弹性圆拱在考虑几何非线性和初始缺陷情况下的动力稳定性分析

本文由虚功原理建立弹性圆拱的平衡方程,用有限差分法对非线性偏微分方程组进行求解(Park法对时间进行差分)。在考虑几何非线性和初始几何缺陷情况下对铰支、固支圆拱在均布突加阶跃荷载作用下的动力稳定性进行分析。结果表明:圆拱中心角的大小、边界条件及初始缺陷幅值都对圆拱失稳模态有影响。文中分析了直接、间接两种失稳形式。并给出了不同初始缺陷及边界条件下圆拱中心角对比值Pd/Pa(Pd为动力稳定临界值,Ps为静力稳定临界值)的影响。     

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．     

Dynamic Elastic Buckling of Complete Spherical Shells with Initial Imperfections∗

The dynamic elastic buckling behavior of a geometrically imperfect complete spherical shell that is subjected to a uniform external step pressure is examined using Sander's equilibrium and kinematic equations, appropriately modified to include the influence of inertia forces and initial stress-free imperfections in the radius. A finite-difference procedure with either the Houbolt or Park methods of time integration is used to predict the axisym-metric dynamic elastic buckling pressures and associated critical mode numbers. The dynamic buckling pressure is significantly smaller than the corresponding static value for small initial imperfections, but is less imperfection     

钢网壳模型的动力稳定性振动台试验研究

对两个钢扁网壳结构模型在地震荷载作用下的动力稳定性进行了振动台试验研究,观察了模型的局部动力失稳和整体动力失稳现象,通过对试验测量数据结果的处理,给出了模型中杆件的内力时程曲线和结点位移时程曲线,对这些时程曲线进行分析,总结了结构产生动力失稳时的特征和规律,同时也给出了部分理论分析的结果,并结合试验结果对理论研究中给出的动力失稳定义和判定准则以及其它结论分别进行了验证和说明．     

Vibrations of Reinforced Cylindrical Shells with Initial Deflections under Nonstationary Loads

The paper addresses dynamic problems for discretely reinforced shells with initial deflections. Timoshenko theory is used. A numerical method of solving such problems is developed and theoretically justified. Numerical results for a specific problem are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 60–68, January 2005.     

Nonlinear Theory of Dynamic Stability for Laminated Composite Cylindrical Shells

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弹性地基上圆底扁球壳的非线性动力问题

本文从Krmn非线性基本微分方程出发,提出了将修正迭代法和伽辽金法联合运用,分析了弹性地基上圆底扁球壳在均布荷载作用下周边固定边界条件的非线性动力响应问题,给出了中心振幅与时间t之间关系的二次近似解析表达式;同时还讨论了Winkler地基参数K对中心最大振幅的影响。此外将本文的部分结果和已有文献结果作了比较,二者吻合较好。     

Dynamic Stability Problems of Anisotropic Cylindrical Shells via a Simplified Analysis

An analytical–numerical method involving a small number of generalized coordinates is presented for the analysis of the nonlinear vibration and dynamic stability behaviour of imperfect anisotropic cylindrical shells. Donnell-type governing equations are used and classical lamination theory is employed. The assumed deflection modes approximately satisfy simply supported boundary conditions. The axisymmetric mode satisfying a relevant coupling condition with the linear, asymmetric mode is included in the assumed deflection function. The shell is statically loaded by axial compression, radial pressure and torsion. A two-mode imperfection model, consisting of an axisymmetric and an asymmetric mode, is used. The static-state response is assumed to be affine to the given imperfection. In order to find approximate solutions for the dynamic-state equations, Hamiltons principle is applied to derive a set of modal amplitude equations. The dynamic response is obtained via numerical time-integration of the set of nonlinear ordinary differential equations. The nonlinear behaviour under axial parametric excitation and the dynamic buckling under axial step loading of specific imperfect isotropic and anisotropic shells are simulated using this approach. Characteristic results are discussed. The softening behaviour of shells under parametric excitation and the decrease of the buckling load under step loading, as compared with the static case, are illustrated.     

Nonaxisymmetric Vibrations of Discretely Reinforced Inhomogeneous Multilayer Cylindrical Shells under Nonstationary Loads

The equations of nonaxisymmetric vibrations of discretely reinforced multilayer cylindrical shells are analyzed. A refined Timoshenko model of shells and beams is used to analyze elements of an elastic structure. The vibration equations for an inhomogeneous elastic system are derived using the Reissner variational principle. The numerical solver of the dynamic equations is based on the integro-interpolation method used to construct finite-difference schemes for equations with discontinuous coefficients. The dynamic behavior of a five-layer cylindrical shell under distributed nonstationary loading is analyzed     

Stability and Natural Vibrations of Shells with Variable Geometric and Mechanical Parameters

The bifurcation stability and natural vibrations of shells of revolution with variable geometric and mechanical parameters are studied by using refined models and the variational–difference method. The qualitative and quantitative effects of the external geometry, material properties, and design features on the critical load and natural frequency are evaluated     

On Free Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Multiple Natural Frequencies

Nonlinear free vibrations of a cylindrical shell fully filled with a perfect incompressible fluid are studied. The case is examined where two natural frequencies of the shell are close __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 127–138, October 2005     

Analysis of the Dynamic Stability of Electrical Graded Piezoelectric Circular Cylindrical Shells

I. INTRODUCTION In recent years, piezoelectric materials have been widely used as sensors and actuators in the areaof smart structures, and shell-type piezoelectric smart structures have become the focus of research.Various analytical and ?nite element models for piezoelectric shells have been developed[1??3]. Inaddition, a series of exact studies on the bending and buckling of piezoelectric circular cylindrical shellhave been presented by Chen et al.[4??7]. Recently, the use of functi…     

Nonlinear Oscillations and Stability of Parametrically Excited Cylindrical Shells

Based on Donnell shallow shell equations, the nonlinear vibrations and dynamic instability of axially loaded circular cylindrical shells under both static and harmonic forces is theoretically analyzed. First the problem is reduced to a finite degree-of-freedom one by using the Galerkin method; then the resulting set of coupled nonlinear ordinary differential equations of motion are solved by the Runge–Kutta method. To study the nonlinear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, Lyapunov exponents, stable and unstable fixed points, bifurcation diagrams, and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric excitation of flexural modes and escape from the pre-buckling potential well. Calculations are carried out for the principal and secondary instability regions associated with the lowest natural frequency of the shell. Special attention is given to the determination of the instability boundaries in control space and the identification of the bifurcational events connected with these boundaries. The results clarify the importance of modal coupling in the post-buckling solution and the strong role of nonlinearities on the dynamics of cylindrical shells.     

Dynamic Stability and Random Vibrations of Rigid and Elastic Wheelsets

A stability analysis and vibration studies are presented for a passenger coach model which is equipped with rigid or elastic wheels. The elastic components between wheel rim and disc act as third suspension reducing the unsprung mass and isolating the passenger coach from the high frequency motion of the wheel rim. The vertical and lateral motion by such a design requires a thorough analysis of the system dynamics. The excitation of the vertical vibrations by stochastic track irregularities results in acceleration amplitudes of the carbody that may generate droning noise. A parameter study of spring and damper coefficients of the system with radialelastic wheels leads to considerably reduced droning noise and lower force level between wheel and rail. Furthermore, the eigenmotion of a rigid and an elastic wheelset rolling on a track, the so-called hunting, is investigated. The variation of the spring and damper coefficients shows limits to guarantee the stability of the system.     

Damping of Free Elastic Vibrations in Linear Systems

The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 110–117, February 2005.     

Effect of Initial Imperfections on the Flexural Eigenvibrations of Cylindrical Shells

The effect of small initial deviations from the ideal circular shape of a shell on the frequencies and modes of flexural eigenvibrations is studied with the use of the linear theory of thin shallow shells. It is assumed that the initial deviations are responsible for interaction between flexural and radial vibrations of the shell. The modal equations are derived by the Bubnov—Galerkin method. It is shown that the initial deviations from the ideal circular shape split the flexural vibration spectrum, and the fundamental frequency decreases compared to that of the ideal shell.     

轴向应力波作用下圆柱壳弹性轴对称动力失稳有限元特征值分析

本文运用有限元特征值分析方法对应力波作用下圆柱壳弹性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的有限元特征方程,在此方程中考虑了应力波效应及横向惯性效应,把圆柱壳弹性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳弹性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

Stability of Laminated Shells Made of Materials with one Plane of Elastic Symmetry

The paper sets forth a technique, based on the Kirchhoff–Love theory of shells, for solving stability problems for thin-walled laminated shells of revolution made of an anisotropic material with one plane of elastic symmetry. The resolving system of differential equations is of the 16th order since the symmetric and asymmetric buckling modes are coupled. The results from a stability analysis of cylindrical shells made of carbon plastics and subjected to compression are analyzed against the angle of the principal directions of elasticity. The influence of boundary conditions is studied. The error due to neglecting the coupling of buckling modes is estimated     

A Refined Asymptotic Model of Fluid-Structure Interaction in Scattering by Elastic Shells

A refined asymptotic model of fluid-structure interaction in scattering by elastic shells is proposed. The model takes into consideration transverse compression of a shell by a fluid and some other phenomena. As an illustration, scattering of a plane acoustic wave by a circular cylindrical shell is considered. Comparison of numerical data corresponding various approximate approaches is provided. This revised version was published online in July 2006 with corrections to the Cover Date.     

板片空间结构初始缺陷的动力稳定性影响分析

对板片空间结构体系的研究大都局限于静力载荷工况,结构在动力载荷作用下的稳定性及失效特征研究仍相对缺乏．板片空间钢结构先天存在各样缺陷,而缺陷对结构稳定性的影响不可忽略．本文引入拉丁超立方法,结合Budiansky-Roth 准则,提出适用于求解含初始缺陷结构动力临界荷载的方法,对板片空间结构初始缺陷的动力稳定性开展研究．研究表明,相比于其它抽样方法,拉丁超立方法能显著减少样本数,有效提高计算效率．针对典型的板片空间结构,施加不同方向的阶跃荷载,分析了节点位置偏差缺陷、杆件截面尺寸缺陷以及板片厚度缺陷对板片空间结构临界承载力的影响．结果显示,节点位置偏差缺陷对该结构临界承载力影响最为显著,其它两类缺陷影响甚微．