主动约束层阻尼圆柱壳体的振动特性研究

基于弹性、粘弹性和压电材料本构方程,应用能量法建立了主动约束层阻尼（ACLD）圆柱壳体的有限元动力学方程。通过对压电传感层自感电压的比例、微分反馈控制,对主动约束层阻尼（ACLD）圆柱壳体进行了主被动一体化振动控制,研究了复合圆柱壳体的动力学响应特性。讨论了主动约束层阻尼（ACLD）片体的位置、覆盖率、粘弹性层厚度及控制增益等关键参数对圆柱壳体振动特性的影响。研究表明：主动约束层阻尼（ACLD）片体的粘贴位置与模态有关,针对不同模态,应采用不同的粘贴位置;覆盖率、粘弹性层厚度及控制增益等直接影响到振幅衰减程度,通过对片体位置、覆盖率、粘弹性层厚度及控制增益等关键参数的优化,能有效降低主动约束层阻尼圆柱壳体的振动,具有十分重要的工程应用价值。     

正交异性圆柱壳受局部外压的临界力

以往计算正交异性圆柱壳的临界力,多从微分方程组出发,编写较长的计算程序,化费很多机时才能得到结果。本文应用Cheng提出的准确四阶控制方程,把问题归化为解无限行列式的特征值。对于全部受外压,周向波数较多的壳导出了一个临界力公式。1.部分长度承受均布外压壳的临界力(图1) 文献[2]建立了正交异性圆柱壳准确的控制方程(本文使用的符号与[2]相同)     

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。     

圆柱薄壳稳定性的一个修正理论

著名的唐乃尔(Donnell)——穆什塔利的简化壳体理论只能较精确地适用于较短圆柱壳稳定性计算.其近似性误差随长度与半径之比的增加而增大.本文考虑了横向切力的影响,对非完善型圆柱壳体推导了几何非线性理论的基本方程,建立了对各种长度半径比的圆柱壳体稳定性均适用的修正理论.     

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。     

具有约束层阻尼贮液圆柱容器的耦振与减振特性分析

该文在对空圆柱层合壳(不充液)振动分析研究的基础上,借助线性势流理论,进一步考虑液固耦合效应,导出了敷有CLD贮液圆柱层合壳谐耦振的一阶常微分矩阵方程,该方程右边多了液动压力项.由于它不能预先给定,导致方程中出现未知项.为了克服这一困难,文中研究了液动压力的解式,并采用新型齐次扩容精细积分技术,提出了一种高效率和高精度的半解析半数值解法.进而还求解了CLD贮液圆柱容器在地面谐运动激励下的响应;通过大量数值计算分析了CLD的厚度、长度、敷设位置以及粘弹芯的复剪切模量对减振效果的影响.计算还表明了有液体的存在,这些影响和空容器时是不一样的.文中方法为CLD贮液容器的控制优化提供了有力手段.     

含有初始凹陷圆柱壳稳定承载能力的实验研究与数值计算

对含有初始轴对称凹陷的圆柱壳在轴向载荷作用下的稳定承载能力进行了研究。首先,通过实验研究,得到了不同凹陷参数及不同壳长条件下的临界载荷。同时,不考虑凹陷成形过程,仅把凹陷部分当做结构的不规则变化时,对含有凹陷圆柱壳建立三维有限元模型进行稳定性分析。在分析中考虑了初始缺陷(圆柱壳成形加工中的不平直度、椭圆度、初始弯曲等因素引起)幅值f0=0.1t和f0=0.2t(t为壳体壁厚),得到了不同凹陷参数及不同壳长的临界载荷。结果表明:含有凹陷圆柱壳稳定承载能力对初始缺陷不太敏感,即:初始缺陷与凹陷相比,对稳定承载能力的影响极小。数值计算结果与实验结果吻合较好,共同给出了含有初始轴对称凹陷圆柱壳的承载能力随凹陷幅值、长度及圆柱壳长度的变化而改变的规律。     

变截面短柱壳的热应力

在变截面薄柱壳平衡方程的一般推导中,常忽略剪力对挠度的影响。但是对于短柱壳,这种影响就不可忽略。从等截面圆柱壳受静荷载的情况来看,在壳体长度与壁厚比值的一定范围内,与不考虑剪力对挠度影响的结果相比,考虑剪力影响后弯矩的修正值可以达到(20-40)%。本文从考虑剪力对挠度的影响出发,导出了截面厚度随壳体轴向坐标线性变化的变截面短圆柱壳在...     

具脱层的正交铺设圆柱壳的初始后屈曲分析

基于非线性弹性理论,建立了含脱层正交铺设圆柱壳的后屈曲控制方程,应用Koiter初始后屈曲理论和小参数摄动法,导出了系统的一阶和二阶摄动控制方程,以及相应的边界条件、位移连续条件和力平衡条件,然后逐阶求解．算例中,讨论了不同脱层深度和长度对脱层复合材料圆柱壳屈曲和初始后屈曲特性的影响,并与已有文献进行了比较．     

含裂纹薄壁圆柱壳弹塑性失稳极限荷载的解析解

为了得到含环向裂纹压弯薄壁圆柱壳失稳的极限荷载,基于Je?ek解析法,先利用裂纹面的平衡方程、变形几何关系和物理方程,得到在压弯荷载作用下圆柱壳轴力与裂纹面挠度的关系式;再利用极值条件,推导出在轴压和弯矩共同作用下含裂纹薄壁圆柱壳失稳时极限荷载的解析表达式。利用数值计算分析裂纹长度、长细比以及端部施加弯矩对圆柱壳极限荷载、弹性区高度和圆柱壳裂纹截面处挠度的影响,通过有限元数值结果验证极限荷载解析解的准确性。计算结果表明:与无裂纹完善构件相比,弯矩对含裂纹圆柱壳的极限荷载Pu的影响最为显著,其降低幅值可达3.78%～23.18%;弯矩的增加也会导致构件弹性区高度逐渐减小,裂纹面处的挠度呈非线性增长。本文研究弥补了目前该类问题缺乏理论解析解的不足。     

Spectral strip-element method for beams treated with active constrained layer damping

For vibration analysis of beams fully treated with active constrained layer damping (ACLD), a new approach called spectral strip-element method (SSEM) based on the spectral finite element method (SFEM) is proposed. It can avoid difficulties in solving the characteristic equation with higher orders and unknown parameters for wave numbers when using the SFEM; simultaneously, advantages of a very few elements and high accuracy of the SFEM are kept. A numerical example shows that the proposed method is very effective and reliable, compared with the exact solutions resulted from the spectral transfer matrix method (STMM).     

Nonaxisymmetric Vibrations of Discretely Reinforced Inhomogeneous Multilayer Cylindrical Shells under Nonstationary Loads

The equations of nonaxisymmetric vibrations of discretely reinforced multilayer cylindrical shells are analyzed. A refined Timoshenko model of shells and beams is used to analyze elements of an elastic structure. The vibration equations for an inhomogeneous elastic system are derived using the Reissner variational principle. The numerical solver of the dynamic equations is based on the integro-interpolation method used to construct finite-difference schemes for equations with discontinuous coefficients. The dynamic behavior of a five-layer cylindrical shell under distributed nonstationary loading is analyzed     

径向余弦冲击的长圆柱壳弹性脉冲屈曲

根据已有的实验现象假定变形模态，采用Ｌａｇｒａｎｇｅ方法分析了单位长度薄圆环在余弦冲击载荷作用下的弹性脉冲动屈曲。导出了动力屈曲方程组，借助数值方法求解方程，并与已有的计算进行了比较，得出结论     

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D) functional graded material(FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse,and rotation deformations. By dint of the differential quadrature method(DQM), the governing equations are discretized to conduct the analysis of natural dynamic charact...     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

MODELING AND DYNAMICS ANALYSIS OF SHELLS OF REVOLUTION BY PARTIALLY ACTIVE CONSTRAINED LAYER DAMPING TREATMENT

A new model for a smart shell of revolution treated with active constrained layer damping （ACLD） is developed, and the damping effects of the ACLD treatment are discussed. The motion and electric analytical formulation of the piezoelectric constrained layer are presented first. Based on the authors~ recent research on shells of revolution treated with passive constrained layer damping （PCLD）, the integrated first-order differential matrix equation of a shell of revolution partially treated with ring ACLD blocks is derived in the frequency domain. By virtue of the extended homogeneous capacity precision integration technology, a stable and simple numerical method is further proposed to solve the above equation. Then, the vibration responses of an ACLD shell of revolution are measured by using the present model and method. The results show that the control performance of the ACLD treatment is complicated and frequency-dependent. In a certain frequency range, the ACLD treatment can achieve better damping characteristics compared with the conventional PCLD treatment.     

Forced vibrations of three-layer elliptic cylindrical shells under distributed loads

The dynamic behavior of a three-layer elliptic cylindrical shell is studied and associated problems are formulated. The refined Timoshenko model is used. The numerical method used to solve the equations of motion is based on the integro-interpolation differencing method. The dynamic behavior of a three-layer elliptic cylindrical shell under a distributed nonstationary load is studied.     

不规则区域平面问题的条形传递函数方法

对条形传递函数方法进行了改进,提出了映射条形传递函数方法,用于处理非正规形状区域的平面问题。在本文方法中,一个非正规区域被映射成为若干矩形子区域的组合,在这些矩形子区域内划分条形单元,进而建立起位移离散模型。利用变分关系对模型处理,可以得到问题的动态控制方程。应用改进后得到的数值传递函数求解,就可以得到系统的动力、静力响应。文后应用上述方法建立了应用模型并给出了数值算法,结果表明本方法继承了原方法精度高、处理规范、便于求解动态问题等,并成功地应用到了非规则区域的平面问题中。     

The dynamic responses of cylindrical shells including geometric and material nonlinearities

The methods of finite-element analysis are applied to the problem of large deflection elastic-plastic dynamic responses of cylindrical shells to transient loading. Assumeddisplacement quadrilateral finite-elements of a cylindrical panel are used to idealize the cylindrical shell structure. The formulation is based upon the Principle of Virtual Work and D'Alembert's Principle. A direct numerical integration procedure is employed to solve the resulting equations of motion timewise. The present predicted dynamic responses of an explosively-loaded clamped cylindrical panel are compared with other independent predictions and with experimentally measured responses; very good agreement is observed.