Analysis for the thermoelastic bending of a functionally graded material cylindrical shell

An analytic study for thermoelastic bending of a functionally graded material (FGM) cylindrical shell subjected to a uniform transverse mechanical load and non-uniform thermal loads is presented. Based on the classical linear shell theory, the equations with the radial deflection and horizontal displacement are derived out. An arbitrary material property of the FGM cylindrical shell is assumed to vary through the thickness of the cylindrical shell, and exact solution of the problem is obtained by using an analytic method. For the FGM cylindrical shell with fixed and simply supported boundary conditions, the effects of mechanical load, thermal load and the power law exponent on the deformation of the FGM cylindrical shell are analyzed and discussed.     

ACTIVE CONTROL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL''''S VIBRATION UNDER HYDROSTATIC PRESSURE

IntroductionDuetotheintrinsicdirectandconversepiezoelectriceffects,piezoelectricmaterialscanbeeffectivelyusedtoproducesensorsoractuatorsfortheactiveshapeorvibrationcontrolostructures.Therefore,theuseofpiezoelectricmaterialsinintelligentstructuresattractedmanyattentionsinrecentyears.Thedesignofsuchactivesystemsrequiresgoodunderstandingofthemechanical_electricinteractionbetweenthestructuresandpiezoelectricmaterials.Manyinvestigationshavebeendoneinthisfield[1].However,mostofthesestudiesarebasedo…     

金属圆柱壳受大质量低速冲击的屈曲变形

对钢质和铜质金属圆柱壳的轴向冲击动力响应进行了实验研究,记录了两种不同材料圆柱壳在大质量低速冲击下的冲击力时程曲线,得到其屈曲模态。采用高速摄像及模拟技术给出了钢质圆柱壳渐进屈曲的全过程,为理解钢质圆柱壳的屈曲机理提供了直观的结果。黄铜质圆柱壳在大质量低速冲击下, 出现整个壳面滿布屈曲波纹的塑性动力屈曲现象,说明高速冲击不是产生塑性动力屈曲的充要条件。像铜这样具有高密度的韧性材料,在大质量低速冲击下,会在轴向产生持续的压缩塑性流作用而出现塑性动力屈曲现象。     

Influence of the boundary conditions on the stress state of a flexible cylindrical shell of variable stiffness in a magnetic field

The effect of the boundary conditions on the stress state of a circular cylindrical shell of variable thickness (stiffness) is analyzed using a geometrically nonlinear problem statement. The cylindrical shell is subject to a magnetic field, external electric current, and nonstationary mechanical load. Numerical results are presented and analyzed     

Effects of the curvature radius of a cylindrical shell on the stress intensity factors of surface cracks

The effects of the curvature radius of a cylindrical shell on stress intensity factors are investigated in circumferential (inner and outer) semielliptical surface cracks in a cylindrical shell. What is new in this paper is to have given: (1) The stress intensity factors for surface cracks in a cylindircal shell are determined by photoelastic technique. (2) By a special method photoelastic slices are handled for obtaining a clear caustic curve, and the stress intensity factors for surface cracks in a cylindrical shell are determined by the caustic method. (3) An approximate equation of curvature correction factor F_c is proposed. (4) Effects of the curvature radius R of a cylindrical shell on the stress intensity factors of surface cracks are obtained. The results of this paper are in fair agreement with already existing analytical results. The approximate equation of curvature correction factor F_c can be widely used for engineering purposes.     

单层偏心圆柱薄壳的自由振动特性分析研究

本文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程。采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较。对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系。本文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法。     

电活性聚合物圆柱壳静态与动态电压下的响应及稳定性

摘要：在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场。这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏。本文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题。采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程。给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏。同时,也讨论了厚度和边界条件对临界电压的影响。圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动。给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性。采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏。最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论。     

The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells

The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell׳s non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge–Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.     

Dynamics of a Semi-Infinite Cylindrical Shell with a Liquid Containing a Vibrating Spherical Segment

A semi-infinite cylindrical shell filled with a perfect incompressible liquid is considered. A vibrating rigid spherical segment placed on the shell axis excites the shell. The Laplace equation is solved under appropriate boundary conditions on the spherical, cylindrical, and flat surfaces bounding the liquid. Possibility is used to reexpand a spherical harmonic function in terms of a system of cylindrical harmonic functions and vice versa. The potential constructed is used to compute the shell deflections and the liquid pressure and velocity.     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

TiNi合金圆柱薄壳静压屈曲失稳特性的实验研究

对马氏体相变支配的伪弹性TiNi合金圆柱薄壳进行了准静态屈曲实验研究和分析,结果表明,TiNi柱壳的屈曲模态以非轴对称钻石型为主,卸载时可恢复,与马氏体相变和相变铰的行为相关,明显不同于传统弹塑性柱壳。还讨论了长径比和边界条件对屈曲模态、比能、临界失稳阈值等的影响。研究发现：随着长径比和边界条件的变化,TiNi圆柱薄壳呈现出多样化的屈曲模态发展。相同长径比下,两端简支的TiNi圆柱薄壳比能Se较大;随着长径比增大,边界条件的影响有逐步弱化趋势。相同边界条件下,长径比较小的TiNi圆柱薄壳比能较大。     

高速碰撞下圆柱壳自由梁的穿孔特性

利用二级轻气炮加载,进行了球状2A12铝弹丸垂直撞击圆柱壳自由梁实验。并进行了弹丸速度、圆柱壳直径和壁厚等因素对穿孔直径影响的数值模拟,数值模拟结果和实验结果基本吻合。通过量纲分析和数值模拟结合,推导了穿孔直径与相关影响参数的经验关系式。研究结果表明:当圆柱壳直径和厚度不变时,高速撞击产生的穿孔直径在径向和轴向都随着弹丸速度增大而增大;当弹丸速度和圆柱壳厚度不变时,高速撞击产生的穿孔直径随着圆柱壳自由梁直径的增大而减小;当弹丸速度和圆柱壳直径不变时,穿孔直径随着圆柱壳厚度的增大而减小。     

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.     

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。     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

非圆柱壳在各种边界条件下的自由振动分析

本文用一种特殊的坐标变换将具有复杂截面形状的柱壳映射成圆柱壳,然后只需对变换后的圆柱壳作振动分析就可获得非圆柱壳在各种边界条件下的固有频率与振型。文中首次系统地给出了椭圆柱壳在各种边界条件下的频率系数,研究了拱预平底截面形状柱壳的自由振动问题。最后讨论了截面形状和边界条件变化对固有频率的影响,并和前人的研究结果作了比较,表明本方法是正确的。     

开口复合材料柱壳屈曲与补救有限元分析

用有限元法对含有轴向裂纹的开口加强复合材料柱壳结构进行了补救研究;分析其压缩屈曲强度与模态情况,得到了裂纹长度与屈曲强度的关系,并与无裂纹的结构进行了对比.结果表明:裂纹长度在200mm以下时,对整个结构承载能力影响很小;当裂纹长度继续增大时,屈曲区域从开口上方转移到裂纹附近,屈曲强度开始急剧下降.为了加强裂纹所在区域结构的承剪能力,进行适当的修补后,可使屈曲模态与无裂纹柱壳相同,且屈曲强度稍有增加,从而证明了所提出补救方法的有效性.     

变厚度圆柱壳的强度优化设计

对在任意轴对称分布荷载作用下体积保持常数的变厚度圆柱壳的强度优化设计问题进行了研究。当中面形状固定时 ,采用阶梯折算法 ,用传递矩阵导出了变厚度圆柱壳的初参数解的显式表达式。根据Huber-Mises-Hencky强度准则 ,将变厚度圆柱壳的强度优化转化为极小化当量应力的非线性规划问题 ,并采用投影梯度法建立了问题的优化方法。文中对几个典型问题进行了计算。与等厚度圆柱壳相比较 ,优化圆柱壳的最大当量应力得到了显著降低。本文的研究方法和结果可以用于指导大型圆柱壳体的加肋设计     

叠层连续柱壳热应力问题的弱形式研究

建立了弹性力学基本方程的弱形式,从而得到叠层连续柱壳混合状态方程的边界条件放在一起的算子方程,扩大了求解空间,给出叠层连续闭口柱壳在热荷载和机械荷载作用下的解析解。     

冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解

柱壳链能引起波形的弥散,具备操控波形的潜力。建立了柱壳链结构的等效连续介质模型和细观有限元模型,研究了质量块冲击作用下柱壳链中的弹性应力波传播过程及其几何弥散特性。基于考虑横向惯性修正的Rayleigh-Love波动方程,建立了柱壳链在质量块冲击下的控制方程,采用Laplace变换及其逆变换获得了位移场、速度场和应变场的解析解,所得结果与细观有限元模拟结果较好吻合。结果表明,在冲击过程中应变和速度峰值均逐渐减小,应变峰值、振荡幅度和波形前沿宽度与泊松比和惯性半径相关,泊松比和惯性半径越大,应变峰值越小,应变分布振荡越剧烈,波形前沿宽度越宽。