基于区域分解的环肋圆柱壳-圆锥壳组合结构振动分析

提出了一种区域分解法来分析不同边界条件下环肋骨圆柱壳-圆锥壳组合结构的振动特性.首先把组合壳体分解为自由的圆柱壳、圆锥壳段;视环肋骨为离散元件,根据肋骨与圆柱壳段之间的变形协调条件,将肋骨的动能和应变能附加于圆柱壳段能量泛函中.然后基于分区广义变分和最小二乘加权残值法将所有分区界面的位移协调方程引入到组合壳体的能量泛函中.圆柱壳段、圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开.以自由-自由、自由-固支和固支-固支边界条件的环肋骨组合壳体为例,采用区域分解法分析了其自由振动及在不同激励下的振动响应.通过与有限元软件ANSYS结果进行对比,发现两种方法计算结果非常吻合,验证了区域分解方法的计算精度和高效性.     

圆柱壳自由振动特性分析方法研究

对传统解析法进行了改进,直接将复特征根代入边界条件构造了特征方阵;并基于圆柱壳Flügge 模型推导了位移形式的传递函数矩阵.在此基础上对比了改进的解析法、传递函数法、有限元法和实验方法获得的两端自由边界条件下圆柱壳的固有频率和模态.研究结果表明:改进的解析方法其特征方阵表达式简单且易于实现;同时通过与有限元和实验方法的对比,验证了改进解析法和位移形式传递函数矩阵的正确性;传递函数法相对于传统解析法对舍入误差敏感,可以通过增加字长的方式进行改善.     

复合材料旋转壳自由振动分析的新方法

提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动. 沿壳体旋转轴线将壳体分解为一些自由的层合壳段, 视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中, 使层合壳的振动分析问题归结为无约束泛函变分问题. 层合壳段位移变量采用Fourier 级数和Chebyshev 多项式展开. 以不同边界条件的层合圆柱壳、圆锥壳及球壳为例, 采用区域分解法分析了其自由振动, 并将计算结果与其他文献值进行了对比. 算例表明, 该方法具有高效率、高精度和收敛性好等优点.     

基于区域分解的薄壁回转壳自由振动分析

提出了一种区域分解法来分析不同组合边界条件的薄壁回转壳的自由振动.首先沿壳体母线方向将壳体分解为一些自由壳段,并采用广义变分和最小二乘加权残值法将壳体分区界面上的位移协调方程引入到壳体的势能泛函中;然后将壳段位移变量以Fourier级数和Chebyshev多项式展开,对总的势能泛函变分后得到回转壳的离散动力学方程.采用区域分解法分析了不同边界条件的圆柱壳、圆锥壳、抛物壳的自由振动,并将计算结果与其它文献值及 ANSYS 结果对比,结果表明:随着回转壳分区数目的增大,区域分解法计算出的壳体频率很快收敛;本文结果与其它方法计算结果非常吻合(相对误差不超过0.4%).采用该方法可高效计算不同组合边界条件回转壳体的低阶和高阶振动频率.     

正交各向异性功能梯度材料开口圆柱壳的自由振动分析

区别于一般圆柱壳,开口圆柱壳沿周向是不封闭的,因此具有四个边界,本文根据轴向梁式振动和轴向曲拱振动特性对各种端部与侧边边界条件下的壳体提出统一的位移振型函数,并根据哈密顿原理建立了材料参数与空间坐标相关的正交各向异性开口圆柱壳的动力变分方程,求出了不同材料属性下开敞圆柱壳固有频率与振型解的一般解析表达式,适用于任意边界条件下不同材料的开敞圆柱壳自由振动分析．     

薄壳的低频振动

用奇异摄动理论给出了一般形状旋转薄壳的低频自由振动解。此时,本征模态在壳内是无矩的,在边界附近存在边界层。文中列出了全部可能的齐次边界条件下的求解步骤和结果。最后,给出了圆柱壳的数值算例。     

功能梯度锥-柱连接壳的环向自由振动分析

论文旨在分析功能梯度锥-柱连接壳的环向自由振动,以提高其结构的振动性能和稳定性.采用Voigt模型和四参数幂函数体积分数描述功能梯度材料属性,基于Donnell薄壳理论推导出锥壳和柱壳的位移与应变关系,分别得出锥壳和柱壳的能量表达式.引入人工弹簧模拟边界和壳体间的连接条件,依据Chebyshev多项式构造位移函数,基于Rayleigh-Ritz法求解FGMs锥-柱连接壳模态频率,分析梯度指数、边界条件和几何参数对模态频率的影响.结果表明：增加陶瓷体积分数能有效提高结构的模态频率,而增大梯度指数则会降低结构的模态频率;边界约束条件越强,FGMs锥-柱连接壳的模态频率越高;随着环向波数的增大,边界条件对结构模态频率的影响越来越弱,边界约束效果作用于圆柱壳明显强于圆锥壳;当环向波数大于3时,随着壳体厚度增大,结构的模态频率呈线性提高,而增大锥柱壳长度比会降低结构模态频率;在锥柱壳长度比一定时,随着锥角的增大会使结构的模态频率先增加到峰值后减小.     

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。     

夹层圆柱壳振动的谱有限元分析

从哈密顿变分原理获得夹层圆柱壳的运动微分方程和边界条件,将谱有限元法用于夹层圆柱壳结构,推导出不同周向模态下夹层圆柱壳单元的动力刚度矩阵和隐式动力形状函数,分析长径比、径厚比、芯表厚度比、芯表模量比对固有频率和模态损耗因子的影响.研究表明:小径厚比、大长径比及大芯表厚度比有利于抑制夹层圆柱壳振动.     

层叠式PVDF压电作动器及圆柱壳的振动主动控制

设计了一个层叠式PVDF压电作动器用于壳结构的振动控制。考虑压电层、粘接层、壳体耦合关系,推导了表面局部粘贴层叠式PVDF压电作动器的圆柱壳的振动控制方程,给出了作动力与压电层和粘接层层数、厚度之间的关系以及作动力与作动器粘贴位置之间的关系。针对一端固定、另一端自由的圆柱壳,进行了振动控制仿真。结果表明层叠式PVDF压电作动器作动力与作动器层数近似成线性关系,增大作动器层数能有效增大作动力,在低控制电压下能显著抑制圆柱壳振动,作动器周向不完全粘贴时,在径向产生的径向作动力对壳体横向振动控制非常有利。说明了层叠式PVDF压电作动器是一种可用于壳体结构振动并具有良好作动效果的作动器。     

Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.     

Free vibration analysis of a finite circular cylindrical shell in contact with unbounded external fluid

The free flexural vibration of a finite cylindrical shell in contact with external fluid is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Donnell–Mushtari shell theory. The fluid is modeled based on the baffled shell model, which is applied to fluid–structure interaction problems. The kinetic energy of the fluid is derived by solving the boundary-value problem. The natural vibration characteristics of the submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, the nondimensionalized added virtual mass incremental factor for the submerged finite shell is derived. This factor can be readily used to estimate the change in the natural frequency of the shell due to the presence of the external fluid. Numerical results showed the efficacy of the proposed method, and comparison with previous results showed the validity of the theoretical results.     

Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid

The free flexural vibration of a hung clamped-free cylindrical shell partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modelled by using the Rayleigh-Ritz method based on Sanders’ shell theory. The kinetic energy of the fluid is derived by solving the boundary-value problem related to the fluid motion. The natural vibration characteristics of the partially submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, the nondimensionalized added virtual mass incremental factor for the partially submerged finite shell is derived. This factor can be readily used to estimate the change in the natural frequency of the shell due to the presence of a fluid.     

局部约束阻尼开口柱壳的减振分析及优化

为了缩减开口柱壳结构的振动,本文基于Lagrange方程以及Sanders薄壳理论建立了局部约束阻尼开口柱壳的动力学模型,分析了粘弹性单元分段数和厚度、阻尼单元占空比以及约束层敷设角和厚度对结构前三阶模态损耗因子和固有频率的影响,得到了各参数对结构振动特性的影响规律.并以前三阶损耗因子为目标,应用NSGA-Ⅱ遗传算法对...     

Thermomechanical vibration analysis of a functionally graded shell with flowing fluid

This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. The new features in this paper are helpful for the application and the design of functionally graded cylindrical shells containing fluid flow.     

Vibration characteristics of offshore cylindrical tanks

The vibration characteristics of offshore cylindrical tanks are studied in this paper. This is a typical topic of liquid-shell interaction system. In this paper, a general analytical method is presented by which the axial modal functions of liquid and shell are represented as the same complete orthogonal series for uncoupling the mode of liquid and shell. Simultaneously, the mode functions are expanded into a uniform convergence series and a linear polynomial, so that the problem of convergence and differentiation of mode series is solved. Therefore, the rather exact natural frequency and its corresponding mode of offshore cylindrical tank with different liquid depths, with arbitrary boundary conditions and with intermediate constraints can be obtained.     

Experiments on the dynamic behavior of fluid-coupled concentric cylinders

This paper describes an experimental vibration study of fluid-coupled coaxial cylinders that simulates the vibration of a reactor vessel with a thermal liner. The model cylinders are made of acrylic. Thickness and gap-size parameter studies are performed by a series of different compinations of three outside cylinders and nine inside cylinders that have variable thicknesses and diameters. Damping ratios are measured on a mode-by-mode basis for several combinations of cylinders. The vibrated cylinders are mounted to a rigid stand, with the cuter cylinder supported at both ends and the inner cylinder supported at either one end (pendulum mode) or both ends, as the case may be. The natural frequencies are obtained first in air and then with coaxial cylinders coupled by water. The mode shapes are obtained by circumferential (shell modes) and axial (shell/beam modes) mapping of the response with two diametrically opposite ‘roving’ Dymac eddy probes. In general, the natural vibration of the system has two distinct responses in-phase and/or out-of-phase modes, i.e., the radial displacement phase relationship between inner and outer cylinders. In the out-of-phase modes the frequency is shown to decrease to either zero or a very low limiting value as the gap size cecreases. The opposite occurs for in-phase modes. Damping ratios are found to be much higher for out-of-phase modes and for relatively rigid cylinders than for in-phase modes and flexible cylinders, respectively.     

爆炸加载下装配垫片对金属柱壳膨胀断裂影响研究

采用多普勒光纤探针测速技术（Doppler pins system，DPS，又称全光纤位移干涉测速技术）和高速摄影技术，研究装配垫片对金属柱壳膨胀断裂的影响，获得了有无垫片对应柱壳外表面位置的速度曲线和垫片对柱壳膨胀断裂影响明显的高速摄影图像。实验结果表明:与无垫片区域相比，垫片区域的柱壳外表面经历了先凸起后内凹的过程，导致垫片对应柱壳的径向运动位移发生反复错位，最终低于无垫片区域约0.34 mm，该位移差可能导致柱壳发生径向剪切断裂；实验结果还表明，在垫片与间隙交界处两侧（沿垫片方向约7.5°、沿间隙方向约9°）处各增加了一条裂纹，该断裂模式既不同于环向拉伸断裂，也不同于45°的剪切断裂，而是由垫片/间隙边界产生的两束稀疏应力波传到柱壳外表面引起的扰动影响所致，这个新的断裂模式与柱壳材料的动态力学性能密切相关。数值模拟结果表明，装配垫片对柱壳断裂机制影响不仅包含该处附加的质量效应，还应考虑炸药通过垫片后作用在柱壳上的冲击加载幅值变化、冲击加载时序与其他部位不同步的差异，以及垫片/间隙交界处引起的表面波传播对柱壳断裂模式的后续发展行为的影响。     

具脱层轴对称层合圆柱壳的振动模态分析

对具环向贯穿脱层的轴对称层合圆柱壳进行振动模态分析.首先,采用Heaviside阶梯函数,构造了一种适合于脱层壳的位移模式.通过对脱层壳的能量分析,应用瑞利--里兹法后,得到用时间函数表示的系统振动控制方程,然后对其求解,得到脱层壳模态分析的特征方程式.算例中,讨论了不同的脱层位置、脱层大小和脱层深度对脱层壳振动模态的影响.     

含环向表面裂纹圆柱壳的波传播特性研究

研究了振动波在含有环向表面裂纹的无限长圆柱壳中的传播特性.圆柱壳体的振动用Flügge方程来描述.运用线弹性断裂力学的理论,考虑到裂纹的张开、滑移和撕裂3种模式以及它们相互之间的耦合,利用分布的线弹簧来模拟裂纹并建立了裂纹所在区域的局部柔度矩阵,得到由此引起的附加位移和壳体中内力之间的关系.在入射波已知的情况下,根据裂纹两侧区域的位移和内力的连续性条件得到了反射和透射波的幅值系数.分析了入射波通过裂纹后的透射、反射系数与激励频率和裂纹尺寸之间的关系.为基于振动功率流方法识别圆柱壳表面损伤提供了理论基础.