New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping（i.e., ACLD）, combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

THE GENERAL SOLUTION FOR THE STRESS PROBLEM OF CIRCULAR CYLINDRICAL SHELLS WITH AN ARBITRARY CUTOUT

In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution can be normal and effective by means of this method. Numerical results for stress concentrations in the shell with a circular, elliptic cutout are graphically presented.

On the Maximum Displacement and Static Buckling of a Circular Cylindrical Shell

The static buckling load of an imperfect circular cylindrical shell is here determined asymptotically with the assumption that the normal displacement can be expanded in a double Fourier series. The buckling modes considered are the ones that are partly in the shape of imperfection, and partly in the shape of some higher buckling mode. Simply-supported boundary conditions are considered and the maximum displacement and the static buckling load are evaluated nontrivially. The results show, among other things, that generally the static buckling load, λs decreases with increased imperfection and that the displacement in the shape of imperfection gives rise to the least static buckling load.

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.

弹性环梁支撑下圆形深基坑支护结构变形解析解

将环梁和支护结构分别视为弹性圆环和弹性圆柱薄壳,基于环梁和圆柱壳的变形协调,得到了具有任意数目弹性环梁支撑圆形深基坑支护结构变形的解析解.在验证解析解合理性和可靠性的基础上,针对某一实际圆形基坑工程,比较了在刚性和弹性环梁支撑下支护结构变形和内力的差异,并分析了支护结构底部边界条件、环梁弹性模量、尺寸和数量以及位置等参数对支护结构变形和内力分布的影响.研究结果表明:相对于刚性环梁支撑,弹性环梁支撑处内力变化较小,环梁弹性模量和尺寸的改变只对基坑挖掘面以上支护结构变形和内力影响显著,而对挖掘面以下的支护结构变形和内力几乎没有影响.该研究成果为圆形基坑支护结构设计提供了理论依据和指导.

开孔硬涂层薄壁圆柱壳复合结构的半解析建模及振动特性分析

针对硬涂层薄壁圆柱壳复合结构的圆形开孔问题,提出了一种参数化的周向区域分解法,并基于Rayleigh-Ritz法建立了开孔硬涂层薄壁圆柱壳复合结构的自由振动半解析模型。以涂敷NiCoCrAlY+YSZ硬涂层材料的开孔薄壁圆柱壳为例,通过对比解析与有限元计算结果验证了该半解析模型的有效性和合理性。同时,探讨了周向均布条件下开孔数量、轴向位置、开孔大小和硬涂层弹性模量对开孔硬涂层薄壁圆柱壳复合结构振动特性的作用规律。结果表明,开孔会增加复合结构的固有频率,但随着周向均布孔数的增加,结构固有频率不断减小,且当开孔数等于周向半波数或其特殊倍数时,结构固有频率会发生突变升高的特殊现象;随着硬涂层弹性模量的增加,结构固有频率均不断增加;随着轴向开孔位置的升高,结构固有频率不断降低,且当开孔数等于周向半波数或其特殊倍数时,降低幅度会大大增加;孔径的增加也会降低结构固有频率,但当开孔数等于周向半波数或其特殊倍数时,结构固有频率会随着孔径的增加而增大。

Effect of matrix cracking on the time delayed buckling of viscoelastic laminated circular cylindrical shells

The effect of matrix cracking on the bifurcation creep buckling of viscoelastic laminated circular cylindrical shells is investigated.The viscoelastic behavior of laminas is modeled by Schapery's integral constitutive equation with growing matrix cracks.The values of damage variables are correlated to non-dimensional density of matrix cracks relying on the formulas from mesomechanics approach,and the evolution equation predicting the growth rate of density of matrix cracks is assumed to follow a power type relation with transverse tensile stress.The governing equations for prebuckling creep deformation and bifurcation buckling of laminated circular cylindrical shells under axial compression are obtained on the basis of the Donnell type shallow shell theory and Kármán-Donnell geometrically nonlinear relationship.Corresponding solution strategy is constructed by integrating finite-difference technique,trigonometric series expansion method and Taylor's numerical recursive scheme for convolution integration.The bifurcation creep buckling of symmetrically laminated glass-epoxy circular cylindrical shells with matrix creep cracking coupled are examined for various geometrical parameters and parameters of damage evolution as well as boundary conditions.The numerical results show that matrix creep cracking remarkably shortens the critic time of bifurcation buckling and reduces the durable critic loads,and its effects become weak and finally vanish with the increase of the ratio of radius to thickness in the case of short laminated circular cylindrical shells,also the influence of the matrix creep cracking is mainly dependent on the boundary conditions at two ends for moderately long circular cylindrical shells.

Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.

NONLINEAR VIBRATION RESPONSE AND BIFURCATION OF CIRCULAR CYLINDRICAL SHELLS UNDER TRAVELING CONCENTRATED HARMONIC EXCITATION

The nonlinear vibration of a cantilever cylindrical shell under a concentrated har- monic excitation moving in a concentric circular path is proposed. Nonlinearities due to large- amplitude shell motion are considered, with account taken of the effect of viscous structure damp- ing. The system is discretized by Galerkin＇s method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifur- cation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.

Nonlinear Dynamics of Clamped Initial Imperfect Functionally Graded Material Circular Cylindrical Shell Considering the Axisymmetric Mode

This paper investigates the dynamic responses of clamped-clamped functionally graded material circular cylindrical shell at both ends with small initial geometric imperfection and subjected to complex loads.The small initial geometric imperfection of the cylindrical shell is characterized with the shape of hyperbolic function.The effects of radial harmonic excitation combined with thermal loads are considered.The classical theory and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the functionally gradient material circular cylindrical shell by the Hamilton’s principle.The partial differential dynamic equations are truncated by the Galerkin technique,using the modal expansion with the inclusion of axisymmetric and asymmetric modes.The effective material properties vary in the radial direction following a power-law distribution accordancewith the volume fractions.The effects of volume fraction indexes,ratios of thickness-radius and lengthradius on the first three dimensionless natural frequencies of the perfect cylindrical shell and its counterpart with imperfection are given.The effects of radial external loads,initial geometric imperfections and volume fraction index on the nonlinear dynamic response of the clamped-clamped FGM circular cylindrical shell are discussed by numerical calculation.

复合材料纵向圆形波纹圆柱壳轴向压缩失效特性研究

结构轻量化、材料高效易造化是航空航天乃至其他工业领域(汽车、建筑、基础设施等)的不断追求。纤维增强复合材料的使用可以有效减轻结构重量,提高承载能力。复合材料纵向圆形波纹结构可以大大提高结构轴向压缩时的载荷/质量效率,从而满足航空航天领域对新型复合材料及结构的强度要求。自行设计模具并制备出复合材料纵向圆形波纹圆柱壳,并对其开展轴向压缩性能研究。结果表明:与等厚度、等横截面积圆柱壳比较,纵向圆形波纹圆柱壳承受轴向载荷的能力明显增强;相同结构、不同厚度的纵向圆形波纹圆柱壳,在压缩过程中其破坏形式因厚度增加而发生改变,由整体的屈曲变形转变为端面局部的压溃失效。建立并验证了数值计算模型,考虑了典型设计参数的影响,结果表明,在制备条件允许的情况下,减小单胞尺寸有利于提高纵向圆形波纹圆柱壳抗轴压性能,而降低高度则效果不明显。本文研究结果可为纵向波纹圆柱壳在结构吸能方面的应用提供参考。

大型圆柱形壳体上圆形焊缝的焊接变形

应用模型试验和数值分析研究了大型圆形壳体上圆形焊缝对法兰平面度的影响。研究表明：圆柱形壳体与法兰对接的圆形焊缝引起法兰平面的外侧倾斜，小圆柱壳体与大容器相贯的圆形焊缝对法兰平面的倾斜没有显著影响，在圆周方向上法兰局部下凹；并用有限元分析实际圆柱形壳体与法兰对接时，由于纵向收缩引起法兰外倾的斜率，其结果与模型试验分析的相吻合。

被动约束层阻尼圆柱壳振动和阻尼分析的一种新矩阵方法

基于线弹性薄壳理论和线粘弹性理论,考虑粘弹性层的剪切耗能作用和各层间的相互作用力,导出了被动约束层阻尼层合圆柱壳在谐激励作用下的一阶常微分矩阵控制方程.然后,借助作者提出的齐次扩容精细积分技术建立了一种新的矩阵方法,并利用该方法研究了层合圆柱壳的振动特性和阻尼特性.该方法与已提出的以位移及其导数作为状态向量的传统传递矩阵法的根本区别在于,控制方程中的状态向量中包含了层合壳的全部位移和整合内力变量,因此,可以方便地适用于各种位移和内力边界条件以及部分环状覆盖约束层阻尼圆柱壳的动态分析.数值算例与解析解和有限元解的结果比较有力说明了该方法的正确性和有效性.

舱壁和环肋加强的无限长圆柱壳声弹耦合模型及其声特性

基于最一般情况 ,借助线弹性薄壳理论 ,建立了加肋圆柱壳声辐射计算模型 ,分析模型考虑了环肋和舱壁对圆柱壳的径向、切向、纵向作用力以及纵向弯矩 .导出了分析模型的声弹耦合控制方程 ,利用傅氏变换和模态展开给出了辐射声压的计算方法 .通过大量数值计算 ,研究了舱壁、环肋刚度与间距以及结构阻尼等因素对辐射声压的影响 .分析模型与工程实际比较接近 ,有较广的应用范围 .

部分覆盖PCLD圆柱壳振动分析的新矩阵方法

基于线弹性薄壳理论和线粘弹性理论,考虑被动约束层阻尼(PCLD)的剪切耗能以及层间的相互作用,首次导出了适用于最一般情况的环状覆盖PCLD圆柱层合壳在谐激励作用下的整合一阶常微分矩阵方程,它的12个状态变量具有明确的物理意义,而且由层合壳完整的位移量和内力量组成,应用范围很广。通过将该模型和齐次扩容精细积分法结合构建了一种高效率和高精度的半解析半数值方法,并与解析解结果进行了对比,验证了该方法的正确性和有效性,借此还分析了PCLD覆盖率和覆盖位置对频率响应函数的影响。

黏弹性圆柱形壳动力学高余维分岔、普适开折问题

讨论两端受到谐波激励的黏弹性圆柱形壳的非线性动力学行为，利用奇异性理论，研究了分岔方程的普适开折问题，严格证明了它是一个高余维分含问题．余维数为５（含有一个模参数），给出了它的所有可能的普适开折形式．在分岔参数满足某些条件时得到该分岔问题的转迁集及分岔图，展示了一些新的动力学行为，改进和完善了奇异性分析方法．

热环境中黏弹性功能梯度材料及其结构的蠕变

基于经典的对应原理,将Mori-Tanaka方法等细观力学结果推广于定常温度环境下的黏弹性情形.根据泊松比与时间呈弱相关的特点,给出Laplace象空间中功能梯度材料的松弛模量和热膨胀系数,并直接建立耦合热应变的多维黏弹性本构关系.在此基础上,求解黏弹性功能梯度圆柱薄壳在热环境中的轴对称弯曲蠕变变形问题.考虑材料热物参数的温度相关性,首先确定稳态温度场,导出相空间中轴对称弯曲变形的解析解,采用数值反演得到蠕变变形.算例表明,蠕变初期,热环境的影响明显,随着时间增加,热应力松弛,影响逐渐消失.当圆柱薄壳受轴压时,相比于两端固支,两端简支的端部变形更加明显.通过圆柱薄壳的轴对称弯曲求解,给出体积含量呈任意分布的黏弹性功能梯度结构在热机载荷下的蠕变分析途径.

外壳板采用纵骨加强的双层加肋圆柱壳水下声辐射分析

建立了外壳板加纵骨的双层加肋圆柱壳水下声辐射计算方法 ,计算模型采用 Donnell壳体理论 ,考虑了环肋、舱壁和实肋板对内外圆柱壳的径向、切向、纵向反作用力以及纵向反弯矩 ,利用傅氏变换和模态展开在波数域建立了计算模型的声弹耦合控制方程。推导了所有结构部件以及水介质的速度阻抗表达式 ,采用数值计算方法在波数域求解出径向振动速度 ,利用稳相法得到远场辐射声压。研究表明 ,如果纵骨沿圆周均匀排列 ,则纵骨的存在不导致圆柱壳周向模态耦合 ,纵骨加强的双层圆柱壳水下声辐射计算可以大大简化。采用文中方法研究了环频率以下外壳板加纵骨的双层加肋圆柱壳水下声辐射特性 ,计算表明 :在较低的频率段 ,外壳板采用纵骨加强使双层加肋圆柱壳水下辐射声压增大 ;增大纵骨刚度 ,结构辐射声压也相应增大 ;纵骨间距对双层加肋圆柱壳水下声辐射影响比较复杂 ,辐射声压谱随纵骨间距变化较大 。