和偏折角等的表达式,考察了侧向炸药覆盖宽度和圆柱壳初始速度等因素对变形型面的影响。研究结果表明:所建立的分析模型能够有效地预测圆柱壳的变形型面,侧向炸药覆盖宽度和爆轰威力是影响圆柱壳最终变形型面的关键因素,可通过调整侧向炸药的覆盖宽度和圆柱壳初始速度实现不同的圆柱壳变形型面。     

深水爆炸冲击波作用下圆柱壳动态响应影响因素的数值模拟研究

 运用通用有限元程序ABAQUS,对圆柱壳在深水爆炸冲击波作用下的动态响应进行了数值模拟,研究了圆柱壳所处深度、爆心方位和预应力对于圆柱壳动态响应的影响。研究结果表明：在同样的水下爆炸冲击波作用下,随着深度的增大,圆柱壳的毁伤逐渐加重,而且响应过程中的变形逐渐增大,低频响应阶段的速度曲线趋于平坦;爆距不变时,不同的爆心方位在不同深度上的毁伤效果存在一定差异;预应力的存在使圆柱壳的毁伤加重,并且预应力对圆柱壳动态响应的影响与爆心方位有关。研究结果对于潜体结构的生命力评估具有一定参考价值。     

水中双层无限长圆柱壳体声散射

研究水下双层无限长圆柱壳体的声散射。采用弹性薄壳理论和Fourier变换方法导出了散射声场的解析解。并分别计算了平面波正横和斜入射单层和双层无限长圆柱壳体的远场散射形态函数。计算表明在不同的入射角,由于不同类型的弹性波被激励,散射波呈现不同的特性。通常双层无限长圆柱壳体的散射特性由外壳、内壳和中间耦合水层共同作用决定。但外壳很薄、内壳较厚、水层较薄时,无限长充水双层圆柱壳体的低频散射特性主要由单层内壳决定。当然这时外壳的共振特性也不能忽略。     

Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm

In this paper, the genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. The optimization process contains six design variables including the shell thickness, the number of stiffeners, the width and height of stiffeners, the stiffeners eccentricity distribution order, and the stiffeners spacing distribution order. The real coding scheme is used for representing the solution string, while the generation number-based adaptive penalty function is applied for penalizing infeasible solutions. In analytical solution, the Ritz method is applied and the stiffeners are treated as discrete elements. Some examples of simply supported cylindrical shells with nonuniform eccentricity distribution and nonuniform rings spacing distribution are provided to demonstrate the optimality of the solution obtained by the GA technique. The effects of objective weighting coefficients and bounding values of the design variables on the optimum solution are studied for various cases. The results show that the optimal solution can vary with the weighting coefficients significantly. It is also found that extreme reduction and augmentation in turn in the structural weight and fundamental frequency can be simultaneously achieved by selecting suitable stiffeners’ geometrical parameters and distributions. Furthermore, the bounding values of the design variables have great effects on the optimum results.     

Influence of initial geometrical imperfections on vibrations of axially compressed stiffened cylindrical shells

The vibrations of stiffened cylindrical shells having axisymmetric or asymmetric initial geometrical imperfections and axial preload are analyzed. The analysis is based on a solution of the von Kárman-Donnell non-linear shell equations, an “exact” solution of the compatibility equation, and a first order approximation by the Galerkin method of the equilibrium equation. The stiffeners are closely spaced and “smeared” stiffener theory is employed. The results of an extensive parametric study carried out on shells similar to those used in vibration and buckling tests at the Technion show that stiffening of the shell will lower the imperfection-sensitivity of its free vibrations, but the decrease depends on the type of stiffening (stringers or rings), the mode shapes of the vibration and the imperfection, the stiffener strength and eccentricity. The imperfection-sensitivity decrease, caused by the stiffeners, is greater for vibration mode shapes with high imperfection-sensitivity than for other vibration mode shapes. The sensitivity differences between stringer and ring-stiffened shells depend especially on the vibration and the imperfection mode shapes, and on their coupling. Small imperfections change the natural frequencies of stiffened shells in the same directions as for isotropic shells, but to a smaller extent. The frequency dependence on the external load is also strongly affected by the imperfection mode shape. The results correlate well with earlier ones for isotropic shells.     

Buckling of 2D-FG Cylindrical Shells under Combined External Pressure and Axial Compression

This paper presents the stability of two-dimensional functionally graded (2D-FG) cylindrical shells subjected to combined external pressure and axial compression loads, based on classical shell theory. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and determined by the rule of mixture. The Euler's equation is employed to derive the stability equations, which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells. The effects of shell geometry, the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM. The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.     

On the durable critic load in creep buckling of viscoelastic laminated plates and circular cylindrical shells

Based on the first order shear deformation theory and classic buckling theory, the paper investigates the creep buckling behavior of viscoelastic laminated plates and laminated circular cylindrical shells. The analysis and elaboration of both instantaneous elastic critic load and durable critic load are emphasized. The buckling load in phase domain is obtained from governing equations by applying Laplace transform, and the instantaneous elastic critic load and durable critic load are determined according to the extreme value theorem for inverse Laplace transform. It is shown that viscoelastic approach and quasi-elastic approach yield identical solutions for these two types of critic load respectively. A transverse disturbance model is developed to give the same mechanics significance of durable critic load as that of elastic critic load. Two types of critic loads of boron/epoxy composite laminated plates and circular cylindrical shells are discussed in detail individually, and the influencing factors to induce creep buckling are revealed by examining the viscoelasticity incorporated in transverse shear deformation and in-plane flexibility.     

Modal densities of stiffened,axially loaded cylindrical shells

Donnell type equations are used to calculate modal densities of thin cylindrical shells, stiffened by closely spaced eccentric rings and stringers, and subjected to axial stresses. The formulation presented degenerates to known results for unstiffened, unloaded shells. The effects of stiffeners and axial stresses on modal densities are examined by numerous examples, and qualitative conclusions referring to radiation efficiency and transmission ratio of the stiffened shells are drawn.     

Vibration of simply supported cylindrical shells with longitudinal stiffeners

The vibration of simply supported cylindrical shells stiffened by discrete longitudinal stiffeners is investigated by using an energy method. Vlasov's thin walled beam theory is used for stringers. Shell theories based on Donnell's approximate theory and Flügge's more exact theory are used for the skin and numerical results indicate that Donnell's approximate theory gives excellent results for the stiffened shells. Sinusoidal wave form is considered in the longitudinal direction, and mode shapes in the circumferential direction are represented by Fourier series. Numerical results on frequencies and mode shapes computed for a shell stiffened by various number of stiffeners are presented and compared favorably with existing experimental results and other analytical solutions.     

TRANSIENT ANALYSIS OF RING-STIFFENED COMPOSITE CYLINDRICAL SHELLS WITH BOTH EDGES CLAMPED

A theoretical method is developed to investigate the effects of ring stiffeners on vibration characteristics and transient responses for the ring-stiffened composite cylindrical shells subjected to the step pulse loading. Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect is adopted to formulate the theoretical model. The ring stiffeners are laminated with a composite material and have a uniform rectangular cross-section. The Rayleigh-Ritz procedure is applied to obtain the frequency equation. The modal analysis technique is used to develop the analytical solutions of the transient response. The analysis is based on an expansion of the loads, displacements in the double Fourier series that satisfy the boundary conditions. The effect of stiffener's eccentricity, number, size, and position on transient response of the shells is examined. The theoretical results are verified by comparison with FEM results.     

TRANSIENT DYNAMIC RESPONSE ANALYSIS OF ORTHOTROPIC CIRCULAR CYLINDRICAL SHELL UNDER EXTERNAL HYDROSTATIC PRESSURE

Following Flügge's exact derivation for the buckling of cylindrical shells, the equations of motion for transient dynamic loading of orthotropic circular cylindrical shells under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The effect of shell's parameters, external hydrostatic pressure and material properties on the shell response has been studied in detail. A part of tables and figures are given in this paper.     

Vibrations of initially stressed cylinders of variable thickness

Natural frequencies and buckling loads for cylindrical shells having linearly varying thickness are obtained by using a segmentation technique. The present results for free vibration of a cylinder compare very well with those obtained previously. The effect of the thickness variation on the frequencies of a cylindrical shell is studied. Frequencies are also calculated for a cylinder of variable thickness under axial compression and a relationship between the frequency and axial compression is obtained for a particular wave number.     

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。