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.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory (FSDT) of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young’s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.     

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...     

New matrix method for response analysis of circumferentially stiffened non-circular cylindrical shells under harmonic pressure

Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order,a new matrix method is pre- sented for steady-state vibration analysis of a noncircular cylindrical shell simply sup- ported at two ends and circumferentially stiffened by rings under harmonic pressure.Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration ap- proach other than the Runge-Kutta-Gill integration method.The transfer matrix can easily be determined by a high precision integration scheme.In addition,besides the normal interacting forces,which were commonly adopted by researchers earlier,the tan- gential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δfunction.The effects of the exciting frequencies on displacements and stresses responses have been investigated.Numerical results show that the proposed method is more efficient than the aforementioned method.     

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。     

黏弹性层合悬臂薄壁圆柱壳的模态特性研究

基于薄壳理论和黏弹性理论, 得出了黏弹性层合悬臂薄壁圆柱壳模态特性的半解析解. 根据乐甫薄壳理论, 建立了基层和黏弹性阻尼层薄壁圆柱壳的一阶状态微分方程, 结合黏弹性阻尼层的变形协调关系和层间作用力关系, 利用传递矩阵法得出了整体结构的传递矩阵, 采用高精度的精细积分法得出了固有频率、模态损耗因子和三维模态振型, 最后通过有限元法进行了比较, 通过算例验证了传递矩阵法对黏弹性层合薄壁圆柱壳模态特性研究的有效性.     

TRANSFER MATRIX METHOD FOR ANALYZING VIBRATION AND DAMPING CHARACTERISTICS OF ROTATIONAL SHELL WITH PASSIVE CONSTRAINED LAYER DAMPING TREATMENT

The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.     

Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature

The nonlinear stability of sandwich cylindrical shells comprising porous functionally graded material(FGM) and carbon nanotube reinforced composite(CNTRC)layers subjected to uniform temperature rise is investigated. Two sandwich models corresponding to CNTRC and FGM face sheets are proposed. Carbon nanotubes(CNTs) in the CNTRC layer are embedded into a matrix according to functionally graded distributions. The effects of porosity in the FGM and the temperature dependence of properties of all constituent materials are considered. The effective properties of the porous FGM and CNTRC are determined by using the modified and extended versions of a linear mixture rule, respectively. The basic equations governing the stability problem of thin sandwich cylindrical shells are established within the framework of the Donnell shell theory including the von K'arm'an-Donnell nonlinearity. These equations are solved by using the multi-term analytical solutions and the Galerkin method for simply supported shells.The critical buckling temperatures and postbuckling paths are determined through an iteration procedure. The study reveals that the sandwich shell model with a CNTRC core layer and relatively thin porous FGM face sheets can have the best capacity of thermal load carrying. In addition, unlike the cases of mechanical loads, porosities have beneficial effects on the nonlinear stability of sandwich shells under the thermal load. It is suggested that an appropriate combination of advantages of FGM and CNTRC can result in optimal efficiency for advanced sandwich structures.     

含轴对称初始缺陷的具有正交各向异性表层的夹层圆柱壳的非线性屈曲

夹层圆柱壳具有很高的结构效能。在许多工程结构中被广泛采用。本文研究分析了含有轴对称初始缺陷的夹层圆柱壳在轴压下的非线性屈曲问题。该夹层壳具有正交各向异性表层和各向同性可承剪的夹心．利用Stein的前屈曲一致理论得出了前屈曲挠度随轴向载荷及缺陷参数的变化情况，运用Galerkin法导出了屈曲控制方程，并进行了数值计算，得到了屈曲载荷、缺陷幅值、缺陷波数、夹心模量等参量之间的关系．结果表明与壳体实际屈曲模态相同的初始缺陷具有很大的危害性，可以通过增加壳体表层的轴向弹性模量或优化夹心的有关参数等途径来提高屈曲载荷，改善壳体屈曲性能。     

Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance

In this article, the nonlinear dynamic responses of sandwich functionally graded(FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell's nonlinear shell theory and Hamilton's principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters,specifically, the radial load, core thickness, foam type, foam coefficient, structure damping,and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.     

主动约束层阻尼部分覆盖圆柱壳耦合振动控制

采用分布参数建模,从Ham ilton变分原理出发推导了主动约束层阻尼(ACLD)覆盖圆柱壳耦合振动的运动微分方程和边界条件,并扩展适合一维连续结构分析的基于解析解的谱传递矩阵法(STMM)用于ACLD部分覆盖圆柱壳。通过数值计算,研究了ACLD的长度和位置对固有频率和模态耗散因子的影响。STMM能有效克服有限元法单元数目多、动力学方程阶数高及ACLD长度和位置变化时须重复建模的缺点,以最少的单元数目建立低阶控制方程。典型算例显示了STMM的有效性和精确性。     

Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix

In this paper, the nonlinear free vibration of the nanotube with damping effects is studied. Based on the nonlocal elastic theory and Hamilton principle, the governing equation of the nonlinear free vibration for the nanotube is obtained. The Galerkin method is employed to reduce the nonlinear equation with the integral and partial differential characteristics into a nonlinear ordinary differential equation. Then the relation is solved by the multiple scale method and the approximate analytical solution is derived. The nonlinear vibration behaviors are discussed with the effects of damping, elastic matrix stiffness, small scales and initial displacements. From the results, it can be observed that the nonlinear vibration can be reduced by the matrix damping. The elastic matrix stiffness has significant influences on the nonlinear vibration properties. The nonlinear behaviors can be changed by the small scale effects, especially for the structure with large initial displacement.     

Vibroacoustic comparisons of composite laminated cylindrical shells according to three shear deformation shell theories

Whether the first-order and Reddy third-order shear deformation shell theories are able to evaluate the vibroacoustic responses of laminated cylindrical shells with normal deformation in the high frequency range or not is examined by comparison with a 3D higher-order shear deformation shell theory. The implicit governing equations of arbitrary angle-ply laminated cylindrical shells are derived from the 3D higher-order and Reddy third-order shell theories, and solved on the basis of the Fourier transform. The Reddy third-order shell theory can be obtained as a special case from the 3D higher-order shell theory. The first-order and Reddy third-order shell theories almost give rise to the same vibrational and acoustic results. These two simple shear deformation shell theories can be used to study far-field acoustic radiation from laminated cylindrical shells from the low to high frequency range, but they show some differences from the 3D higher-order shell theory in high frequency vibration of shells. Nevertheless, the differences of vibrational responses seem not to be distinct. The helical wave spectra of the higher-order radial displacements are nearly separate from those of the low-order radial displacement and play a minor role in far-field acoustic radiation, which makes the two simple shell theories applicable in prediction of acoustic power of the cylindrical shells in the much higher frequency range. Moreover, it also results in the fact that far-field sound is least sensitive in comparison with near-field sound and vibration of shells.     

INITIALLY TENSIONED ORTHOTROPIC CYLINDRICAL SHELLS CONVEYING FLUID: A VIBRATION ANALYSIS

A linear analysis of the vibratory behaviour of initially tensioned orthotropic circular cylindrical shells conveying a compressible inviscid fluid is presented. The model is based on the three-dimensional nonlinear theory of elasticity and the Eulerian equations. A nonlinear strain–displacement relationship is employed to derive the geometric stiffness matrix due to initial stresses and hydrostatic pressures. Frequency-dependent fluid mass, damping and stiffness matrices associated with inertia, Coriolis and centrifugal forces, respectively, are derived through the fluid–structure coupling condition. The resulting equation governing the vibration of fluid-conveying shells is solved by the finite element method. The free vibration of initially tensioned orthotropic cylindrical shells conveying fluid is investigated; numerical examples are given and discussed.     

可控约束阻尼层板的杂交控制

用局部压电层控制约束阻尼约束层产生一种新的主、被动杂交控制形式,称为可控制 约束层。本文根据弹性材料、粘弹性材料、压电材料的本构关系和变形连续条件,建立了可控约束阻尼层板的控制微方程;从理论上证明了用离散小压电片组合来代替整体压电层而不影响作动效果,改善了结构的工艺性;利用Ｇａｌｅｒｋｉｎ方法和ＧＨＭ方法建立了系统的近似低阶方程对一试验模型进行了控制数值模拟和试验实现,结果表明这种杂交控制对控制     

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.     

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.     

Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

For the first time, a new cross-section profile and efficient method are developed for the vibration analysis of isotropic and orthotropic cylindrical shells having circumferentially varying profile of a cardioid cross-section expressed as an arbitrary function, under thermal gradient effect. The governing equations of orthotropic cylindrical shells with varying thermal gradient around its circumference are derived as a boundary-value problem and solved numerically as an initial-value problem, based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method. As a semi-analytical procedure, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction and also to reduce the two-dimensional problem to one-dimensional one. The thermal gradient is assumed to arise due to the variation of Young's moduli and shear modulus, along the circumferential direction of the shell. The results are obtained to indicate the effects of cardioid cross-section on the natural frequencies and corresponding mode shapes in the thermal environment as well as the sensitivity of the vibration behavior to the thermal gradient ratio and the orthotropy of the shell is also investigated for different types of vibration modes. In general, close agreement between the obtained results and those of other researchers has been found.     

夹芯圆柱壳在水下爆炸载荷作用下的抗冲击特性

采用声固耦合方法对夹芯圆柱壳和等质量的普通圆柱壳在爆炸载荷作用下的应变、速度和加速度进行有限元计算。结果表明:夹芯防护层对爆炸冲击波可起到较好的衰减作用,即通过芯层的塑性变形,耗散了冲击过程中产生的大部分能量,对里面的圆柱壳体起到较好的保护作用,由于夹芯防护层的存在,与等质量的普通圆柱壳相比,夹芯圆柱壳能够承受更强的爆炸冲击波,降低结构的整体变形。