模态数量对薄壁短圆柱壳振动响应分析的影响

采用振型叠加法研究薄壁短圆柱壳受谐波激励的振动响应分析时模态截断数量的影响,且考虑简支-简支、固支-固支和固支-自由三种约束条件。首先基于Love壳体理论建立薄壁短圆柱壳的动力学模型。然后,给出采用振型叠加法进行薄壁短圆柱壳受径向谐波激励时的振动响应求解方法。在三种不同约束条件下,计算采用不同模态截断数量时的稳态响应的振动幅值,对比其一致性,并与实测结果进行比较。结果表明,在这三种约束条件下计算受谐波激励薄壁短圆柱壳的振动响应,需要截取前8阶模态函数用于表征位移模式;模态数据超过8阶对响应计算的精度没有明显改善,实测振动响应结果与解析结果基本吻合。     

Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells

This paper presents an analytical procedure and closed-form vibration solutions with analytically determined coefficients for orthotropic circular cylindrical shells having classical boundary conditions. This analysis is based upon the Donnell-Mushtari shell theory. This is the simplest thin shell theory and its results for the lowest frequencies of a closed cylinder may not be as accurate. It is known that the exact procedure is complicated for orthotropic shells and this complexity has apparently prevented most researchers from getting results. Using the separation of variables method, the closed-form natural frequencies are successfully obtained in this work. They are found in a compact form. Moreover, the characteristics of the eigenvalues are examined. The exact solutions are validated through numerical comparisons with available solutions in literatures and the semi-analytical differential quadrature finite element method (S-DQFEM) solutions calculated by the authors.     

篦齿对悬臂薄壁圆柱壳模态特性的影响研究

采用传递矩阵方法研究外壁带有周向篦齿(即密封齿)薄壁圆柱壳的模态振动特性。在悬臂边界条件下,首先基于Love壳体理论建立带篦齿薄壁圆柱壳的动力学方程,通过传递矩阵法和高精度的精细积分法对其模态特性进行分析,求得各阶模态对应的固有频率和三维模态振型,并通过有限元法对分析结果进行比较,最后讨论篦齿布置形式、篦齿高度和篦齿道数对悬臂薄壁圆柱壳振动特性的影响。结果表明,传递矩阵法适合于求解带篦齿悬臂薄壁圆柱壳的模态振动特性,篦齿结构的布置形式、高度和道数均对薄壁圆柱壳构件的振动特性有较大影响。     

Stresses in rotating composite cylindrical shells

Stresses in composite cylindrical shells rotating with a constant speed about their longitudinal axis are analyzed. Each ply or ply group is treated as a separate thin layer of homogeneous and orthotropic material under the interfacial stresses as surface loading. There is no limitation on the total thickness of the shell. The circumferential stress, motivated by the conventional thin shell theory, is assumed to vary linearly through the thickness of the layer. The radial stress is determined in terms of the circumferential stress through the equilibrium condition, and an average compatibility condition through the thickness of the thin layer is used. Numerical results using the present analysis show nearly perfect agreement with the exact solution for homogeneous and isotropic cylinders. Some results for cylinders having orthotropic layers are presented for illustrative purposes.     

薄壁圆柱壳构件受迫振动的响应特征研究

针对固支-自由约束条件下受径向谐波激励或径向冲击激励的薄壁圆柱壳构件,开展其受迫振动下的响应特征分析。首先基于Love壳体理论建立了薄壁圆柱壳构件的动力学模型,然后,根据固支-自由约束条件特点,采用轴向梁函数和周向三角函数组合的振型函数以及振型叠加法,获得了考虑粘性阻尼的薄壁圆柱壳模态坐标振动方程,进而求解受径向谐波激励或冲击激励的振动响应。通过一个具体算例,进行了不同位置上的响应幅度与相位的变化分析,并对比了模态阻尼比和激励力幅值对响应幅值的影响。     

柱壳结构损伤识别方法

摘 要:对柱壳结构的损伤部位和程度进行识别是柱壳结构进行安全性评定的一个重要环节。本文对柱壳结构损伤前后动力特性进行了分析,采用摄动法推导了由于单元损伤引起的各阶模态振型改变系数;推导了模态应变能变化与单元损伤之间的关系;采用单元模态应变能的变化率作为柱壳结构损伤诊断的标识量,证明了单元模态应变化率对损伤的敏感性。对柱壳结构损伤识别方法进行了研究,所提出的方法仅需要量测的低阶模态信息和刚度矩阵就能完成结构的损伤识别。最后,以一混凝土柱壳结构为工程实例,对其在不同损伤情况下的损伤进行了分析,结果表明,所提出的损伤识别方法能够很好地识别不同损伤组合下的损伤部位和程度,同时能较好地识别结构小损伤,因而证明了本文所提出的方法的正确性和有效性。 关键词:柱壳结构;损伤识别;动力特性;损伤标识量;模态应变能     

基于波传播方法的边界条件对圆柱壳振动特性的影响分析

在波传播分析方法基础上,采用一种改进傅立叶级数的方法建立了弹性约束边界条件下圆柱壳结构模态分析模型,结合模态叠加理论,给出了圆柱壳结构在任意径向点力激励下的振动响应.通过与商业分析软件ANSYS的结果比较验证了本文方法的高效性与精确性,随后详细分析了边界约束刚度对圆柱壳结构自由振动特性和结构振动响应的影响,并给出了刚度影响的一般性规律.     

Influences of elastic foundations and boundary conditions on the buckling of laminated shell structures subjected to combined loads

This article presents to study the stability of laminated orthotropic cylindrical and truncated conical shells resting on elastic foundations and subjected to combined loads with the clamped and simply supported boundary conditions. Here, axial tensile loads separately applied to the small and large bases of a laminated truncated conical shell, respectively. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells on the Pasternak type elastic foundation. Applying Galerkin method, the critical combined loads of laminated orthotropic conical shells on the Pasternak type elastic foundation with different boundary conditions are obtained. The appropriate formulas for single-layer and laminated cylindrical shells on the Pasternak type elastic foundation made of orthotropic and isotropic materials are found as special cases. Finally, influences of the boundary conditions, the elastic foundation, the number and ordering of the layers and variations of the shell characteristics on the critical combined loads are investigated. The results are compared with their counterparts in the literature.     

METHOD OF INITIAL FUNCTIONS FOR THE ANALYSIS OF LAMINATED CIRCULAR CYLINDRICAL SHELLS UNDER AXISYMMETRIC LOADING

The method of initial functions has been used for the static analysis of an infinite and simply supported, orthotropic, and laminated, circular cylindrical shell of revolution subjected to axisymmettic load. In this method the three-dimensional state equations for an individual ply of a laminated shell are established without making any a priori assumptions regarding the distribution of stresses and displacements across the thickness of the shell By using the continuity conditions of displacements and stresses on each interface between adjacent layers, the state equation far the laminate is obtained. Using the Cayley-Hamilton theorem, the transfer matrix that maps the initial state vector into the field is evaluated explicitly, leading to an exact solution of the problem (MIF—exact). Alternatively, depending on the number of terms retained in the series expansion of the transfer matrix, different-order theories of MIF are derived. The results of different-order MIF theories, classical theories, and shear deformation shell theories are compared with the results of MIF—exact to assess their accuracy and limitations.     

Analytical solution of the dynamic behavior of non-homogenous orthotropic cylindrical shells on elastic foundations under moving loads

An analytical study on the dynamic behavior of an infinitely long, non-homogenous orthotropic cylindrical shell resting on elastic foundations subjected to combined action of the axial tension, internal compressive load and ring-shaped compressive pressure with constant velocity is presented. The problem is studied on the basis of the theory of vibrations of cylindrical shells. Formulas are derived for the maximum static and dynamic displacements, dynamic factors and critical velocity for homogenous and non-homogenous orthotropic cylindrical shells on Winkler or Pasternak elastic foundations and subjected to moving loads. A parametric study is conducted to demonstrate the effects of various parameters, such as Winkler or Pasternak foundations, the non-homogeneity and orthotropy of materials, the radius-to-thickness ratio and the velocity of the moving load on the dynamic displacements, dynamic factors and critical values of the velocity for cylindrical shells.     

Buckling behavior under radial loading of orthotropic oval cylindrical shells with parabolically varying thickness

In this article, the framework of the Flügge's shell theory, the transfer matrix approach, and the Romberg integration method have been employed to investigate the buckling analysis of a radial loaded oval cylindrical shell with parabolically varying thickness along its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling.     

A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells

An exact free vibration analysis of doubly-curved laminated composite shallow shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT). In essence, the HSDT has been exploited to develop first the dynamic stiffness (DS) element matrix and then the global DS matrix of composite cylindrical and spherical shallow shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton’s principle is used to derive the governing differential equations and the related natural boundary conditions. The equations are solved symbolically in an exact sense and the DS matrix is formulated by imposing the natural boundary conditions in algebraic form. The Wittrick–Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio, radius-to-length ratio and stacking sequence on the natural frequencies and mode shapes is investigated in details. Results are compared with those available in the literature. Finally some concluding remarks are drawn.     

Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads

Considering rotary, in-plane inertias, and fluid velocity potential, the dynamic characteristics of fluid-conveying functionally graded materials (FGMs) cylindrical shells subjected to dynamic mechanical and thermal loads are investigated, where material properties of FGM shells are considered as graded distribution across the shell thickness according to a power-law, and dynamic thermal loads applied on the shell is considered as non-linear distribution across the thickness of the shell. The linear response characteristics of fluid-conveying FGM cylindrical shells are obtained by using modal superposition and Newmark’s direct time integration method.     

Active control of functionally graded laminated cylindrical shells

An analytical method on active vibration control of smart FG laminated cylindrical shells with thin piezoelectric layers is presented based on Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the smart FG laminated cylindrical shell act as distributed sensor and actuator, which are used to control vibration of the smart FG laminated cylindrical shell under thermal and mechanical loads. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of the smart FG laminated cylindrical shell with thin piezoelectric layers. Constant-gain negative velocity feedback approach is used for active vibration control with the structures subjected to impact, step and harmonic excitations. The influences of different piezoelectric materials (PZT-4, BaTiO₃ and PZT-5A) and various loading forms on the active vibration control are described in the numerical results.     

A higher-order shear deformation theory of laminated elastic shells

A higher-order shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. The theory is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces of the shell. The Navier-type exact solutions for bending and natural vibration are presented for cylindrical and spherical shells under simply supported boundary conditions.     

Elasticity Solution of a Laminated Clamped Cylindrical Shell with Piezoelectric Layer under Dynamic Load

Dynamic elasticity solution for a clamped, laminated cylindrical shell with two orthotropic layers bounded with a piezoelectric layer and subjected to impulse load distributed on inner surface is presented. The piezoelectric layer serves as sensor/actuator. The governing elasticity PDE equations are reduced to ordinary differential equations by means of Legendre polynomial expansion for displacement and electric potential in the axial direction. The resulting equations are transferred into state space form and reduced to an eigenvalue problem by using Galerkin's finite element in radial direction. The static and dynamic results are presented for [0/90/Piezo] lamination. The radius to thickness ratio effect on dynamic behavior is studied. The results are compared for different thickness ratios and applied electric loads with simply-supported shell results. Time responses for sensor and actuated shell are presented and natural frequencies are compared with simply-supported shell results.     

环加肋圆柱壳屈曲分析的有限条法

导出了有限条法分析环加肋圆柱壳在静水压力作用下总体屈曲的计算格式，将环加肋圆柱壳作为一个构造上的正交各向异性壳处理，推导了考虑环向加肋影响后有限条元的正交各向异性弹性矩阵。对两端简支环加助圆柱壳总体屈曲临界载荷的计算表明，本文方法计算结果与解析解符合良好。有限条法是分析密加肋圆柱壳屈曲问题的有效数值方法。     

复合材料正交加筋层合圆柱壳结构阶梯式挖补修理的参数化研究

利用三维参数化有限元分析模型,对复合材料正交加筋层合圆柱壳结构的阶梯式挖补修理进行了参数分析.主要考虑了载荷情况、阶梯数、铺层顺序以及补片铺层错误等修理参数对阶梯式挖补修理结构胶层剥离应力和剪切应力分布情况的影响规律,并利用绝对值的平均值和均方差来描述胶层剪切应力剥离应力的分布情况,以确定最优的阶梯式挖补修理参数.基于该文建立的三维有限元模型可以深入地了解复合材料正交加筋层合圆柱壳结构阶梯式挖补修理区域胶层应力分布的详细情况,而且参数化分析结论也可为复合材料正交加筋层合板圆柱壳结构的阶梯式挖补修理方案的设计和分析提供参考.     

On the solution of eigenvalue problems of laminated non-homogeneous orthotropic circular shells with clamped edges subjected to hydrostatic pressure

This article presents a method to study the free vibration and stability of laminated homogeneous and non-homogeneous orthotropic cylindrical, truncated and complete conical shells of general staking with clamped edges under a hydrostatic pressure. Based on the Love first approximation theory, the basic relations, the modified Donnell-type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells, the material properties of which vary piecewise continuously in the thickness direction. To solve this problem an unknown parameter λ was included in the approximation functions. Applying Galerkin methods, the buckling pressures and fundamental natural frequencies of laminated homogeneous and non-homogeneous orthotropic conical shells are obtained. The parameter λ which is included in the obtained formulas is obtained from the minimum conditions of critical stresses and frequencies. The different generalized values are obtained for the parameter λ for buckling pressures and frequencies of cylindrical shells, truncated and complete conical shells. The appropriate formulas for single-layer and laminated cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of conical shell characteristics on the critical hydrostatic pressure and natural frequencies are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells

A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis–Lagrange (M–L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.