The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges

The problem of the existence of natural oscillations of a thin elastic orthotropic circular closed cylindrical shell with free and hinge-mounted ends and of an open cylindrical shell with free and hinge-mounted edges, when the two boundary generatrices are hinge-mounted is investigated. Dispersion equations and asymptotic formulae for finding the natural frequencies of possible vibration modes are obtained using the system of equations corresponding to the classical theory of orthotropic cylindrical shells. A mechanism is proposed by means of which the vibrations can be separated into possible types. Approximate values of the dimensionless characteristic of the natural frequency and the attenuation characteristic of the corresponding vibration modes are obtained using the examples of closed and open orthotropic cylindrical shells of different lengths.     

在任意不定常温度场和任意法向动载荷联合作用下中心开孔圆底扁球壳的动力问题

本文得出了在任意不定常温度场和任意法向动载荷联合作用下中心开孔圆底扁球壳的动力问题的解析解.我们假设温度沿壳体厚度直线分布.在第一部分.我们研究了常用边界条件下的中心开孔圆底扁球壳的自由振动.作为例子,我们计算了一边缘夹紧的扁球壳的自然基频(m=0),所得结果与E.Reissner[1]的结果作了比较.频率方程的解法是钱伟长[2]提出来的.这将在附录3中介绍.在第二部分,我们研究了在任意谐温度场和任意谐法向动载荷联合作用下的中心开孔圆底扁球壳的强迫振动.在第三部分,我们研究了在任意不定常温度场和任意法向动载荷联合作用下的具有初始条件的上述壳体的强迫振动.在附录1和2中,我们讨论了如何用应力函数来表示位移边界条件和m=1情形的边界条件.     

Nonlinear vibration and stability of a rotary truncated conical shell with intercoupling of high and low order modals

Truncated conical shell is an important structure that has been widely applied in many engineering fields. The present paper studies the internal dynamic properties of a truncated rotary conical shell and considers the intercoupling of the high and low order modals by utilizing the Harmonic Balance Method. To disclose the detailed intercoupling characteristics of the high order and low order modals of the system, a truncated shallow shell is studied and the internal response properties of the system are investigated by using the Multiple Scale Method. The nonlinear dynamic stabilities of the system are also analyzed using the Incrementation Harmonic Balance Method. Abundant dynamic characteristics are found in the research. The research results show that the high order modals of rotating conical shells have a significant effect on the curves of vibration amplitude and frequency of the shells.     

Forced Vibration of Three-Layered Spherical and Ellipsoidal Shells under Axisymmetric Loads

A variant of vibration theory for three-layered shells of revolution under axisymmetric loads is elaborated by applying independent kinematic and static hypotheses to each layer, with account of transverse normal and shear strains in the core. Based on the Reissner variational principle for dynamic processes, equations of nonlinear vibrations and natural boundary conditions are obtained. The numerical method proposed for solving initial boundary-value problems is based on the use of integrodifferential approach for constructing finite-difference schemes with respect to spatial and time coordinates. Numerical solutions are obtained for dynamic deformations of open three-layered spherical and ellipsoidal shells, over a wide range of geometric and physical parameters of the core, for different types of boundary conditions. A comparative analysis is given for the results of investigating the dynamic behavior of three-layered shells of revolution by the equations proposed and the shell equations of Timoshenko and Kirhhoff-Love type, with the use of unified hypotheses across the heterogeneous structure of shells.     

主动约束阻尼开口柱壳的NLMS反馈减振控制

为缩减开口柱壳结构的振动,给出了一种局部主动约束阻尼（ALCD）敷设结构,并结合Lagrange方程和Sanders薄壳理论构建了压电耦合开口柱壳的动力学模型,根据推得的系统状态空间形式,应用归一化最小均方差自适应滤波算法（NLMS）和线性二次规划算法（LQR）设计了一种自适应反馈控制器,通过数值仿真研究了控制参数对开口柱壳中点动态特性和控制电压的影响.结果表明:NLMS反馈控制方法能在不同控制电压频率、滤波阶数和自适应步长下保证对开口柱壳减振的有效性;增加自适应步长和滤波阶数能进一步提高减振控制的响应速率,但会导致控制电压超调量增加,而取较大的滤波阶数和较高频率控制电压可以减小噪声扰动,增加控制系统的可靠性.     

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．     

双层柱壳在流场中辐射声场压力的解析解

应用Donnell壳体理论,对加强内外壳体的横向构件,利用交界面的变形协调条件,等价为作用在壳体上的反力和反力矩,把双层柱壳振动辐射声场压力的求解,归结为求解结构动力方程、流场Helmholtz方程、流体和结构交界面上连续性条件组成的声-流体-结构的耦合振动方程.通过复杂的求解方法,可直接求得双层柱壳近场声压.     

Oscillations of one-dimensional linear systems with mobile weights under the action of longitudinal impacts : PMM vol. 42, no. 6, 1978, pp. 1141–1145

Longitudinal osciallations of a one-dimensional system which can be represented by a rod interacting with various kinds of inertial mobile media, are considered. It is assumed that the media do not react with each other, can only move along the rod and, that there is no internal interaction between the elements of the media. The model can be used to study the oscillations of sufficiently long chains of rigid bodies to which other mobile bodies are attached by means of deformable elements, oscillations of one-dimensional systems of rigid bodies with cavities partially filled with fluid, etc. A transitional mode of motion in similar systems was studied in [1].     

Asymptotic solutions of non-classical boundary-value problems of the natural vibrations of orthotropic shells

The natural vibrations of orthotropic shells are considered in a three-dimensional formulation for different versions of the boundary conditions on the faces: rigid clamping rigid clamping, rigid clamping free surface, and mixed conditions. Asymptotic solutions of the corresponding dynamic equations of the three-dimensional problem of the theory of elasticity are obtained. The principal values of the frequencies of natural vibrations are determined. It is shown that three types of natural vibrations occur in the shell: two shear vibrations and a longitudinal vibration, which are due solely to the boundary conditions on the faces. It is proved that each boundary layer has its own natural frequency. The boundary-layer functions are determined and the rates at which they decrease with distance from the faces inside the shell are established.     

Axisymmetrical vibrations of shells of revolution under abrupt loading

A frequency method is proposed for solving the problem of the vibrations of shells of revolution taking into account the energy dissipation under arbitrary force loading and on collision with a rigid obstacle. The Laplace transform is taken of the equation of the vibrations of a shell of revolution with non-zero initial conditions. For the inhomogeneous differential equation obtained, a variational method is used to solve the boundary-value problem, which consists of finding the Laplace-transformed boundary transverse and longitudinal forces and bending moments as functions of the boundary displacements. The equations of equilibrium of nodes, i.e. the corresponding equations of the finite-element method, are then compared, using results obtained earlier [1–4]. Amplitude-phase-frequency characteristics (APFCs) for the shell cross-sections selected are plotted. An inverse Laplace transformation is carried out using the clear relationship between the extreme points of the APFCs and the coefficients of the corresponding terms of the series in an expansion vibration modes [3]. In view of the fact that the proposed approach is approximate, numerical testing is used.     

The equations of the perturbed motion of a rocket as a thin-walled structure with a liquid

The perturbed motion of a rocket as an elastic thin-walled structure with compartments partially filled with liquid propellant is considered. It is assumed that the normal modes of the hydroelastic oscillations of the rocket are determined under the condition that the velocity potential on the free surface of the liquid is equal to zero and with standard remaining conditions. Certain features of these modes with zero fundamental frequencies are pointed out and the “loss” of mass effect associated with this is explained. Equations are derived for the perturbed motion of a rocket taking account of the hydroelastic oscillations of its structure and the oscillations of the liquid with deviations of the free surface from the equilibrium position under the action of mass forces. The coefficients of these equations, characterizing the relation between the different type of oscillations, are expressed in terms of known hydrodynamic parameters and the values of the oscillation modes at certain points.     

Vibrations of thin cylindrical shells with a periodic structure

Free vibrations of thin linear–elastic Kirchhoff–Love cylindrical shells, having a periodic structure along one direction tangent to the shell midsurface, is considered. In order to take into account the effect of the periodicity cell size in this problem, a new averaged non–asymptotic model of such shells, proposed by Tomczyk (2006), is applied. The new additional higher–order free vibration frequencies dependent on the microstructure size will be derived and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Static and dynamic buckling modes of spherical shells subjected to external pressure

We investigate the possibilities for simplification of previously proposed refined linearized equations of perturbedmotion to identify, by dynamic method, the buckling mode shapes of isotropic spherical shells undergoing external hydrodynamic pressure. In the analysis of classical flexural buckling shapes of spherical shells, it is shown that preserving of nonconservative parametric terms in governing equations of formulated problem, which are related with loading of the shell with follower pressure practically does not affect the value of critical load and the resulting bucklingmode shapes in shell.     

Frequencies of Free Acoustic Oscillations in a Fluid Separating Rigid and Elastic Tube Walls of Finite Length

A solution of the problem of determining the frequencies and mode shapes of free nonsymmetric oscillations in an annular volume filled with an ideal compressible fluid is constructed. The inner tube and the end plane walls are ideally rigid. A thin elastic shell with edges clamped to the end walls is located on the outer tube boundary. A phenomenon of a decrease in the fundamental frequency as the thickness of a fluid layer adjacent to the elastic wall decreases is confirmed. Bibliography: 8 titles.     

Symmetric and Asymmetric Underplatform Dampers for Turbine Blades

Friction damping devices like underplatform dampers are widely used in turbomachinery applications to reduce vibration amplitudes and to increase lifetime and reliability of the bladed disk. Nowadays, in practical applications, a variety of different underplatform damper geometries is applied. Nevertheless, a detailed study of the in.uence of the geometric and dynamic properties of the damper is still not available. Within this paper the most frequently applied damper types like cylindrical and wedge as well as asymmetrical dampers are investigated and compared to each other with respect to their effectiveness. Especially the in.uence of the damper geometry on the resonance frequency and vibration amplitude is pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The dynamic behaviour of elastic coaxial cylindrical shells conveying fluid

The dynamic behaviour of elastic coaxial cylindrica shells, which interact with a flow of compressible fluid in the inner shell or in the annular gap between the shells when both flows are present, is investigated by the finite element method. A number of test problems is considered in the case of cantilevered coaxial shells. The effect on the stability limit of the gap between the two shells is investigated for different values of the stiffness parameters of the outer shell and the fluid flow. An important difference is found with existing solutions in cases when the loss of stability of the coaxial shells occurs at higher oscillation modes. It is established that, for a certain value of the gap between the shells, the elasticity of the outer shell may have a stabilizing effect. It is shown that the presence of internal and annular flows simultaneously has a considerable stabilizing effect, while a loss of stability when the flow rates increase occurs at extremely high oscillation modes.     

A novel numerical solution strategy for solving nonlinear free and forced vibration problems of cylindrical shells

Nonlinear vibration analysis of circular cylindrical shells has received considerable attention from researchers for many decades. Analytical approaches developed to solve such problem, even not involved simplifying assumptions, are still far from sufficiency, and an efficient numerical scheme capable of solving the problem is worthy of development. The present article aims at devising a novel numerical solution strategy to describe the nonlinear free and forced vibrations of cylindrical shells. For this purpose, the energy functional of the structure is derived based on the first-order shear deformation theory and the von–Kármán geometric nonlinearity. The governing equations are discretized employing the generalized differential quadrature (GDQ) method and periodic differential operators along axial and circumferential directions, respectively. Then, based on Hamilton's principle and by the use of variational differential quadrature (VDQ) method, the discretized nonlinear governing equations are obtained. Finally, a time periodic discretization is performed and the frequency response of the cylindrical shell with different boundary conditions is determined by applying the pseudo-arc length continuation method. After revealing the efficiency and accuracy of the proposed numerical approach, comprehensive results are presented to study the influences of the model parameters such as thickness-to-radius, length-to-radius ratios and boundary conditions on the nonlinear vibration behavior of the cylindrical shells. The results indicate that variation of fundamental vibrational mode shape significantly affects frequency response curves of cylindrical shells.     

Prediction of the dynamic response of a mini-cantilever beam partially submerged in viscous media using finite element method

In this work, the use of mini cantilever beams for characterization of rheological properties of viscous materials is demonstrated. The dynamic response of a mini cantilever beam partially submerged in air and water is measured experimentally using a duel channel PolyTec scanning vibrometer. The changes in dynamic response of the beam such as resonant frequency, and frequency amplitude are compared as functions of the rheological properties (density and viscosity) of fluid media. Next, finite element analysis (FEA) method is adopted to predict the dynamic response of the same cantilever beam. The numerical prediction is then compared with experimental results already performed to validate the FEA modeling scheme. Once the model is validated, further numerical analysis was conducted to investigate the variation in vibration response with changing fluid properties. Results obtained from this parametric study can be used to measure the rheological properties of any unknown viscous fluid.     

Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction

This paper presents an investigation on partially fluid-filled cylindrical shells made of functionally graded materials (FGM) surrounded by elastic foundations (Pasternak elastic foundation) in thermal environment. Material properties are assumed to be temperature dependent and radially variable in terms of volume fraction of ceramic and metal according to a simple power law distribution. The shells are reinforced by stiffeners attached to their inside and outside in which the material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The formulations are derived based on smeared stiffeners technique and classical shell theory using higher-order shear deformation theory which accounts for shear flexibility through shell's thickness. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The governing equations of liquid motion are derived using a finite strip element formulation of incompressible inviscid potential flow. The dynamic pressure of the fluid is expanded as a power series in the radial direction. Moreover, the quiescent liquid free surface is modeled by concentric annular rings. A detailed numerical study is carried out to investigate the effects of power-law index of functional graded material, fluid depth, stiffeners, boundary conditions, temperature and geometry of the shell on the natural frequency of eccentrically stiffened functionally graded shell surrounded by Pasternak foundations.